DEFINITION

Ecology (from Greek: ?????, "house"; -????a, "study of"[A]) is the scientific study of the relationships that living organisms have with each other and with their natural environment. Topics of interest to ecologists include the composition, distribution, amount (biomass), number, and changing states of organisms within and among ecosystems. Ecosystems are composed of dynamically interacting parts including organisms, the communities they make up, and the non-living components of their environment. Ecosystem processes, such as primary production, pedogenesis, nutrient cycling, and various niche construction activities, regulate the flux of energy and matter through an environment. These processes are sustained by the biodiversity within them. Biodiversity refers to the varieties of species in ecosystems, the genetic variations they contain, and the processes that are functionally enriched by the diversity of ecological interactions.

Ecology is an interdisciplinary field that includes biology and Earth science. The word "ecology" ("Φkologie") was coined in 1866 by the German scientist Ernst Haeckel (1834–1919). Ancient Greek philosophers such as Hippocrates and Aristotle laid the foundations of ecology in their studies on natural history. Modern ecology transformed into a more rigorous science in the late 19th century. Evolutionary concepts on adaptation and natural selection became cornerstones of modern ecological theory. Ecology is not synonymous with environment, environmentalism, natural history, or environmental science. It is closely related to evolutionary biology, genetics, and ethology. An understanding of how biodiversity affects ecological function is an important focus area in ecological studies. Ecologists seek to explain:

Life processes and adaptations
Distribution and abundance of organisms
The movement of materials and energy through living communities
The successional development of ecosystems, and
The abundance and distribution of biodiversity in the context of the environment.
Ecology is a human science as well. There are many practical applications of ecology in conservation biology, wetland management, natural resource management (agroecology, agriculture, forestry, agroforestry, fisheries), city planning (urban ecology), community health, economics, basic and applied science, and human social interaction (human ecology). Ecosystems maintain biophysical feedback mechanisms that modulate metabolic rates and evolutionary dynamics between living (biotic) and nonliving (abiotic) components of the planet. Ecosystems sustain life-supporting functions and produce natural capital through the regulation of continental climates, global biogeochemical cycles, water filtration, soils, food, fibres, medicines, erosion control, and many other natural features of scientific, historical, economic, or intrinsic value.
[http://en.wikipedia.org/wiki/Ecology]

"ΤΟ ΑΛΛΗΛΟΣΧΕΤΙΖΟΜΕΝΟ ΣΥΜΠΛΕΓΜΑ ΟΡΓΑΝΙΣΜΩΝ- ΖΩΩΝ, ΦΥΤΩΝ ΚΑΙ ΜΙΚΡΟΒΙΩΝ- ΟΠΟΥΔΗΠΟΤΕ ΚΑΙ ΑΝ ΒΡΙΣΚΟΝΤΑΙ, ΕΙΝΑ ΤΟ ΘΕΜΑ ΤΗΣ ΟΙΚΟΛΟΓΙΑΣ"
[Bernal, 1982, 1007#cptResource194#]

"ΟΙΚΟΥΜΕΝΙΚΟ ΚΑΙ ΕΞΙΣΟΥ ΑΠΕΙΛΗΤΙΚΟ ΓΙΑ ΟΛΟΥΣ, ΕΙΝΑΙ ΤΟ ΠΡΩΤΟ ΜΗ ΔΙΑΙΡΕΤΟ ΠΡΟΒΛΗΜΑ ΠΟΥ ΚΑΛΕΙΤΑΙ ΝΑ ΛΥΣΕΙ ΜΙΑ ΔΙΑΙΡΕΜΕΝΗ ΑΝΘΡΩΠΟΤΗΤΑ... Η ΟΙΚΟΛΟΓΙΚΗ ΠΑΡΕΜΒΑΣΗ ή ΘΑ ΕΙΝΑΙ ΟΙΚΟΥΜΕΝΙΚΗ ή ΔΕΝ ΘΑ ΥΠΑΡΞΕΙ ΠΟΤΕ"
[ΒΗΜΑ, 18 ΙΟΥΛ 1993, Β8 Κ. ΤΣΟΥΚΑΛΑΣ]

GENERIC

_GENERIC:
* entity.model.information.system.weak.science#cptCore406#

SCIENTIST#cptEconomy364.45#

DEFINITION

nounPHILOSOPHY
noun: epistemology
the theory of knowledge, especially with regard to its methods, validity, and scope. Epistemology is the investigation of what distinguishes justified belief from opinion.
[google dic] 2014-06-29

Epistemology The philosophical study of knowledge and belief
[http://en.wikipedia.org/wiki/Verification_theory]

Epistemology or theory of knowledge is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief.

The term "epistemology" is based on the Greek words "επιστήμη or episteme" (knowledge or science) and "λόγος or logos" (reason).[1] It was introduced into English by the Scottish philosopher James Frederick Ferrier (1808-1864).[2]

Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims. In other words, epistemology primarily addresses the following questions: "What is knowledge?", "How is knowledge acquired?", and "What do people know?".
[http://en.wikipedia.org/wiki/Epistemology]

As sociology is the science (logy) about society (socio), the same
epistemology is the science about epistem=science.
In other words epistemology defines the concept 'science'.
Here is my perception on 'science' and of course I mension other 'views' on science.
[hmnSngo.1999-09-24_nikkas]

ΑΠΟΨΕΙΣ ΓΙΑ ΤΗΝ ΕΠΙΣΤΗΜΗ ονομάζω ΑΠΟΨΕΙΣ#cptCore505.a# σχετικές με την 'επιστημη'.
[hmnSngo.1995.04_nikos]

ΕΧΕΙ ΑΝΑΦΕΡΟΜΕΝΟ το 'σύνολο' των ΘΕΩΡΙΩΝ για την 'ΕΠΙΣΤΗΜΗ'.
[hmnSngo.1993.09_nikos]

Much of the philosophy of science is indistinguishable from epistemology, the theory of knowledge,

"Science, Philosophy of," Microsoft(R) Encarta(R) 97 Encyclopedia. (c) 1993-1996 Microsoft Corporation. All rights reserved.

Epistemology (Grk., episteme, "knowledge"; logo, "theory"), branch of philosophy that addresses the philosophical problems surrounding the theory of knowledge. Epistemology is concerned with the definition of knowledge and related concepts, the sources and criteria of knowledge, the kinds of knowledge possible and the degree to which each is certain, and the exact relation between the one who knows and the object known.

"Epistemology," Microsoft(R) Encarta(R) 97 Encyclopedia. (c) 1993-1996 Microsoft Corporation. All rights reserved.

"ΘΕΩΡΙΑ ΤΗΣ ΓΝΩΣΗΣ, ΓΝΩΣΙΟΛΟΓΙΑ, ΕΠΙΣΤΗΜΟΛΟΓΙΑ: ΚΛΑΔΟΣ ΤΗΣ ΦΙΛΟΣΟΦΙΑΣ ΠΟΥ ΜΕΛΕΤΑ
 ΤΗ ΦΥΣΗ ΚΑΙ ΤΙΣ ΔΥΝΑΤΟΤΗΤΕΣ ΤΗΣ ΓΝΩΣΗΣ,
 ΤΙΣ ΣΧΕΣΕΙΣ ΓΝΩΣΗΣ ΚΑΙ ΠΡΑΓΜΑΤΙΚΟΤΗΤΑΣ,
 ΤΙΣ ΓΕΝΙΚΕΣ ΠΡΟΥΠΟΘΕΣΕΙΣ ΤΗΣ ΓΝΩΣΗΣ ΚΑΙ
 ΤΟΥΣ ΟΡΟΥΣ ΤΗΣ ΕΓΚΥΡΟΤΗΤΑΣ ΚΑΙ ΤΗΣ ΓΝΗΣΙΟΤΗΤΑΣ ΤΗΣ.
[ΗΛΙΤΣΕΦ ΚΛΠ, ΦΙΛΟΣΟΦΙΚΟ ΛΕΞΙΚΟ 1985, Β320#cptResource164#]

SCIENCES that study "science".

Being a maniforld phenomenon, science is studied in the framework of approaches based on
 logic and methodology,
 social psychology,
 economic statistics,
 information theory,
 cybernetics, etc.
[Ilyin et al, 1988, 5#cptResource258#]

SCIENCES (which STUDY SCIENCE)
 ΓΝΩΣΙΟΛΟΓΙΑ
 ΕΠΙΣΤΗΜΗ ΤΗΣ ΕΠΙΣΤΗΜΗΣ,
 ΕΠΙΣΤΗΜΟΛΟΓΙΑ
 ΙΣΤΟΡΙΑ ΤΗΣ ΕΠΙΣΤΗΜΗΣ
 ΚΟΙΝΩΝΙΟΛΟΓΙΑ ΤΗΣ ΕΠΙΣΤΗΜΗΣ
 ΛΟΓΙΚΗ ΤΗΣ ΕΠΙΣΤΗΜΗΣ
 ΨΥΧΟΛΟΓΙΑ ΤΗΣ ΓΝΩΣΗΣ
 ΨΥΧΟΛΟΓΙΑ ΤΗΣ ΕΠΙΣΤΗΜΟΝΙΚΗΣ ΔΡΑΣΤΗΡΙΟΤΗΤΑΣ

THEORY-OF-KNOWLEDGE-ACQUISITION

Specific theories of knowledge acquisition:
Empiricism
Main article: Empiricism
In philosophy, empiricism is generally a theory of knowledge emphasizing the role of experience, especially experience based on perceptual observations by the five senses. Certain forms treat all knowledge as empirical,[citation needed] while some regard disciplines such as mathematics and logic as exceptions.[citation needed]

Rationalism
Main article: Rationalism
Rationalists believe that knowledge is primarily (at least in some areas) acquired by a priori processes or is innate—e.g., in the form of concepts not derived from experience. The relevant theoretical processes often go by the name "intuition".[citation needed] The relevant theoretical concepts may purportedly be part of the structure of the human mind (as in Kant's theory of transcendental idealism), or they may be said to exist independently of the mind (as in Plato's theory of Forms).
The extent to which this innate human knowledge is emphasized over experience as a means to acquire knowledge varies from rationalist to rationalist. Some hold that knowledge of any kind can only be gained a priori,[citation needed] while others claim that some knowledge can also be gained a posteriori.[citation needed] Consequently, the borderline between rationalist epistemologies and others can be vague.

Constructivism
Main article: Constructivist epistemology
Constructivism is a view in philosophy according to which all knowledge is "constructed" in as much as it is contingent on convention, human perception, and social experience.[citation needed] Constructivism proposes new definitions for knowledge and truth that forms a new paradigm, based on inter-subjectivity instead of the classical objectivity and viability instead of truth. The constructivist point of view is pragmatic as Vico said: "the truth is to have made it".
It originated in sociology under the term "social constructionism" and has been given the name "constructivism" when referring to philosophical epistemology, though "constructionism" and "constructivism" are often used interchangeably.[citation needed]Constuctivism has also emerged in the field of International Relations, of which the writings of Alexander Wendt are most popular. Describing the characteristic nature of International reality marked by 'anarchy' he says, "anarchy is what states make of it."
[http://en.wikipedia.org/wiki/Epistemology]

METHOD-OF-KNOWLEDGE-ACQUISITION

Methods of obtaining knowledge:
Knowledge may originate or be derived from the following origins or methods:
* Observation or experience. This may be more or less sophisticated, ranging from a simple, "I saw" to carefully designed controlled experimentation.
* Reason or logic. Taking other knowledge as data, by logical operations knowledge can be inferred. For example the theoretical construct, the electron, is derived by logical inferences from observations and experiment. Such knowledge, being derivative, can not be better than the knowledge upon which it is founded.
o Modelling a situation sometimes allows those with a hands-on viewpoint to learn how-to do something. This pragmatic approach is often seen in computer programming.
* Testimony. Knowledge based on the acceptance of testimony involves accepting what others say. For example, I only know that Kent is a county of England, that the First World War was horrendous and that David Beckham earns $30 million per year because I have learned these things from other people. This seems to be a common way we get knowledge but is seen by philosophers as problematic. See Testimony, philosophical problems of.
o Authority. Knowledge based on authority may rely upon the reputation of an individual such as Aristotle or Einstein or perhaps on institutional authority such as that of the Roman Catholic Church or Oxford University. Note that an authority may adopt knowledge upon other criteria such as divine revelation or observation as well as upon authority. Authority may have a political basis in the sense that some political process, perhaps involving status as well as simple voting, peer review, or comment. This is familiar to participants in academia.
* Revelation. Many people believe knowledge may be obtained via revelation or even divine revelation, which may be directly from God or another spirit, perhaps conveyed through a religious text or texts, such as the Bible.
[http://en.wikipedia.org/wiki/Methods_of_obtaining_knowledge]

_SPECIFIC:
* ΑΞΙΩΜΑΤΙΚΗ ΜΕΘΟΔΟΣ##
ΓΕΝΕΤΙΚΗ_ΜΕΘΟΔΟΣ/GENETIC METHOD##
ΣΥΓΚΡΙΤΙΚΗ_ΜΕΘΟΔΟΣ/COMPARATIVE METHOD##
ΣΥΣΤΗΜΙΚΗ_ΠΡΟΣΕΓΓΙΣΗ##

AXIOMATIC-METHOD

name::
* McsEngl.axiomatic-method,
* McsEngl.axiomatic'method@cptCore385i,
* McsElln.ΑΞΙΩΜΑΤΙΚΗ-ΜΕΘΟΔΟΣ,
* McsElln.ΑΞΙΩΜΑΤΙΚΗ'ΜΕΘΟΔΟΣ@cptCore468,

_DEFINITION:
The axiomatic method involves replacing a coherent body of propositions (i.e. a mathematical theory) by a simpler collection of propositions (i.e. axioms). The axioms are designed so that the original body of propositions can be deduced from the axioms.
[http://en.wikipedia.org/wiki/Axiomatic_method] 2007-09-14

ΑΞΙΩΜΑΤΙΚΗ ΜΕΘΟΔΟΣ είναι ΑΠΟΨΗ ΓΙΑ ΤΗ ΣΚΕΨΗ ...
[hmnSngo.1995.04_nikos]

"ΑΞΙΩΜΑΤΙΚΗ ΜΕΘΟΔΟΣ: ΤΡΟΠΟΣ ΚΑΤΑΣΚΕΥΗΣ ΕΠΙΣΤΗΜΟΝΙΚΗΣ ΘΕΩΡΙΑΣ, ΟΠΟΥ ΤΗ ΒΑΣΗ ΤΗΣ ΘΕΩΡΙΑΣ ΑΠΟΤΕΛΟΥΝ ΟΡΙΣΜΕΝΕΣ ΑΡΧΙΚΕΣ ΘΕΣΕΙΣ (ΠΡΟΤΑΣΕΙΣ) ΑΞΙΩΜΑΤΑ, ΑΙΤΗΜΑΤΑ ΑΠΟ ΤΑ ΟΠΟΙΑ ΟΛΕΣ ΟΙ ΥΠΟΛΟΙΠΕΣ ΠΡΟΤΑΣΕΙΣ ΤΗΣ ΘΕΩΡΙΑΣ ΠΡΕΠΕΙ ΝΑ ΕΞΑΧΘΟΥΝ ΜΕ ΚΑΘΑΡΑ ΛΟΓΙΚΟ ΤΡΟΠΟ, ΜΕ ΑΠΟΔΕΙΞΕΙΣ. Η ΣΥΓΚΡΟΤΗΣΗ ΤΗΣ ΕΠΙΣΤΗΜΗΣ ΜΕ ΤΗΝ ΑΞΙΩΜΑΤΙΚΗ ΜΕΘΟΔΟ ΟΝΟΜΑΖΕΤΑΙ ΣΥΝΗΘΩΣ ΠΑΡΑΓΩΓΙΚΗ. ΟΛΕΣ ΟΙ ΕΝΝΟΙΕΣ ΤΗΣ ΠΑΡΑΓΩΓΙΚΗΣ ΘΕΩΡΙΑΣ (ΕΚΤΟΣ ΑΠΟ ΤΟΝ ΟΡΙΣΜΕΝΟ ΑΡΙΘΜΟ ΤΩΝ ΑΡΧΙΚΩΝ) ΕΙΣΑΓΟΝΤΑΙ ΜΕΣΩ ΟΡΙΣΜΩΝ ΟΙ ΟΠΟΙΟΙ ΚΑΘΟΡΙΖΟΥΝ ΤΙΣ ΕΝΝΟΙΕΣ ΜΕΣΩ ΑΛΛΩΝ ΕΝΝΟΙΩΝ, ΟΙ ΟΠΟΙΕΣ ΕΧΟΥΝ ΕΙΣΑΧΘΕΙ ΝΩΡΙΤΕΡΑ".
[ΗΛΙΤΣΕΦ ΚΛΠ, ΦΙΛΟΣΟΦΙΚΟ ΛΕΞΙΚΟ 1985, Α180#cptResource164#]

In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system; usually though the effort towards complete formalisation brings diminishing returns in certainty, and a lack of readability for humans. Therefore discussion of axiomatic systems is normally only semi-formal. A formal theory typically means an axiomatic system, for example formulated within model theory. A formal proof is a complete rendition of a mathematical proof within a formal system.
...
Outside of mathematics

It is easy to see that the axiomatic method has limitations outside mathematics. For example, in political philosophy axioms that lead to unacceptable conclusions are likely to be rejected wholesale; so that no one really assents to version 1 above. In mathematics, axiomatization is the formulation of a system of statements (i.e. axioms) that relate a number of primitive terms in order that a consistent body of propositions may be derived deductively from these statements. Thereafter, the proof of any proposition should be, in principle, tracable back to these axioms.
[http://en.wikipedia.org/wiki/Axiomatization]

GENETIC-METHOD

name::
* McsEngl.genetic-method,
* McsEngl.genetic'method@cptCore385i,
* McsElln.ΓΕΝΕΤΙΚΗ-ΜΕΘΟΔΟΣ,
* McsElln.ΓΕΝΕΤΙΚΗ-ΜΕΘΟΔΟΣ-ΕΡΕΥΝΑΣ,

_DEFINITION:
ΓΕΝΕΤΙΚΗ ΜΕΘΟΔΟΣ είναι ΑΠΟΨΗ ΓΙΑ ΤΗ ΣΚΕΨΗ ...
[hmnSngo.1995.04_nikos]

"ΓΕΝΕΤΙΚΗ ΜΕΘΟΔΟΣ. ΜΕΘΟΔΟΣ ΕΠΙΣΤΗΜΟΝΙΚΗΣ ΓΝΩΣΗΣ ΠΟΥ ΕΡΕΥΝΑ
 ΤΗΝ ΕΜΦΑΝΙΣΗ,
 ΤΗΝ ΠΡΟΕΛΕΥΣΗ ΚΑΙ
 ΤΗΝ ΕΔΡΑΙΩΣΗ
ΤΩΝ ΦΑΙΝΟΜΕΝΩΝ ΠΟΥ ΑΝΑΠΤΥΣΣΟΝΤΑΙ"
[ΗΛΙΤΣΕΦ ΚΛΠ, ΦΙΛΟΣΟΦΙΚΟ ΛΕΞΙΚΟ 1985, Α340#cptResource164#]

BOOK

Rey, Georges. (1997)
Contemporary Philosophy of Mind: a Contentiously Classical Approach 1997

COGNITIVISM

name::
* McsEngl.cognitivism@cptCore385.i,

In psychology, cognitivism is a theoretical approach in understanding the mind, which argues that mental function can be understood by quantitative, positivist and scientific methods, and that such functions can be described as information processing models.
[http://en.wikipedia.org/wiki/Cognitivism_%28psychology%29]

EMBODIED-PHILOSOPHY

name::
* McsEngl.embodied'cognition@cptCore385.i,
* McsEngl.embodied'cognition'thesis@cptCore385.i,
* McsEngl.embodied'mind'thesis@cptCore385.i,
* McsEngl.embodied'philosophy@cptCore385.i,

Embodied philosophy (also known as the embodied mind thesis, embodied cognition or the embodied cognition thesis) usually refers to a set of arguments proposed by various authors including George Lakoff, Mark Johnson, Mark Turner, and Rafael E. Nu'n~ez, which suggest that the mind can only be well understood by taking into account the body and the more primitive underpinnings of the mind. This view is, therefore, opposed to other views of cognition, such as cognitivism, computationalism and Cartesian dualism.
[http://en.wikipedia.org/wiki/Embodied_cognition]

FUNCTIONALISM

Functionalism is a theory of the mind in contemporary philosophy, developed largely as an alternative to both the identity theory of mind and behaviorism. Its core idea is that mental states (beliefs, desires, being in pain, etc.) are constituted solely by their functional role — that is, their causal relations to other mental states, sensory inputs, and behavioral outputs. Since mental states are identified by a functional role, they are said to be multiply realizable; in other words, they are able to be manifested in various systems, even perhaps computers, so long as the system performs the appropriate functions. While functionalism has its advantages, there have been several arguments against it, claiming that it is an insufficient account of the mind.
[http://en.wikipedia.org/wiki/Functionalism_%28philosophy_of_mind%29]

EDELMAN-GERALD (1929-) materialist

name::
* McsEngl.EDELMAN-GERALD (1929-) materialist,

Gerald Maurice Edelman (born 1929-07-01) is an American biologist who won the Nobel Prize in Physiology or Medicine in 1972 for his work on the immune system.[1] Edelman's Nobel Prize-winning research concerned discovery of the structure of antibody molecules.[2] In interviews, he has said that the way the components of the immune system evolve over the life of the individual is analogous to the way the components of the brain evolve in a lifetime. This is the continuity between his Nobel-Prize-winning work and his highly influential later work on neural darwinism.
Education
Gerald Edelman was born in 1929 in Ozone Park, Queens, New York to Edward Edelman, a physician, and Anna Freedman Edelman.[3] After being raised in New York, he attended college in Pennsylvania where he graduated magna cum laude with a B.S. from Ursinus College in 1950 and received an M.D. from the University of Pennsylvania in 1954.[3]
After a year at the Johnson Foundation for Medical Physics, he became a house officer at the Massachusetts General Hospital and then practiced medicine in France while serving with US Army Medical Corps.[3] Edelman joined the Rockefeller Institute for Medical Research as a graduate fellow in 1957, receiving a Ph.D. in 1960.[3] Rockefeller made him the Assistant (later Associate) Dean of Graduate Studies until 1966, when he became a professor at the school.[3] In 1992, he moved to California and became a professor of neurobiology at The Scripps Research Institute.[4] Edelman also serves as the founder and director of The Neurosciences Institute, a nonprofit research centre in San Diego that studies the biological basis of higher brain function in humans, and is on the scientific board of the World Knowledge Dialogue project [5]
Nobel Prize
 Please help improve this article by expanding this section.
See talk page for details. Please remove this message once the section has been expanded.
While in Paris serving in the Army, Edelman read a book that sparked his interest in antibodies.[6] He decided that, since the book said so little about antibodies, he would investigate them further upon returning to the United States, which led him to study physical chemistry for his 1960 Ph.D.[6] Research by Edelman and his colleagues and Rodney Robert Porter in the early 1960s produced fundamental breakthroughs in the understanding of the antibody's chemical structure, opening a door for further study.[7] For this work, Edelman and Porter shared the Nobel Prize in Physiology or Medicine in 1972.[1]

Theory of mind
Edelman is noted for his theory of mind, published in a trilogy of technical books, and in briefer form for a more general audience in Bright Air, Brilliant Fire (1992) and more recently in Wider than the Sky (2004). Neural Darwinism (1987) contains a theory of memory that is built around the idea of plasticity in the neural network in response to the environment. Topobiology (1988) contains a theory of how the original neuronal network of a newborn's brain is established during development of the embryo. The Remembered Present (1990) contains a theory of consciousness.
Edelman has asked whether we should attempt to construct models of functioning minds or models of brains which, through interactions with their surroundings, can develop minds. Edelman's answer is that we should make model brains and pay attention to how they interact with their environment. Edelman accepts the existence of qualia and incorporates them into his brain-based theory of mind. His concept of qualia attempts to avoid the pitfalls of the idea of special qualia with non-functional properties, which was criticized by Daniel Dennett.
Edelman expounds a biological theory of consciousness, based on his studies of the immune system, which he explicitly locates within Darwin's Theory of Natural Selection and Darwinian theories of population dynamics. He rejects dualism and also dismisses newer hypotheses such as the so-called 'computational' model of consciousness, which liken the brain's functions to the operations of a computer.
Edelman argues that the mind and consciousness are wholly material and purely biological phenomena, occurring as highly complex cellular processes within the brain, and that the development of consciousness and intelligence can be satisfactorily explained by Darwinian theory.
[http://en.wikipedia.org/wiki/Gerald_Edelman]

SPECIFIC

_SPECIFIC:
* AGNOSTICISM/ΑΓΝΩΣΤΙΚΙΣΜΟΣ##
* CONSTRUCTIVISM#cptCore385.1: attSpe#
* EMPIRICISM##
* INTUITIONISM/ΕΝΟΡΑΤΙΣΜΟΣ##
* IRRATIONALISM/ΑΝΟΡΘΟΛΟΓΙΣΜΟΣ##
* OBJECTIVISM##
* PHENOMENALISM/ΦΑΙΝΟΜΕΝΑΛΙΣΜΟΣ##
* RATIONALISM/ΟΡΘΟΛΟΓΙΣΜΟΣ##
* SENSUALISM/ΑΙΣΘΗΣΙΑΡΧΙΑ##
* STRUCTURALISM##
* SUBJECTIVISM/ΥΠΟΚΕΙΜΕΝΙΣΜΟΣ##

ΑΝΑΛΥΤΙΚΗ ΘΕΩΡΙΑ ΤΗΣ ΕΠΙΣΤΗΜΗΣ,
ΑΣΤΙΚΗ ΘΕΩΡΙΑ ΤΗΣ ΕΠΙΣΤΗΜΗΣ
ΜΑΡΞΙΣΤΙΚΗ ΕΠΙΣΤΗΜΟΛΟΓΙΑ

sciSci'school.SPECIFIC-DIVISION.INDUCTION-DEDUCTION

name::
* McsEngl.sciSci'school.SPECIFIC-DIVISION.INDUCTION-DEDUCTION,

_SPECIFIC:
* critical_rationalism##
* EMPIRICISM/ΕΜΠΕΙΡΙΣΜΟΣ##
* epistemological_idealism
* fallibilism
* formal_epistemology
* genetic_epistemology
* naturalized_epistemology
* objectivist_epistemology
* scientific_skepticism
* social_epistemology
* structuralism
* RATIONALISM

For the rationalists, of whom the French philosopher Renι Descartes, the Dutch philosopher Baruch Spinoza, and the German philosopher Gottfried Wilhelm Leibniz were the leaders, the main source and final test of knowledge was deductive reasoning based on self-evident principles, or axioms.
"Epistemology," Microsoft(R) Encarta(R) 97 Encyclopedia. (c) 1993-1996 Microsoft Corporation. All rights reserved.

sciSci'school.SPECIFIC-DIVISION.REFEREINO (what is)

name::
* McsEngl.sciSci'school.SPECIFIC-DIVISION.REFEREINO (what is),

_SPECIFIC:
* agnosticism
* objectivism
* phenomenalism
* subjectivism

sciSci'school.SPECIFIC-DIVISION.TRUTH

name::
* McsEngl.sciSci'school.SPECIFIC-DIVISION.TRUTH,

Neopragmatism
A contemporary extension of pragmatism, where Truth is considered to be that which works.
[http://en.wikipedia.org/wiki/Contemporary_philosophy]

sciSci'school.SPECIFIC-DIVISION.GENERAL-CONCEPTS

name::
* McsEngl.sciSci'school.SPECIFIC-DIVISION.GENERAL-CONCEPTS,

_SPECIFIC:
* conceptualism
* nominalism
* realism

The general-concepts exists outside of our brains:
* "nominalists" = no, only names
* "conceptualists" = no, exists as concepts.
* "realists" = yes.

sciSci'school.SPECIFIC-DIVISION.ACQUISITION

name::
* McsEngl.sciSci'school.SPECIFIC-DIVISION.ACQUISITION,

_SPECIFIC:
* constructivism
* empiricism
* innatism
* intuistionism
* irrationalism
* rationalism

sciSci'school.SPECIFIC-DIVISION.HUMAN

name::
* McsEngl.sciSci'school.SPECIFIC-DIVISION.HUMAN,

_SPECIFIC:
* platonic_epistemology

sciSci'school.SPECIFIC-DIVISION.PLACE

name::
* McsEngl.sciSci'school.SPECIFIC-DIVISION.PLACE,

_SPECIFIC:
* ancient_indian_epistemology##
* ΚΥΚΛΟΣ ΤΗΣ ΒΙΕΝΝΗΣ,

ΜΑΝΑΣ

ΤΣΙΤΑ

ΤΣΙΤΑ: ΕΝΝΟΙΑ ΤΗΣ ΑΡΧΑΙΑΣ ΙΝΔΙΚΗΣ ΘΕΩΡΙΑΣ ΤΗΣ ΓΝΩΣΗΣ ΚΑΙ ΤΗΣ ΨΥΧΟΛΟΓΙΑΣ, ΠΟΥ ΥΠΟΔΗΛΩΝΕΙ ΤΟ ΣΥΝΟΛΟ ΤΩΝ ΒΑΘΜΙΔΩΝ ΑΝΑΠΤΥΞΗΣ ΤΟΥ ΝΟΥ, ΟΙ ΟΠΟΙΕΣ ΚΑΘΟΡΙΖΟΥΝ ΤΙΣ ΔΙΑΦΟΡΕΣ ΚΑΤΑΣΤΑΣΕΙΣ ΤΗΣ ΠΝΕΥΜΑΤΙΚΗΣ ΖΩΗΣ.
[ΗΛΙΤΣΕΦ ΚΛΠ, ΦΙΛΟΣΟΦΙΚΟ ΛΕΞΙΚΟ 1985, Ε236#cptResource164#]

RADICAL-CONSTRUCTIVISM

Ernst von Glasersfeld is a prominent proponent of radical constructivism, which claims that knowledge is the self-organized cognitive process of the human brain. That is, the process of constructing knowledge regulates itself, and since knowledge is a construct rather than a compilation of empirical data, it is impossible to know the extent to which knowledge reflects an ontological reality.
[http://en.wikipedia.org/wiki/Constructivist_epistemology]

SENSUALISM

name::
* McsEngl.SENSUALISM,
* McsEngl.sensualism@cptCore463,
* McsElln.ΑΙΣΘΗΣΙΟΚΡΑΤΙΑ,
* McsElln.ΑΙΣΘΗΣΙΑΡΧΙΑ,
* McsElln.ΣΕΝΣΟΥΑΛΙΣΜΟΣ,

_DEFINITION:
ΑΙΣΘΗΣΙΑΡΧΙΑ είναι ΑΠΟΨΗ ΓΙΑ ΤΗ ΣΚΕΨΗ ...
[hmnSngo.1995.04_nikos]

Sensualism is a philosophic current in the theory of knowledge, according to which sensations and perception are basic and most important form of true cognition. It is opposing realism. Base principle of sensualism — «there is not anything in mind, which hasn't been in feelings».
The great philosophers of sensualism are:
* John Locke
* E'tienne Bonnot de Condillac
[http://en.wikipedia.org/wiki/Sensualism]

"ΑΙΣΘΗΣΙΑΡΧΙΑ: ΚΑΤΕΥΘΥΝΣΗ ΣΤΗ ΘΕΩΡΙΑ ΤΗΣ ΓΝΩΣΗΣ, ΣΥΜΦΩΝΑ ΜΕ ΤΗΝ ΟΠΟΙΑ ΟΙ ΑΙΣΘΗΣΕΙΣ ΕΙΝΑΙ Η ΚΥΡΙΑ ΠΗΓΗ ΑΞΙΟΠΙΣΤΗΣ ΓΝΩΣΗΣ. ΣΕ ΑΝΤΙΘΕΣΗ ΜΕ ΤΟΝ ΟΡΘΟΛΟΓΙΣΜΟ (ΝΟΗΣΙΑΡΧΙΑ, ΡΑΣΙΟΝΑΛΙΣΜΟ), Η ΑΙΣΘΗΣΙΑΡΧΙΑ ΤΕΙΝΕΙ ΝΑ ΘΕΩΡΗΣΕΙ ΟΛΟ ΤΟ ΠΕΡΙΕΧΟΜΕΝΟ ΤΗΣ ΓΝΩΣΗΣ ΩΣ ΠΡΟΙΟΝ ΤΗΣ ΔΡΑΣΤΗΡΙΟΤΗΤΑΣ ΤΩΝ ΑΙΣΘΗΤΗΡΙΩΝ ΟΡΓΑΝΩΝ. Η ΑΙΣΘΗΣΙΑΡΧΙΑ ΣΥΓΓΕΝΕΥΕΙ ΜΕ ΤΟΝ ΕΜΠΕΙΡΙΣΜΟ, ΠΟΥ ΘΕΩΡΕΙ ΤΗΝ ΑΙΣΘΗΤΗΡΙΑΚΗ ΕΜΠΕΙΡΙΑ ΩΣ ΤΗ ΜΟΝΑΔΙΚΗ ΠΗΓΗ ΑΞΙΟΠΙΣΤΗΣ ΓΝΩΣΗΣ"
[ΗΛΙΤΣΕΦ ΚΛΠ, ΦΙΛΟΣΟΦΙΚΟ ΛΕΞΙΚΟ 1985, Α51#cptResource164#]

INTUITION

name::
* McsEngl.intuition@cptCore385,

Intuition is apparent ability to acquire knowledge without a clear inference or reasoning process.
It is "the immediate apprehension of an object by the mind without the intervention of any reasoning process" [Oxford English Dictionary].
Intuition, by definition, has no objective validity. However it is extremely widespread as an apparent phenomenon. For this reason, it has been the subject of study in Psychology, as well as a topic of interest in the supernatural.
[http://en.wikipedia.org/wiki/Intuition_%28knowledge%29]

sciSci'THEORY-OF-JUSTIFICATION

name::
* McsEngl.sciSci'THEORY-OF-JUSTIFICATION,
* McsEngl.justification'theory@cptCore385i,
* McsEngl.theory-of-justification@cptCore385i,

Theory of justification is a part of epistemology that attempts to understand the justification of propositions and beliefs. Epistemologists are concerned with various epistemic features of belief, which include the ideas of justification, warrant, rationality, and probability. Of these four terms, the term that has been most widely used and discussed in the past twenty years is "justification". Loosely speaking, justification is the reason why someone (properly) holds the belief, the explanation as to why the belief is a true one, or an account of how one knows what one knows.
If A makes a claim, and B then casts doubt on it, A's next move would normally be to provide justification. Empiricism (the evidence of the senses), authoritative testimony (the appeal to criteria and authority), and logical deduction are often involved in justification. Justification based theories of knowledge can be divided into irrationalism, which appeals to irrational criteria and authorities (feelings, faith) and panrationalism, which appeals to rational criteria and authorities (observation, intellectual intuition).
[http://en.wikipedia.org/wiki/Theory_of_justification]

Theories of Justification
There are several different views as to what entails justification, mostly focusing on the question "How sure do we need to be that our beliefs correspond to the actual world?" Different theories of justification require different amounts and types of evidence before a belief can be considered justified. Interestingly, theories of justification generally include other aspects of epistemology, such as knowledge.
Theories of justification include:
* Foundationalism - Self-evident basic beliefs justify other non-basic beliefs.
* Coherentism - Beliefs are justified if they cohere with other beliefs a person holds, each belief is justified if it coheres with the overall system of beliefs.
* Internalism - The believer must be able to justify a belief through internal knowledge.
* Externalism - Outside sources of knowledge can be used to justify a belief.
* Foundherentism - A combination of Foundationalism and Coherentism that states beliefs are justified based on both positive reasons for justification and coherence with previously justified beliefs. (Proposed by Susan Haack).
[http://en.wikipedia.org/wiki/Theory_of_justification]

DEFINITION

GENERIC

_GENERIC:
* entity.model.information.system.weak.science#cptCore406#

EVOLUTION#cptCore546.171#

1846:
Διαμορφώνεται στην αγγλία σαν ξεχωριστή επιστήμη.
[Ο ΣΥΜΒΟΥΛΟΣ ΤΩΝ ΝΕΩΝ, 1966, 4-250#cptResource12#]

SPECIFIC

DEFINITION

GENERIC

_GENERIC:
* entity.model.information.system.weak.science#cptCore406#

EVOLUTION#cptCore546.171#

1941-1950: ΕΠΑΝΑΣΤΑΣΗ
Με την επιβεβαίωση ότι για οτιδήποτε κληρονομείται είναι υπεύθυνο ένα χημικό μόριο, το DNA. Η επανάσταση αυτή θεωρείται η πιο μεγάλη στον αιώνα μας, ακόμα και αυτή της διάσπασης του ατόμου.
[ΒΗΜΑ, 3 ΙΟΥΛ. 1994, Α36 ΣΤ. ΑΛΑΧΙΩΤΗΣ]

1906: name
The word itself was coined in 1906 by the British biologist William Bateson.
"Genetics," Microsoft(R) Encarta(R) 97 Encyclopedia. (c) 1993-1996 Microsoft Corporation. All rights reserved.

1900:
The science of genetics began in 1900, when several plant breeders independently discovered the work of the Austrian monk Gregor Mendel, which, although published in 1866, had been virtually ignored.
"Genetics," Microsoft(R) Encarta(R) 97 Encyclopedia. (c) 1993-1996 Microsoft Corporation. All rights reserved.

1856: ΓΕΝΝΗΣΗ
Από τον καλόγερο Mendel.
[ΒΗΜΑ, 3 ΙΟΥΛ. 1994, Α36 ΣΤ. ΑΛΑΧΙΩΤΗΣ]

genetics'DNAcptCore733: attPar##

name::
* McsEngl.genetics'DNAcptCore733: attPar,

genetics'GENE#cptCore731: attPar#

name::
* McsEngl.genetics'GENE,

DEFINITION

Geography (from Greek ?e???af?a - geographia, lit. "earth describe-write"[1]) is the science that studies the lands, features, inhabitants, and phenomena of Earth.[2] A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes (276-194 BC). Four historical traditions in geographical research are the spatial analysis of natural and human phenomena (geography as a study of distribution), area studies (places and regions), study of man-land relationship, and research in earth sciences.[3] Nonetheless, modern geography is an all-encompassing discipline that foremost seeks to understand the Earth and all of its human and natural complexities—not merely where objects are, but how they have changed and come to be. Geography has been called "the world discipline" and "the bridge between the human and the physical science". Geography is divided into two main branches: human geography and physical geography.[4][5][6]
[http://en.wikipedia.org/wiki/Geography]

ΓΕΩΓΡΑΦΙΑ είναι ΕΠΙΣΤΗΜΗ...
[hmnSngo.1995.04_nikos]

GENERIC

_GENERIC:
* entity.model.information.system.weak.science#cptCore406#

EVOLUTION#cptCore546.171#

_QUERY:
* History#ql:[Field FdTimeSubject:geography]##viewTime:geography#

DEFINITION

GENERIC

_GENERIC:
* entity.model.information.system.weak.science#cptCore406#

EVOLUTION#cptCore546.171#

_QUERY:
* History#ql:[Field FdTimeSubject:geology]##viewTime:geology#

DEFINITION

ΑΠΟΨΕΙΣ ΓΙΑ ΤΗ ΔΗΜΟΣΙΑ ΔΙΟΙΚΗΣΗ ονομάζω καθε ΑΠΟΨΗ#cptCore505.a# για τη 'δημοσια διοικηση'.
[hmnSngo.1995.04_nikos]

Θεωρίες για τη διοίκηση κοινωνίας είναι το 'σύνολο' των θεωριών που ασχολούντι με τη διοίκηση κοινωνίας.

_DEFINITION:
Political science is a branch of social science concerned with theory, description, analysis and prediction of
- political behavior,
- political systems and
- politics broadly-construed.
[http://en.wikipedia.org/wiki/Political_science]

sciGov'Doctor-of-public-administration

name::
* McsEngl.sciGov'Doctor-of-public-administration,
* McsEngl.doctor-of-public-adminstration@cptCore403i, {2012-05-26}
* McsEngl.D.P.A@cptCore403i, {2012-05-26}

The Doctor of Public Administration (D.P.A.) is a terminal applied-research doctoral degree in the field of public administration (government), which is a sub-discipline of political science. The D.P.A. requires significant coursework beyond the masters level and a dissertation that contributes to theory or practice. Upon successful completion, the title of "Doctor" is awarded and the post-nominals of D.P.A. or DPA can be used.
[http://en.wikipedia.org/wiki/Doctor_of_Public_Administration]

sciGov'EVOLUTION#cptCore546.171#

name::
* McsEngl.sciGov'EVOLUTION,

HISTORY OF SCIENCE {POLITICAL'THEORY}

{time.century20.middle}:
In the US, civil servants and academics such as Woodrow Wilson promoted American civil service reform in the 1880s, moving public administration into academia.[7] However, "until the mid-20th century and the dissemination of the German sociologist Max Weber's theory of bureaucracy" there was not "much interest in a theory of public administration."[8]

sciGov'Field#cptCore406.1#

name::
* McsEngl.sciGov'Field,

_Field:
* international-relations#cptCore321.2#

sciGov'Lean-government

_CREATED: {2012-05-26}

name::
* McsEngl.sciGov'Lean-government,
* McsEngl.lean-government@cptCore403i, {2012-05-26}

Lean Government refers to the application of Lean production principles and methods to identify and implement the most efficient and value added way to provide government services. Government agencies have found that Lean methods enable them to better understand how their processes work, to quickly identify and implement improvements, and to build a culture of continuous improvement.[1] Numerous government agencies, ranging from the U.S. Environmental Protection Agency to the States of Iowa and Minnesota, are using Lean to improve the quality, transparency, and speed of government processes. Lean government proponents generally believe that the government should cut out "waste" and "inefficiency" from government organizations, which will result in overall better services and more value for tax-supported programs and services. Proponents also generally see Lean government as a means to expand the capacity of government to provide more services per unit of investment.[2] As in the manufacturing and service sectors, some government agencies are implementing Lean methods in conjunction with Six Sigma process improvement approaches.[3]
Lean government does not necessarily promote low taxes, only efficient use of those taxes levied. Tax policy is discerned by the legislative and executive branches of government with oversight of the judicial branch of government. Lean government is implemented by the administrative function of government through executive order, legislative mandate, or departmental administrative decisions. Lean government can be applied in legislative, executive, and judicial branches of government.
[http://en.wikipedia.org/wiki/Lean_Government]

sciGov'Policy-analysis

name::
* McsEngl.sciGov'Policy-analysis,
* McsEngl.policy-analysis@cptCore403i, {2012-05-26}

Policy analysis is "determining which of various alternative policies will most achieve a given set of goals in light of the relations between the policies and the goals".[1] However, policy analysis can be divided into two major fields. Analysis of policy is analytical and descriptive—i.e., it attempts to explain policies and their development. Analysis for policy is prescriptive—i.e., it is involved with formulating policies and proposals (e.g., to improve social welfare).[2] The area of interest and the purpose of analysis determines what type of analysis is conducted. A combination of policy analysis together with program evaluation would be defined as Policy studies.[3]
Policy Analysis is frequently deployed in the public sector, but is equally applicable to other kinds of organizations. Policy analysis has its roots in systems analysis as instituted by United States Secretary of Defense Robert McNamara during the Vietnam War.[4]
[http://en.wikipedia.org/wiki/Policy_analysis]

sciGov'Policy-studies

name::
* McsEngl.sciGov'Policy-studies,
* McsEngl.policy-studies@cptCore403i, {2012-05-26}

Policy Studies is the combination of policy analysis and program evaluation.[1] It "involves systematically studying the nature, causes, and effects of alternative public policies, with particular emphasis on determining the policies that will achieve given goals."[2]
Policy Studies also examines the conflicts and conflict resolution that arise from the making of policies in civil society, the private sector, or more commonly, in the public sector (ie government).
It is frequently focused on the public sector but is equally applicable to other kinds of organizations (e.g., the not-for-profit sector). Some policy study experts graduate from public policy schools with public policy degrees. Alternatively, experts may have backgrounds in policy analysis, program evaluation, sociology, psychology, philosophy, economics, anthropology, geography, law, political science, social work, environmental planning and public administration.
Traditionally, the field of policy studies focused on domestic policy, with the notable exceptions of foreign and defense policies. However, the wave of economic globalization, which ensued in the late 20th and early 21st centuries, created a need for a subset of policy studies that focuses on global governance, especially as it relates to issues that transcend national borders such as climate change, terrorism, nuclear proliferation, and economic development. This subset of policy studies, which is often referred to as international policy studies, typically requires mastery of a second language and attention to cross-cultural issues in order to address national and cultural biases. For example, the Monterey Institute of International Studies at Middlebury College offers Master of Arts programs that focus exclusively on international policy through a mix of interdisciplinary and cross-cultural analysis called the "Monterey Way".[3]
[http://en.wikipedia.org/wiki/Policy_studies]

sciGov'Political-philosophy

name::
* McsEngl.sciGov'Political-philosophy,
* McsEngl.political-philosophy@cptCore349,

_DEFINITION:
Political philosophy is the study of fundamental questions about the state, government, politics, liberty, justice, property, rights, law and the enforcement of a legal code by authority: what they are, why (or even if) they are needed, what makes a government legitimate, what rights and freedoms it should protect and why, what form it should take and why, what the law is, and what duties citizens owe to a legitimate government, if any, and when it may be legitimately overthrown—if ever. In a vernacular sense, the term "political philosophy" often refers to a general view, or specific ethic, belief or attitude, about politics that does not necessarily belong to the technical discipline of philosophy.
http://en.wikipedia.org/wiki/Political_philosophy

sciGov'Public-administration-theory

name::
* McsEngl.sciGov'Public-administration-theory,
* McsEngl.public-administration-theory@cptCore403i,

Public administration theory is the amalgamation of history, organizational theory, social theory, political theory and related studies focused on the meanings, structures and functions of public service in all its forms.
A standard course of study in PhD programs dedicated to public administration, public administration theory often recounts major historical foundations for the study of bureaucracy as well as epistemological issues associated with public service as a profession and as an academic field.
Important figures of study include: Max Weber, Frederick Winslow Taylor, Luther Gulick, Mary Parker Follett, Chester Barnard, Herbert A. Simon, and Dwight Waldo. In more recent times, the field has had three main branches: new public management, classic public administration and postmodern public administration theory. The last grouping is often viewed as manifest in the Public Administration Theory Network (PAT-NET) and its publication, Administrative Theory & Praxis.
[http://en.wikipedia.org/wiki/Public_administration_theory]

sciGov'Public-image-of-politician

name::
* McsEngl.sciGov'Public-image-of-politician,
* McsEngl.public-image-of-politician@cptCore403i,

Γιάννα Παπαδάκου
Αρχείο Α.Τσοχατζόπουλου: Ο Νίκος και τα 270.000 για επικοινωνιακή προβολή
Το προσχέδιο της πρότασης - Οι καναπέδες στο σπίτι της Αρεοπαγίτου κόστισαν 34.800 ευρώ και το κρόσι 2.626 ευρώ
ΔΗΜΟΣΙΕΥΣΗ: 24/05/2012, 20:06
Επικοινωνιακή επίθεση με στόχο να εξωραϊσει την εικόνα του ετοίμαζε ο Ακης Τσοχατζόπουλος

Ακόμα και «επικοινωνιακές» συμβουλές ζήτησε να πάρει ο πρώην υπουργός Ακης Τσοχατζόπουλος, από τον...Νίκο, ένα πρόσωπο του οποίου το επώνυμο παραμένει άγνωστο. Από το αρχείο του Ακη Τσοχατζόπουλου προκύπτει ότι ο «Νίκος» υπέβαλε πρόταση στον πρώην υπουργό για επικοινωνιακή επίθεση σε έντυπα και διαδικτυακά σάϊτ με στόχο να βελτιώσει την εικόνα του.

Η πρόταση περιλαμβάνει συνεχείς εμφανίσεις επί 18 μήνες στα ΜΜΕ και συγκρότηση ειδικής ομάδας εργασίας δημοσιογράφων με αποστολή να εξωραϊσει την εικόνα του Τσοχατζόπουλου. Προτείνεται μάλιστα να υπάρχει ένα παραπολιτικό σχόλιο ανα 20ημερο σε 13 έντυπα και περίπου 15 σάϊτ και μπλογκ.

Για την 18μηνη συνεργασία ο «Νίκος» ζητάει αμοιβή 270.000 ευρώ. Το 30% εξ αυτών απαιτεί να καταβληθούν με την υπογραφή του συμφωνητικού. Ο «Νίκος» υποβάλλει παράλληλα στο Τσοχατζόπουλο και πλάνο πολιτικής παρέμβασης με τη διενέργεια ακόμη και δημοσκοπήσεων με κατευθυνόμενα ερωτήματα για «τα πολιτικά παιχνίδια και τις σκευωρίες κατά πολιτικών από συγκεκριμένα συμφέροντα».

Το προσχέδιο πρότασης

Σύμφωνα με δημοσιογραφικές πληροφορίες το προσχέδιο πρότασης του «Νίκου» προς τον κ. Άκη Τσοχατζόπουλο, προτείνονται τα εξής:

Τακτική παραπολιτική παρουσία στα έντυπα: «Αδέσμευτος Τύπος», «ΑΞΙΑ», «Το Ποντίκι», «Βραδυνή», «Λόγος», «Παρασκευή+13», «Καρφί», «Παρασκήνιο», «Παρών», «Εξπρές», «Ναυτεμπορική», «Δημοκρατία», «Ελεύθερος Τύπος». (γίνεται λόγος για ένα παραπολιτικό σχόλιο ανά 20ήμερο)
Συνέντευξη στην εφημερίδα «Καθημερινή», όποτε υπάρξει σχετικό αίτημα (θετική παρουσία).
Ολοκληρωμένο πρόγραμμα παρουσίας σε σειρά ενημερωτικών sites - blogs από δύο φοιτητές πανεπιστημιακής εκπαίδευσης, οι οποίοι θα προωθούν συγκεκριμένες θέσεις τόσο στα συγκεκριμένα sites-blogs όσο και στα social media. Προτείνονται οι ιστοσελίδες: Press-gr.blogspot.com, citypress.gr.blogspot.com, tro-ma-ktiko.blogspot.com, zoomnews.gr, tsiliadoros.blogspot.com, kripsinos.blogspot.com, taxalia.blospot.com (το πρώτο στη Θεσσαλονίκη), newsbomb.gr, newscode.gr, voria.gr (το δεύτερο στη Θεσσαλονίκη), i-reporter.blogspot.com, Greece-salonica.blogspot.com.
Προτείνονται επίσης, σύμφωνα πάντα με τον «Νίκο»: 60 δίκτυα στα social media, (facebook, twitter, κλπ),
Δύο κεντρικά παραπολιτικά στην εφημερίδα «Πρώτο Θέμα» μέχρι την 30ή Μαΐου
Ένα πρωτοσέλιδο δημοσίευμα της εφημερίδας «Δημοκρατία» σχετικά με την κατάρρευση της σκευωρίας κατά Α.Τ.
Ένα άρθρο στην «Κυριακάτικη Ελευθεροτυπία» σχετικά με την εξέλιξη του θέματος του Α.Τ. μετά τον θόρυβο που προεκλήθη (προτεινόμενη περίοδος 2011)
Δημοσκόπηση της εταιρείας Alco (εναλλακτικά της εταιρείας Rass). Στο πλαίσιο ευρύτερης δημοσκόπησης με συγκεκριμένο ερώτημα για «τα πολιτικά παιχνίδια και τις σκευωρίες κατά πολιτικών από συγκεκριμένα συμφέροντα». (Προτεινόμενη περίοδος Μάιος-Ιούνιος 2011).
Συνεχής θετική αρθρογραφία στη «Free Bess» (εφημερίδα Θεσσαλονίκης «Καρφίτσα»).
[http://www.tovima.gr/politics/article/?aid=459262&h1=true]

sciGov'Public-policy-school

name::
* McsEngl.sciGov'Public-policy-school,
* McsEngl.public-policy-school@cptCore403i, {2012-05-26}

Public policy schools teach students policy analysis, policy studies, public policy, political economy, urban planning, public administration, public affairs, and public management.
Public policy schools offer a wide range of public policy degrees. Master of Public Policy (MPP), the Master of Public Administration (MPA), the Master of Public Affairs (MPAff), the Master of Urban Planning (MUP), and the Master of International Affairs (MIA). Schools with an international and interdisciplinary focus award Master of Arts in International Policy Studies. [1] [2] Some schools also offer executive master's degrees in the same topics for mid-career individuals. Doctoral degrees include PhDs in Public Policy, Policy Studies, and Public Administration, as well as the Doctor of Public Administration (DPA).
In North America, students pursue a public policy degree after having completed an undergraduate degree in some other field, or can complete both degrees concurrently at select schools. North American public policy programs are generally located in an autonomous graduate or professional school within a larger university.
[http://en.wikipedia.org/wiki/Public_policy_schools]

sciGov'Referent#cptCore546.79#

name::
* McsEngl.sciGov'Referent,

Political scientists study
- the allocation and transfer of power in decision-making,
- the roles and systems of governance including governments and international organizations,
- political behavior and
- public policies.
They measure the success of governance and specific policies by examining many factors, including stability, justice, material wealth, and peace. Some political scientists seek to advance positive theses by analyzing politics. Others advance normative theses, by making specific policy recommendations.
[http://en.wikipedia.org/wiki/Political_science]

sciGov'ResourceInfHmnn#cptResource843#

name::
* McsEngl.sciGov'ResourceInfHmnn,

BIBLIOGRAPHY#ql:political'theory##viewResource:POLITICAL'THEORY#

Osborne, D., and T. Gaebler. REINVENTING GOVERNMENT. Addison-Wesley, 1992.
Το βιβλίο όχι μόνο έγινε μπεστ-σέλερ αλλά άσκησε συγχρόνως σημαντική επιρροή.
[ΤΟ ΒΗΜΑ, 15 ΜΑΙΟΥ 1994, Β10]

sciGov'Scientist

name::
* McsEngl.sciGov'Scientist,
* McsEngl.conceptCore403.1,
* McsEngl.political-scientist@cptCore403.1, {2012-05-10}
* McsEngl.scientist.political@cptCore403.1, {2012-05-10}

_GENERIC:
* worker.scientist#cptEconomy364.45#

Ancient, medieval and incipient modernist
* Confucius (551-479 BCE)
* Socrates (470-399 BCE)
* Mozi (470-390 BCE)
* Xenophon (427-355 BCE)
* Plato (427-347 BCE)
* Diogenes of Sinope (412-323 BCE)
* Aristotle (384-322 BCE)
* Mencius (372-289 BCE)
* Chanakya (350-283 BC)
* Xun Zi (310-237 BCE)
* Han Feizi (?-233 BCE)
* Cicero (106-43 BCE)
* Pliny the Younger (63-113 CE)
* Saint Augustine (354-430 CE)
* Al-Farabi (870-950)
* Averroes (1126-1198)
* Maimonides (1135-1204)
* St. Thomas Aquinas (1225-1274)
* Marsilius of Padua (1270-1342)
* William of Ockham (1285–1349)
* Ibn Khaldun (1332-1406)
* Niccolo` Machiavelli (1469-1527)
* Martin Luther (1483-1546)
* John Calvin (1509-1564)
* Richard Hooker (1554-1600)
[http://en.wikipedia.org/wiki/Political_theorist]

Modern (born pre-19th century)
* Jean Bodin (1530-1596)
* Francis Bacon (1561-1626)
* Hugo Grotius (1583-1645)
* Thomas Hobbes (1588-1679)
* James Harrington (1611-1677)
* Benedict Spinoza (1632-1677)
* John Locke (1632-1704)
* Montesquieu (1689-1755)
* David Hume (1711-1776)
* Jean-Jacques Rousseau (1712-1788)
* Immanuel Kant (1724-1804)
* William Blackstone (1723-1780)
* Adam Smith (1723-1790)
* Edmund Burke (1729-1797)
* Thomas Paine (1737-1809)
* Thomas Jefferson (1743-1826)
* Jeremy Bentham (1748-1832)
* William Godwin (1756-1836)
* Mary Wollstonecraft (1759-1797)
* Henri de Saint-Simon (1760-1825)
* Benjamin Constant (1767-1830)
* Georg W. F. Hegel (1770-1831)
* Charles Fourier (1772-1837)
* James Mill (1773-1836)
* Arthur Schopenhauer (1788-1860)
* Thomas Carlyle (1795-1881)
* Auguste Comte (1798-1857)
[http://en.wikipedia.org/wiki/Political_theorist]

Born in 19th century
* Ludwig Andreas Feuerbach (1804-1872)
* Alexis de Tocqueville (1805-1859)
* Max Stirner (1806-1856)
* John Stuart Mill (1806-1873)
* Pierre-Joseph Proudhon (1809-1865)
* S?ren Kierkegaard (1813-1855)
* Mikhail Bakunin (1814-1876)
* Henry David Thoreau (1817-1862)
* Karl Marx (1818-1883)
* Friedrich Engels (1820-1895)
* Herbert Spencer (1820-1903)
* Peter Kropotkin (1842-1921)
* Friedrich Nietzsche (1844-1900)
* Eduard Bernstein (1850-1932)
* John Dewey (1859-1952)
* Max Weber (1864-1920)
* Benedetto Croce (1866-1952)
* Vladimir Lenin (1870-1924)
* Rosa Luxemburg (1870-1919)
* Bertrand Russell (1872-1970)
* Muhammad Iqbal (1877-1938)
* Martin Buber (1878-1965)
* Otto Bauer (1881-1938)
* Georg Luka'cs (1885-1971)
* Sergio Panunzio (1886-1944)
* Martin Heidegger (1889-1976)
* Antonio Gramsci (1891-1937)
* Walter Benjamin (1892-1940)
* Max Horkheimer (1895-1973)
* Herbert Marcuse (1898-1979)
* Ludwig Wittgenstein (1899-1951)
* Leo Strauss (1899-1973)
* Alfred Sohn-Rethel (1899-1990)
* Friedrich Hayek (1899-1992)
[http://en.wikipedia.org/wiki/Political_theorist]

Born in 20th century
* Erich Fromm (1900-1980)
* Michael Oakeshott (1901-1990)
* Karl Popper (1902-1994)
* Theodor Adorno (1903-1969)
* Raymond Aron (1905-1983)
* Jean-Paul Sartre (1905-1980)
* Hannah Arendt (1906-1975)
* Sayyid Qutb (1906-1966)
* Isaiah Berlin (1909-1997)
* Albert Camus (1913-1960)
* Roland Barthes (1915-1980)
* Fazlur Rahman (1919-1988)
* Louis Althusser (1918-1990)
* Paulo Freire (1921-1997)
* John Rawls (1921-2002)
* Cornelius Castoriadis (1922-1997)
* Frantz Fanon (1925-1961)
* Gilles Deleuze (1925-1995)
* Michel Foucault (1926-1984)
* Jean Baudrillard (1929-2007)
* Ju"rgen Habermas (1929- )
* Jacques Derrida (1930-2004)
* Fe'lix Guattari (1930-1992)
* Ronald Dworkin (1931- )
* Charles Taylor (1931- )
* Guy Debord (1931-1994)
* Antonio Negri (1933- )
* Fredric Jameson (1934- )
* Wendell Berry (1934 - )
* Robert Nozick (1938-2002)
* E'tienne Balibar (1942- )
* Slavoj Z(iz(ek (1947- )
[http://en.wikipedia.org/wiki/Political_theorist]

Others: This section is for people whose inclusion in the above list is being discussed. Their status as philosophers in general and political philosophers specifically is generally verifiable, but controversial. They are listed in order of birth:
* Thomas Muntzer (1490–1525)
* Rifa' al-Tahtawi (1801-1873)
* Sun Yat-sen (1866-1925)
* Wilhelm Reich (1897-1957)
* Ayn Rand (1905-1982)
* Kancha Ilaiah (1952-)
[http://en.wikipedia.org/wiki/Political_theorist]

sciGov'WHOLE

_WHOLE:
* social-science,

sciGov'GENERIC

_GENERIC:
* science-social#cptCore330.13#
* MULTIAUTHOR_VIEW#cptCore989.9#
* OTHERVIEW#cptCore505#

DEFINITION

Jurisprudence is the theory and philosophy of law. Scholars of jurisprudence, or legal theorists (including legal philosophers and social theorists of law), hope to obtain a deeper understanding of the nature of law, of legal reasoning, legal systems and of legal institutions. Modern jurisprudence began in the 18th century and was focused on the first principles of the natural law, civil law, and the law of nations.[1] General jurisprudence can be broken into categories both by the type of question scholars seek to answer and by the theories of jurisprudence, or schools of thought, regarding how those questions are best answered. Contemporary philosophy of law, which deals with general jurisprudence, addresses problems in two rough groups:[2]

1.) Problems internal to law and legal systems as such.
2.) Problems of law as a particular social institution as it relates to the larger political and social situation in which it exists.
Answers to these questions come from four primary schools of thought in general jurisprudence:[2]

Natural law is the idea that there are rational objective limits to the power of legislative rulers. The foundations of law are accessible through human reason and it is from these laws of nature that human-created laws gain whatever force they have.[2]
Legal positivism, by contrast to natural law, holds that there is no necessary connection between law and morality and that the force of law comes from some basic social facts although positivists differ on what those facts are.[3]
Legal realism is a third theory of jurisprudence which argues that the real world practice of law is what determines what law is; the law has the force that it does because of what legislators, judges, and executives do with it. Similar approaches have been developed in many different ways in sociology of law.
Critical legal studies is a younger theory of jurisprudence that has developed since the 1970s which is primarily a negative thesis that the law is largely contradictory and can be best analyzed as an expression of the policy goals of the dominant social group.[4]
Also of note is the work of the contemporary Philosopher of Law Ronald Dworkin who has advocated a constructivist theory of jurisprudence that can be characterized as a middle path between natural law theories and positivist theories of general jurisprudence.[5]

The English term is based on the Latin word jurisprudentia: juris is the genitive form of jus meaning "law", and prudentia means "prudence" (also: discretion, foresight, forethought, circumspection; refers to the exercise of good judgment, common sense, and even caution, especially in the conduct of practical matters). The word is first attested in English in 1628,[6] at a time when the word prudence had the now obsolete meaning of "knowledge of or skill in a matter". The word may have come via the French jurisprudence, which is attested earlier.
[http://en.wikipedia.org/wiki/Jurisprudence]

sciLaw'GENERIC

_GENERIC:
* entity.model.information.system.weak.science#cptCore406#

sciLaw'WHOLE

_WHOLE:
* science.socHmn##

sciLaw'Islamic

_CREATED: {2012-05-16}

name::
* McsEngl.sciLaw'Islamic,
* McsEngl.conceptCore326.2,
* McsEngl.fiqh@cptCore326.2, {2012-05-16}
* McsEngl.islamic-jurisprudence@cptCore326.2, {2012-05-16}

Fiqh (Arabic: ???? [fiqh]) is Islamic jurisprudence. Fiqh is an expansion of the code of conduct (Sharia) expounded in the Quran, often supplemented by tradition (Sunnah) and implemented by the rulings and interpretations of Islamic jurists.
Fiqh deals with the observance of rituals, morals and social legislation in Islam. There are four prominent schools (madh'hab) of fiqh within Sunni practice and two within Shi'a practice. A person trained in fiqh is known as a Faqih (plural Fuqaha).[1]
[http://en.wikipedia.org/wiki/Fiqh]

sciLaw'law#cptCore23#

name::
* McsEngl.sciLaw'law,

sciLaw'Natural-law

name::
* McsEngl.sciLaw'Natural-law,
* McsEngl.natural-law@cptCore326i, {2012-04-30}

Natural law, or the law of nature (Latin: lex naturalis), is a system of law which is purportedly determined by nature, and thus universal.[1] Classically, natural law refers to the use of reason to analyze human nature -- both social and personal -- and deduce binding rules of moral behavior. Natural law is contrasted with the positive law (meaning "man-made law", not "good law"; cf. posit) of a given political community, society, or nation-state, and thus serves as a standard by which to critique said positive law.[2] According to natural law theory, which holds that morality is a function of human nature and reason can discover valid moral principles by looking at the nature of humanity in society, the content of positive law cannot be known without some reference to natural law (or something like it). Used in this way, natural law can be invoked to criticize decisions about the statutes, but less so to criticize the law itself. Some use natural law synonymously with natural justice or natural right (Latin ius naturale)[citation needed]

Although natural law is often conflated with common law, the two are distinct in that natural law is a view that certain rights or values are inherent in or universally cognizable by virtue of human reason or human nature, while common law is the legal tradition whereby certain rights or values are legally cognizable by virtue of judicial recognition or articulation.[3] Natural law theories have, however, exercised a profound influence on the development of English common law,[4] and have featured greatly in the philosophies of Thomas Aquinas, Francisco Suarez, Richard Hooker, Thomas Hobbes, Hugo Grotius, Samuel von Pufendorf, John Locke, Francis Hutcheson, Jean Jacques Burlamaqui, and Emmerich de Vattel. Because of the intersection between natural law and natural rights, it has been cited as a component in United States Declaration of Independence and the Constitution of the United States, as well as in the Declaration of the Rights of Man and of the Citizen. Declarationism states that the founding of the United States is based on Natural law.
[http://en.wikipedia.org/wiki/Natural_law]

sciLaw'Sociology-of-law

_CREATED: {2012-04-21}

name::
* McsEngl.sciLaw'Sociology-of-law,
* McsEngl.conceptCore326.1,
* McsEngl.sociology-of-law@cptCore326.1,

The sociology of law (or legal sociology) is often described as a sub-discipline of sociology or an interdisciplinary approach within legal studies.[1] While some socio-legal scholars see the sociology of law as "necessarily" belonging to the discipline of sociology,[2] others see it as a field of research caught up in the disciplinary tensions and competitions between the two established disciplines of law and sociology.[3] Yet, others regard it neither as a sub-discipline of sociology nor as a branch of legal studies and, instead, present it as a field of research on its own right within a broader social science tradition. For example, Roger Cotterrell describes the sociology of law without reference to mainstream sociology as "the systematic, theoretically grounded, empirical study of law as a set of social practices or as an aspect or field of social experience".[4]

Irrespective of whether the sociology of law is defined as a sub-discipline of sociology, an approach within legal studies, or a field of research in its own right, it remains intellectually dependent mainly on mainstream sociology, and to lesser extent on other social sciences such as social anthropology, political science, social policy, criminology and psychology, i.e. it draws on social theories and employs social scientific methods to study law, legal institutions and legal behaviour.[5]

More specifically, the sociology of law consists of various sociological approaches to the study of law in society, which empirically examine and theorize the interaction between law and legal institutions, on the one hand, and other (non-legal) social institutions and social factors, on the other.[6] Areas of socio-legal inquiry include the social development of legal institutions, forms of social control, legal regulation, the interaction between legal cultures, the social construction of legal issues, legal profession, and the relation between law and social change.

The sociology of law also benefits from and occasionally draws on research conducted within other fields such as comparative law, critical legal studies, jurisprudence, legal theory, law and economics and law and literature.
[http://en.wikipedia.org/wiki/Sociology_of_law]

DEFINITION

DEFINITION

_DESCRIPTION:
Logic the science of REASONING (= information processing).
[hmnSngo.2014-02-06]
===
To accommodate all the variations, a logic may be defined as any precise notation for expressing
statements that can be judged true or false.
[http://www.jfsowa.com/pubs/fflogic.pdf]
===
Logic (from the Greek ?????? logike)[1] refers to both the study of modes of reasoning (which are valid and which are fallacious)[2] and the use of valid reasoning. In the latter sense, logic is used in most intellectual activities, including philosophy and science, but in the first sense is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take. In mathematics, it is the study of valid inferences within some formal language.[3] Logic is also studied in argumentation theory.[4]
Logic was studied in several ancient civilizations, including India,[5] China,[6] and Greece. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric.
Logic is often divided into three parts, inductive reasoning, abductive reasoning, and deductive reasoning.
[http://en.wikipedia.org/wiki/Logic] 2012-09-15,
===
Logic (from the Greek ?????? logike)[1] is the philosophical study of valid reasoning.[2] Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms which arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic is applied in most major areas: metaphysics, ontology, epistemology, and ethics. In mathematics, it is the study of valid inferences within some formal language.[3] Logic is also studied in argumentation theory.[4]

Logic was studied in several ancient civilizations, including India,[5] China[6] and Greece. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric.

Logic is often divided into three parts, inductive reasoning, abductive reasoning, and deductive reasoning.
[http://en.wikipedia.org/wiki/Logic]

Noun
* S: (n) logic (the branch of philosophy that analyzes inference)
* S: (n) logic (reasoned and reasonable judgment) "it made a certain kind of logic"
* S: (n) logic (the principles that guide reasoning within a given field or situation) "economic logic requires it"; "by the logic of war"
* S: (n) logic (the system of operations performed by a computer that underlies the machine's representation of logical operations)
* S: (n) logic, logical system, system of logic (a system of reasoning)
[wn, 2007-11-21]

sciLgc'GENERIC

_GENERIC:
* science.information.human#cptCore50.24#
* SCIENCE#cptCore401#

sciLgc'WHOLE

_WHOLE:
* PHILOSOPHY#cptCore349#

sciLgc'Area-of-study#cptCore406.8#

name::
* McsEngl.sciLgc'Area-of-study,

* homo.produfino.INFERUDINO#cptCore475.153#

Logic has two broad divisions:
- mathematical logic (formal symbolic logic) and
- what is now called philosophical logic, the logic of language.
[http://en.wikipedia.org/wiki/Philosophy]

sciLgc'argument

name::
* McsEngl.sciLgc'argument,
* McsEngl.pruvero@cptCore548i,
* McsEngl.argument'in'logic@cptCore548i,
* McsEngl.logical'argument@cptCore548i,

_DEFINITION:
* PROVERO is the logero that describes a pruvuino.
[hmnSngo.2007-10-21_KasNik]

* argument IS the expression in a language of reasoning.
[hmnSngo.2007-10-19_KasNik]

In Logic, an argument is a set of declarative sentences (statements) known as the premises, and another declarative sentence (statement) known as the conclusion in which it is asserted that the truth of the conclusion follows from (is entailed by) the premisses. Such an argument may or may not be valid. Note: in Logic declarative sentences (statements) are either true or false (not valid or invalid); arguments are valid or invalid (not true or false). Many authors in Logic now use the term 'sentence' to mean a declarative sentence rather than 'statement' or 'proposition' to avoid certain philosophical implications of these last two terms.
[http://en.wikipedia.org/wiki/Logical_argument]

sciLgc'ARGUMENT-MAP

name::
* McsEngl.sciLgc'ARGUMENT-MAP,
* McsEngl.argument'map@cptCore548i,

_DEFINITION:
An Argument map is a visual representation of the structure of an argument in informal logic. It includes the components of an argument such as a main contention, premises, co-premises, objections, rebuttals and lemmas.
Argument Maps are often used in the teaching of reasoning and critical thinking, and can support the analysis of pros and cons when deliberating over wicked problems.
[http://en.wikipedia.org/wiki/Argument_map]

Argument Mapping Software
* Argunet (open source, cross platform/java)
* Araucaria (open source, cross platform/java)
* Argumentative (open source, windows)
* Athena (free for non-commercial use, windows and perhaps linux and os x)
* Compendium: designed to support deliberation over issues, ideas and arguments in Wicked problems. Provides visual templates for Argumentation Schemes (free source, cross platform/java)
* Reason!Able (commercial, Windows), superseded by Rationale
* Rationale (commercial, Windows); supports simple "Reasoning" maps and more advanced "Analysis" maps
* truthmapping.com online collaborative argument mapping.
* debatemapper.com online collaborative debate mapping.
[http://en.wikipedia.org/wiki/Argument_map] 2007-10-19

sciLgc'DECIDABILITY

name::
* McsEngl.sciLgc'DECIDABILITY,
* McsEngl.decidability'in'logic@cptCore548,
* McsEngl.decidable'logic@cptCore548,

_DEFINITION:
A logical system or theory is decidable if the set of all well-formed formulas valid in the system is decidable. That is, there exists an effective method such that for every formula in the system the method is capable of deciding whether the formula is valid (is a theorem) in the system or not.

Example: Propositional logic is decidable, because there exists for it an algorithm—truth-table construction—such that for every formula which combines M atomic formulas there is a maximum number N = 2M of steps such that after completing those N steps the algorithm will always decide whether the formula is valid or not. Here, a "step" of the algorithm has been (arbitrarily) defined as completion of a row of the truth-table.
[http://en.wikipedia.org/wiki/Decidability_%28logic%29]

sciLgc'formula

name::
* McsEngl.sciLgc'formula,
* McsEngl.formula'in'logic@cptCore548,

_DESCRIPTION:
For example the sentence "Tom does not love Mary" can be formalized as the formula:
loves(tom,mary)

sciLgc'inference-rule

name::
* McsEngl.sciLgc'inference-rule,
* McsEngl.inference'rule'in'logic@cptCore548,
* McsEngl.rule-of-inference'in'logic@cptCore548,

_DEFINITION:
A rule of inference is a truth-preserving transformation:
when applied to a true statement, the result is guaranteed to be true.
[http://www.jfsowa.com/pubs/fflogic.pdf]
===
In logic, a rule of inference is a function from sets of formulae to formulae. The argument is called the premise set (or simply premises) and the value the conclusion. They can also be viewed as relations holding between premises and conclusions, whereby the conclusion is said to be inferable (or derivable or deducible) from the premises. If the premise set is empty, then the conclusion is said to be a theorem or axiom of the logic.
[http://en.wikipedia.org/wiki/Rule_of_inference] 2007-09-14

sciLgc'logical-connective

name::
* McsEngl.sciLgc'logical-connective,
* McsEngl.logical-operator@cptCore496i,
* McsEngl.logical-connective@cptCore496i,
* McsEngl.propositional-operator@cptCore496i,
* McsEngl.sciLgc'connective, {2014-02-27}

_DEFINITION:
In logic, a logical connective, also called a logical operator or propositional operator, is a logical constant which represents a syntactic operation on a sentence, or the symbol for such an operation that corresponds to an operation on the logical values of those sentences.
[http://en.wikipedia.org/wiki/Logical_operator]

_SPECIFIC:
The basic logical operators are :
* Negation (not) (¬ or ~)
* Conjunction (and) (\wedge or &)
* Disjunction (or) (\vee)
* Material implication (if...then) (\rightarrow, \Rightarrow or \supset)
* Biconditional (xnor) (\equiv or \leftrightarrow)
Some others are:
* Exclusive disjunction (xor) (\not\equiv)
* Joint denial (nor) (?)
* Alternative denial (nand) (?)
* Material nonimplication (?)
* Converse nonimplication (?)
* Converse implication (?)
* Tautology (\top)
* Contradiction (\bot)
[http://en.wikipedia.org/wiki/Logical_operator]

_FONT.SYMBOL:
alt34 "  (forAll, universal_quantifier)
alt36 $  (exists, existential_quantifier)
alt39 '  ()
alt133 Ζ  (emptySet)
alt134 Η  (intersection)
alt135 Θ  (union)
alt136 Ι  (implication)
alt137 Κ  (includes|contains|isSuperset)
alt138 Λ  ()
alt139 Μ  ()
alt140 Ν  (isSubset|isContained)
alt141 Ξ  (isMember)
alt142 Ο  (isNotMember)
alt146 Τ  (TradeMark)

sciLgc'proof

name::
* McsEngl.sciLgc'proof,
* McsEngl.proof.logic,

_DEFINITION:
In logic, and in particular proof theory, a proof procedure is a method of proving statements.
A statement p that is provable from a non-empty set Γ of statements in a theory K is called a deduction of p from Γ in K.
If Γ is empty then p is either a theorem of K (i.e., p \in K) or an axiom of K if K is axiomatic.
We express that p is deducible (or provable or derivable or demonstrable) from Γ in K in symbols as
\Gamma \vdash_K p.
[http://en.wikipedia.org/wiki/Proof_procedure]

sciLgc'relation-to-natural-language

name::
* McsEngl.sciLgc'relation-to-natural-language,

_DESCRIPTION:
1. Language and Logic
No discussions about logic have been more confused and confusing than the debates about how logic is related to natural languages. Historically, logic evolved from language. Its name comes from the Greek logos, which means word or reason and includes any language or method of reasoning used in any of the -ology fields of science and engineering. Aristotle developed formal logic as a systematized method for reasoning about the meanings expressed in ordinary language. For the next two millennia, formal logic was expressed in a stylized or controlled subset of a natural language: originally Greek, then Latin, and later modern languages.
In the 19th and 20th centuries, mathematicians took over the development of logic in notations that
diverged very far from its roots, but every operator of any version of logic is a specialization of some word or phrase in natural language: ? for there exists, ? for every, ? for and, ? for or, ? for if-then, ~ for not, ? for possibly, and ? for necessarily. The metalevel words for talking about logic and deduction are the same words used for the corresponding concepts in natural languages: truth, falsity, reasoning, assumption, conclusion, and proof. Although mathematical logic may look very different from ordinary language, every formula in any notation for logic can always be translated to a sentence that has the same meaning. Furthermore, every step of every proof in any formal logic can be translated to an argument in ordinary language that is just as correct and cogent as the formal version.
What makes formal logic hard to use is its rigidity and its limited set of operators. Natural languages
are richer, more expressive, and much more flexible. That flexibility permits vagueness, which some
logicians consider a serious flaw, but a precise statement on any topic is impossible until all the details
are determined. As a result, formal logic can only express the final result of a lengthy process of
analysis and design. Natural language, however, can express every step from the earliest hunch or
tentative suggestion to the finished specification.
[http://www.jfsowa.com/pubs/fflogic.pdf]

sciLgc'SCHOOL

name::
* McsEngl.sciLgc'SCHOOL,

_SCHOOL:
* ARISTOTLE'S_LOGIC#cptCore558: attSpe#
* FORMAL_LOGIC#cptCore496: attSpe#
* INFORMAL_LOGIC#cptCore542: attSpe#

sciLgc'school.INDIAN

name::
* McsEngl.sciLgc'school.INDIAN,
* McsEngl.indian'logic@cptCore548i,

The development of Indian logic can be said to date back to the anviksiki of Medhatithi Gautama (c. 6th century BCE), the Sanskrit grammar rules of Pa-n.ini (c. 5th century BCE), the Vaisheshika school's analysis of atomism (c. 2nd century BCE), the tetralemma of Nagarjuna (c. 2nd century CE), and the analysis of inference by Gotama (c. 2nd–3rd century CE), founder of the Nyaya school of Hindu philosophy. Indian logic stands as one of the three original traditions of logic, alongside the Greek and Chinese traditions.
[http://en.wikipedia.org/wiki/Indian_logic]

sciLgc'school.HIGHER-ORDER--LOGIC (hol)

_CREATED: {2013-01-02} {2000-08-01}

name::
* McsEngl.sciLgc'school.HIGHER-ORDER--LOGIC (hol),
* McsEngl.conceptCore548.1,
* McsEngl.conceptCore1049,
* McsEngl.higher-order-logic,
* McsEngl.higher-order-predicate-calculus,
* McsEngl.hol@cptCore1049,

_DESCRIPTION:
Higher-order logic or HOL goes beyond FOL by allowing function variables and predicate variables to be governed by quantifiers. An example of a higher-order formula is the axiom of induction:
#forall P( (P(0)#and#forall n(P(n)#then P(n+1))#then#forall nP(n)).
This formula may be read For every predicate P, if P is true of 0, and for every n, P(n) implies P(n+1), then P is true of every n. This is the only axiom for arithmetic that requires more expressive power than first-order logic.
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

sciLgc'school.TEMPORAL-LOGIC

_CREATED: {2012-11-25} {2007-09-15}

name::
* McsEngl.sciLgc'school.TEMPORAL-LOGIC,
* McsEngl.conceptCore583,
* McsEngl.temporal-logic,
* McsEngl.temporal'logic@cptCore583,

_DESCRIPTION:
In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. It is sometimes also used to refer to tense logic, a particular modal logic-based system of temporal logic introduced by Arthur Prior in the 1960s. Subsequently it has been developed further by computer scientists, notably Amir Pnueli, and logicians.
...
Any logic which views time as a sequence of states is a temporal logic,
[http://en.wikipedia.org/wiki/Temporal_logic] 2007-09-15

sciLgc'Resource

name::
* McsEngl.sciLgc'Resource,

Kelly, John. 1997. The Essence of Logic. Prentice Hall.

sciLgc'THEORY

name::
* McsEngl.sciLgc'THEORY,

* ARGUMENTATION_THEORY#cptCore547#

sciLgc'THEOREM

name::
* McsEngl.sciLgc'THEOREM,
* McsEngl.theorem'in'logic-548,

DEFINIITON:
In logic, a theorem is a statement in a formal language that can be derived by applying rules and axioms from a deductive system. This definition in logic is crucial in fields such as proof theory that study the general properties of provable and unprovable statements.
...
Logic, especially in the field of proof theory, considers theorems as statements (called formulas or well formed formulas) of a formal language. A set of deduction rules, also called transformation rules or a formal grammar, must be provided. These deduction rules tell exactly when a formula can be derived from a set of premises.
[http://en.wikipedia.org/wiki/Theorem]

DEFINITION

Besides his categories for representing ontology, Aristotle developed formal logic as a precise method for reasoning with them and about them.
[http://www.jfsowa.com/ontology/ontoshar.htm]

GENERIC

_GENERIC#ql:cptCore558 attSpe#

APODEIXIS

name::
* McsEngl.demonstration'in'aristotle@cptCore558,
* McsEngl.apodeixis'in'aristotle@cptCore558,

_DEFINITION:
A demonstration (apodeixis) is "a deduction that produces knowledge". Aristotle's Posterior Analytics contains his account of demonstrations and their role in knowledge. From a modern perspective, we might think that this subject moves outside of logic to epistemology. From Aristotle's perspective, however, the connection of the theory of sullogismoi with the theory of knowledge is especially close.
[Smith, Robin, "Aristotle's Logic", The Stanford Encyclopedia of Philosophy (Summer 2007 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2007/entries/aristotle-logic/>.]

category

resourceInfHmn#cptResource843#

SYLLOGISM

name::
* McsEngl.syllogism-of-aristotle@cptCore558,
* McsEngl.assertion-of-aristotle@cptCore558,

_DEFINITION:
Syllogisms. Besides his categories for representing ontology, Aristotle developed formal logic as a precise method for reasoning with them and about them. His major contribution was the invention of syllogisms as formal patterns for representing rules of inference. The following table lists the names of the four types of propositions used in syllogisms and the corresponding sentence patterns that express them.

Type  Name  Pattern
A  Universal affirmative   Every A is B.
I  Particular affirmative   Some A is B.
E  Universal negative   No A is B.
O  Particular negative   Some A is not B.
With letters such as A and B in the sentence patterns, Aristotle introduced the first known use of variables in history. Each letter represents some category, which the Scholastics called praedicatum in Latin and which became predicate in English. If necessary, the verb form is may be replaced by are, has, or have in order to make grammatical English sentences. Although the patterns may look like English, they are limited to a highly stylized or constrained syntax, which is sometimes called controlled natural language. Such language can be read as if it were natural language, but the people who write it must have some training before they can write it correctly. The advantage of controlled language is that it can be automatically analyzed by computer and be translated to logic.

To make the rules easier to remember, the medieval Scholastics developed a system of mnemonics for naming and classifying them. They started by assigning the vowels A, I, E, and O to the four basic types of propositions. The letters A and I come from the first two vowels of the Latin word affirmo (I affirm), and the letters E and O come from the word nego (I deny). These letters are the vowels used in the names of the valid types of syllogisms. The following table shows examples of the four types of syllogisms named Barbara, Celarent, Darii, and Ferio. The three vowels in each name specify the types of propositions that are used as the two premises and the conclusion.

 Barbara
A:   Every animal is material.
A:   Every human is an animal.
A:  \ Every human is material.
 Celarent
E:   No spirit is a body.
A:   Every human is a body.
E:  \ No spirit is a human.
 Darii
A:   Every beast is irrational.
I:   Some animal is a beast.
I:  \ Some animal is irrational.
 Ferio
E:   No plant is rational.
I:   Some body is a plant.
O:  \ Some body is not rational.
Barbara, Celarent, Darii, and Ferio are the four types of syllogisms that make up Aristotle's first figure. Another fifteen types are derived from them by rules of conversion, which change the order of the terms or the types of statements. Barbara and Darii are the basis for the modern rule of inheritance in type hierarchies. Celarent and Ferio are used to detect and reason about constraints and constraint violations in a type hierarchy. Those four rules are also the foundation for a subset of first-order logic called description logic, two versions of which are DAML and OIL.
[http://www.jfsowa.com/ontology/ontoshar.htm]
===
Syllogisms are structures of sentences each of which can meaningfully be called true or false: assertions (apophanseis), in Aristotle's terminology. According to Aristotle, every such sentence must have the same structure: it must contain a subject (hupokeimenon) and a predicate and must either affirm or deny the predicate of the subject. Thus, every assertion is either the affirmation kataphasis or the denial (apophasis) of a single predicate of a single subject.
[Smith, Robin, "Aristotle's Logic", The Stanford Encyclopedia of Philosophy (Summer 2007 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2007/entries/aristotle-logic/>.]

NAME

name::
* McsEngl.term'in'aristotle@cptCore558,

_DEFINITION:
Subjects and predicates of assertions are terms. A term (horos) can be either individual, e.g. Socrates, Plato or universal, e.g. human, horse, animal, white. Subjects may be either individual or universal, but predicates can only be universals: Socrates is human, Plato is not a horse, horses are animals, humans are not horses.
[Smith, Robin, "Aristotle's Logic", The Stanford Encyclopedia of Philosophy (Summer 2007 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2007/entries/aristotle-logic/>.]

wholeNo-relation#cptCore546.15#

DEFINITION

GENERIC

_GENERIC:
formal-logic#ql:[Level CONCEPT:rl? conceptCore496]##cptCore496#

DEFINITION

GENERIC

_GENERIC:
* OTHERVIEW#cptCore505#

WHOLE

_WHOLE:
* VIEW_MARXIST#cptCore763#

ENGELS'LAWS

name::
* McsEngl.ENGELS'LAWS,

Engels' laws of dialectics

Engels determines three laws of dialectics from his reading of Hegel's Science of Logic[4]. They are:
* The law of the unity and conflict of opposites;
* The law of the passage of quantitative changes into qualitative changes;
* The law of the negation of the negation

The first of Engel's laws or expressions was seen by both Hegel and Lenin as the central feature of a dialectical understanding of things[5] [6] and originates with the ancient Ionian philosopher Heraclitus. [7]

The second is taken by Hegel from Aristotle, and is equated with what scientists call "phase transitions". It may be traced to the ancient Ionian philosophers (particularly Anaximenes), from whom Aristotle inherited the concept, as well as by Hegel and Engels, and in each case the phase transitions of water is one of the main expositions of quantity into quality and vice versa.

The third, the negation of the negation, is Hegel's distinct expression. It was the expression through which (amongst other things) Hegel's dialectic became fashionable during his life-time.

Engels presupposes, in drawing up these laws, a holistic approach outlined in point 1) above, and point 1) of Lenin's three elements of dialectic below, and emphasises elsewhere point 2) above, that all things are in motion. [8]
[http://en.wikipedia.org/wiki/Dialectical_materialism]

DEFINITION

GENERIC

_GENERIC:
formal logic#cptCore496#

resourceInfHmn#cptResource843#

FAQ
ftp://rtfm.mit.edu/pub/usenet-by-group/comp.answers/fuzzy-logic

James Brule, "Fuzzy systems - a tutorial", 1985
(http://life.anu.edu.au/complex_systems/fuzzy.html)

STB Software Catalog
http://krakatoa.jsc.nasa.gov/stb/catalog.html)
includes a few fuzzy tools.

H.J. Zimmerman, "Fuzzy Sets, Decision Making and Expert Systems", Kluwer, Dordrecht, 1987.

"Fuzzy Logic, State of the Art", Ed. R. Lowen, Marc Roubens, Theory and Decision Library, D: System theory, Knowledge Engineering and Problem Solving 12, Kluwer, Dordrecht, 1993, ISBN 0-7923-2324-6.

DEFINITION

fol'AXIOM

name::
* McsEngl.fol'AXIOM,
* McsEngl.axiom'in'fol@cptCore408,

fol'FIRST'ORDER

name::
* McsEngl.fol'FIRST'ORDER,

The "first-order" bit says that we consider predicates (or relations) on the one hand, and individuals on the other; that atomic sentences are constructed by applying the former to the latter; and that quantification is permitted only over the individuals.
[rbj]

fol'FORMULA

name::
* McsEngl.fol'FORMULA,
* McsEngl.formula'in'fol@cptCore408,

SPESIFEPTO:
* THEOREM

fol'INFERENCE-RULE

name::
* McsEngl.fol'INFERENCE-RULE,
* McsEngl.inference'rule'in'fol@cptCore408,

_DEFINITION:
An inference rule relates
- a fixed number of well-formed formulas, called premises, to
- one well-formed formula, called conclusion.
[http://en.wikipedia.org/wiki/First_order_logic]

fol'OPERATOR

name::
* McsEngl.fol'OPERATOR,
* McsEngl.operator'in'fol@cptCore408,

functions written with single characters are called operators, but they form terms just like other functions.
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

fol'PREDICATE

name::
* McsEngl.fol'PREDICATE,

GENERAL: Predicate-Logic-Predicate#ql:pdl'predicate#

fol'REASONING

name::
* McsEngl.fol'REASONING,

fol'SCIENCE

name::
* McsEngl.fol'SCIENCE,

* COMPUTER_SCIENCE#cptIt366#
* LINGUISTICS
* MATHEMATICS
* PHILOSOPHY

First-order logic (FOL) is a language in symbolic science, which is used by mathematicians, philosophers, linguists, and computer scientists.
[http://en.wikipedia.org/wiki/First-order_logic]

fol'THEORY

name::
* McsEngl.fol'THEORY,
* McsEngl.first'order'theory@cptCore408,

_DEFINITION:
A first-order theory consists of a set of axioms (usually finite or recursively enumerable) and the statements deducible from them.
[http://en.wikipedia.org/wiki/First-order_logic]

SPESIFEPTO:
The usual set theory ZFC is an example of a first-order theory, and it is generally accepted that all of classical mathematics can be formalized in ZFC.
[http://en.wikipedia.org/wiki/First-order_logic]

fol'QUANTIFIER

name::
* McsEngl.fol'QUANTIFIER,

fol'VARIABLE

name::
* McsEngl.fol'VARIABLE,

fol'GENERIC

_GENERIC:
* Predicate-Logic#ql:[Level CONCEPT:rl? conceptCore1030]##cptCore1030#
* FORMAL_LOGIC#cptCore496#
* FORMAL_LANGUAGE#cptCore1018#

fol'EVOLUTION#cptCore546.171#

name::
* McsEngl.fol'EVOLUTION,

Kant famously claimed that logic was the one completed science, and that Aristotle had more or less discovered everything about it there was to know. This opinion stood unchallenged until Frege invented first-order logic.
[http://en.wikipedia.org/wiki/Syllogism]

fol'WholeNo-relation#cptCore546.15#

name::
* McsEngl.fol'WholeNo-relation,

DEFINITION

flogic'GENERIC

_GENERIC:
* science.logic#cptCore548#
* math's-field#cptCore89.3#
* entity.model.information.system.weak.science#cptCore406#

* language.human#cptCore93#
* FORMAL_LANGUAGE#cptCore1018#
* braining.infing.human#cptCore475.148#

flogic'WHOLE

_WHOLE:
* PHILOSOPHY#cptCore349#
* MATHEMATICAL_LOGIC#cptCore89.35#
* mathematics science#cptCore89#

flogic'WholeNo-relation#cptCore546.15#

name::
* McsEngl.flogic'WholeNo-relation,

flogic'Area-of-study#cptCore406.8#

name::
* McsEngl.flogic'Area-of-study,

the study of the principles and criteria of valid inference and demonstration.
[http://en.wikipedia.org/wiki/Logic]

Since the mid-nineteenth century formal logic has been studied in the context of foundations of mathematics, where it was often called symbolic logic.
[http://en.wikipedia.org/wiki/Logic]

flogic'EVOLUTION#cptCore546.171#

name::
* McsEngl.flogic'EVOLUTION,

{time.1995 Mechanization:
Marciszewski, W. and Murawski, R. (1995) Mechanization of Reasoning in a Historical Perspective, Volume 43 of Pozna{\'n Studies in the Philosophy of the Sciences and the Humanities}. Rodopi, Amsterdam.

{time.1967
van Heijenoort, J. (ed.) (1967) From Frege to Godel: {A Source Book in Mathematical Logic 1879--1931}. Harvard University Press.

{time.1958 Carnap:
Carnap, R. (1958) Introduction to Symbolic Logic and its Applications. Dover. Translated by William H. Meyer and John Wilkinson; original German edition 'Einfuhring in die symbolische Logik' published by Julius Springer in 1954.

1956: Tarski:
Tarski, A. (ed.) (1956) Logic, Semantics and Metamathematics. Clarendon Press.

1940: Church:
Church, A. (1940) A formulation of the Simple Theory of Types. Journal of Symbolic Logic, 5, 56--68.

1919: Whitehead:
Whitehead, A. N. (1919) An Introduction to Mathematics. Williams and Norgate.

{time.1910 Principia:
Whitehead, A. N. and Russell, B. (1910) Principia Mathematica (3 vols). Cambridge University Press.

1900:
Starting around 1900, the term logic tradition was beginning to be eclipsed by the advent of predicate logic. Predicate logic was the creation of Frege (whose landmark Begriffsschrift was little read before 1950), Charles Peirce, Ernst Schroder, and Peano. It reached full fruition in the hands of Bertrand Russell and A. N. Whitehead, whose Principia Mathematica, published 1910-13, made splendid use of predicate logic. Since the development of predicate logic, term logics have not been popular in the West, except perhaps as simplifications for beginning students.
[http://en.wikipedia.org/wiki/Term_Logic]

{time.1879 Frege:
Frege, G. (1879) Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Louis Nebert, Halle. English translation, 'Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought' in [vanh], pp. 1--82.

[frege-beg] devised his 'Begriffsschrift' ('concept-script' or 'ideography') for formal logic and mathematics, with the particular aim of carrying through what later became known as the logicist programme. He wanted to prove that not only the reasoning used in mathematics, but the underlying assumptions too, and therefore the whole of mathematics, are just pure logic. This would show that mathematics is analytic, refuting Kant's dictum that it is synthetic a priori. Frege made all his deductions using a precisely defined formal deductive system. For this reason above all others he is nowadays commonly regarded as the founding father of modern logic. Moreover, he independently invented quantifiers, and drew attention to numerous important distinctions (e.g. between x and {x} and between and ). However his Begriffsschrift, whatever its merits, was a two-dimensional system of lines which was quite unlike conventional mathematical notation, and was a nightmare for printers.

{time.1854 BOOLE:
Ο Αγγλος μαθηματικός G. Boole διατύπωσε τους βασικούς κανόνες με τους οποίους οι λογικές προτάσεις μπορούν να παρουσιαστούν με μαθηματικά σύμβολα και εξήγησε, πως μια λογική πρόταση μπορεί να χαρακτηριστεί σαν αληθινή ή ψεύτικη.
[ΒΑΤΙΚΙΩΤΗΣ, 26#cptResource709#]

{1848 Boole:
Boole, G. (1848) The calculus of logic. The Cambridge and Dublin Mathematical Journal, 3, 183--198.

{time.1651}: Hobbes
Hobbes, T. (1651) Leviathan. Andrew Crooke.

flogic'LAW

name::
* McsEngl.flogic'LAW,
* McsEngl.law'in'formallogic@cptCore496,

ΝΟΜΟΤΕΛΕΙΕΣ:
1) LAW OF IDENTITY
2) LAW OF NON-CONTRADICTION
3) LAW OF THE EXCLUDED MIDDLE
4) LAW OF SUFFICIENT REASON...
These laws express the definitiveness, the non-contradiction and the provability of thought...
They are reflection of the links and relations between the things of the material world.
[Getmanova, Logic 1989, 21#cptResource19#]

flogic'LOGICAL-CONSTANT

name::
* McsEngl.flogic'LOGICAL-CONSTANT,
* McsEngl.logical'constant@cptCore496,

_DEFINITION:
In symbolic logic, a logical constant is a symbol that has the same semantic value in all models. Two important types of logical constants are logical connectives and quantifiers.
...
One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; that is, what special feature of certain constants that makes them logical in nature?
[http://en.wikipedia.org/wiki/Logical_constant]

flogic'ORDER

name::
* McsEngl.flogic'ORDER,
* McsEngl.order'in'formallogic@cptCore496,

The "order" of a logic specifies what entities "For all" and "Exists" may quantify over.
** First-order logic can only quantify over sets of {atomic} {proposition}s. (E.g. For all p . p => p).
** Second-order logic can quantify over functions on propositions, and
** higher-order logic can quantify over any type of entity.
[FOLDOC 1998.02] 1998-04-30

flogic'PREDICATE

name::
* McsEngl.flogic'PREDICATE,
* McsEngl.predicate'in'logic@cptCore496,
* McsElln.ΠΡΟΤΑΣΙΑΚΟΣ'ΤΥΠΟΣ@cptCore496,

_DEFINITION:
In formal semantics a predicate is an expression of the semantic type of sets. An equivalent formulation is that they are thought of as indicator functions of sets, i.e. functions from an entity to a truth value.
[http://en.wikipedia.org/wiki/Predicate_%28logic%29]
===
Predicate
 An operator in logic which returns either true or false.
[http://mathworld.wolfram.com/Predicate.html]
===
"Εκφράσεις, ως η ανωτέω [ο χ είναι άρτιος αριθμός], εις τας οποίας το σύμβολον χ δεν έχει μόνιμον σημασίαν, δηλαδή παριστά μιαν μεταβλητήν, και αι οποίαι καθίστανται 'προτάσεις', όταν η μεταβλητή χ αντικατασταθή από τυχόν ΣΥΓΚΕΚΤΡΙΜΕΝΟΝ στοιχείον α ενός μη κενού συνόλου Ε, ή ως άλλως λέγομεν, όταν η μεταβλητή χ λάβη ως ΤΙΜΗΝ το α, καλούνται ΠΡΟΤΑΣΙΑΚΟΙ ΤΥΠΟΙ ή ΑΝΟΙΚΤΑΙ ΠΡΟΤΑΣΕΙΣ"
[ΣΤΑΙΚΟΣ, 1971, 11#cptResource755#]

flogic'proposition

name::
* McsEngl.flogic'proposition,
* McsEngl.proposition'in'logic@cptCore496,
* McsElln.ΛΟΓΙΚΗ-ΠΡΟΤΑΣΗ,

_DEFINITION:
"Δια του όρου ΠΡΟΤΑΣΙΣ ή και άλλως ΛΟΓΙΚΗ ΠΡΟΤΑΣΙΣ εννοούμεν μιαν έκφρασιν με πλήρες νόημα, η οποία επιδέχεται ένα ακριβώς εκ των χαρακτηρισμών αληθής, ψευδής και με την αυτήν πάντοτε σημασίαν"
[ΣΤΑΙΚΟΣ, 1971, 11#cptResource755#]

flogic'REASONING

name::
* McsEngl.flogic'REASONING,
* McsEngl.reasoning'in'formallogic@cptCore496,
* McsEngl.reasoning'mechanism'in'formallogic@cptCore496,
* McsEngl.infrencing'in'formallogic@cptCore496,
* McsEngl.inference'procedure'in'formallogic@cptCore496,

SPESIFEPTO:
* REASONING_IN_PREPOSITIONAL_LOGIC##
* REASONING_IN_PREDICATE_LOGIC##

flogic'value

name::
* McsEngl.flogic'value,
* McsEngl.logical'value@cptCore496,
* McsEngl.truth'value'in'formalLogic@cptCore496,
* McsEngl.value'in'logic@cptCore496,

_DEFINITION:
In logic and mathematics, a logical value, also called a truth value, is a value indicating to what extent a proposition is true.
In classical logic, the only possible truth values are true and false. However, other values are possible in other logics: fuzzy logic and other forms of multi-valued logic use more truth values than simply true and false.
[http://en.wikipedia.org/wiki/Logical_value]

_GENERIC:
* REFEREINO#cptCore546.79#

flogic'SCHOOL

name::
* McsEngl.flogic'SCHOOL,

Note that there are many different systems of formal logic each one with its own set of well-formed formulas, rules of inference and, sometimes, semantics. See for instance temporal logic, modal logic, or intuitionistic logic.
Quantum logic is also a form of logic quite different from the ones mentioned earlier.
[http://en.wikipedia.org/wiki/Rule_of_inference]

Any logic which uses the existential quantifier or the universal quantifier is said to be a first-order logic.
Any logic which views time as a sequence of states is a temporal logic, and
any logic which uses only two truth values is a binary logic.
[http://en.wikipedia.org/wiki/Temporal_logic]

flogic.CLASSICAL

name::
* McsEngl.flogic.CLASSICAL,
* McsEngl.classical'logic@cptCore523,

_DEFINITION:
Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties[1]; non-classical logics are those that lack one or more of these properties, which are:
1. Law of the excluded middle and Double negative elimination;
2. Law of noncontradiction;
3. Monotonicity of entailment and Idempotency of entailment;
4. Commutativity of conjunction;
5. De Morgan duality: every logical operator is dual to another.
Classical logic is bivalent, i.e. it uses only Boolean-valued functions. And while not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics.[2][3]
1. Gabbay, Dov, (1994). 'Classical vs non-classical logic'. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, (Eds), Handbook of Logic in Artificial Intelligence and Logic Programming, volume 2, chapter 2.6. Oxford University Press.
2. Shapiro, Stewart (2000). Classical Logic. In Stanford Encyclopedia of Philosophy [Web]. Stanford: The Metaphysics Research Lab. Retrieved October 28, 2006, from http://plato.stanford.edu/entries/logic-classical/
3. Haack, Susan, (1996). Deviant Logic, Fuzzy Logic: Beyond the Formalism. Chicago: The University of Chicago Press.
[http://en.wikipedia.org/wiki/Classical_logic]

Examples of classical logics
* Aristotle's Organon introduces his theory of syllogisms, which is a logic with a restricted form of judgments: assertions take one of four forms, All Ps are Q, Some Ps are Q, No Ps are Q, and Some Ps are not Q. These judgments find themselves if two pairs of two dual operators, and each operator is the negation of another, relationships that Aristotle summarised with his square of oppositions. Aristotle explicitly formulated the law of the excluded middle and law of non-contradiction in justifying his system, although these laws cannot be expressed as judgments within the syllogistic framework.

* George Boole's algebraic reformulation of logic, his system of Boolean logic;

* The first-order logic found in Gottlob Frege's Begriffsschrift.
[http://en.wikipedia.org/wiki/Classical_logic]

flogic.CLASSICAL.NO

name::
* McsEngl.flogic.CLASSICAL.NO,
* McsEngl.non'classical'logic@cptCore523,

Non-classical logics

* Computability logic is a semantically constructed formal theory of computability, as opposed to classical logic, which is a formal theory of truth; integrates and extends classical, linear and intuitionistic logics.
* Fuzzy logic rejects the law of the excluded middle and allows as a truth value any real number between 0 and 1.
* Intuitionistic logic rejects the law of the excluded middle, double negative elimination, and the De Morgan's laws;
* Linear logic rejects idempotency of entailment as well;
* Modal logic extends classical logic with non-truth-functional ("modal") operators.
* Paraconsistent logic (e.g., dialetheism and relevance logic) rejects the law of noncontradiction;
* Relevance logic, linear logic, and non-monotonic logic reject monotonicity of entailment;

In Deviant Logic, Fuzzy Logic: Beyond the Formalism, Susan Haack divided non-classical logics into deviant, quasi-deviant, and extended logics.[3]
[http://en.wikipedia.org/wiki/Classical_logic]

flogic.CONTEXT-LOGIC

name::
* McsEngl.flogic.CONTEXT-LOGIC,
* McsEngl.context'logic@cptCore496,

_DEFINITION:
Context logic is an extension of first order logic in which sentences are not simply true, but are true within a context. The key extension is a modality ist , read "is true", which takes two arguments: a context and a formula. It asserts that the formula is true in the specified context. Contexts are logical individuals and, as such, can be quantified over. Furthermore, it is possible to write axioms that span several contexts. These lifting axioms provide a very powerful and expressive means of shifting information from one context to another. They can be used to perform renaming, change structure, and make implicit assumptions explicit. Context logic allows us to restate the disambiguation axiom without renaming, as in the second axiom in Figure 3. We use context logic to solve the problems of representing a single information source in logic, integrating heterogeneous information sources, and representing the semantic distinctions required by a client.
[KSL-95-12]

flogic.NONMONOTONIC

name::
* McsEngl.flogic.NONMONOTONIC,
* McsEngl.nonmonotonic'logic@cptCore496,

_DEFINITION:
A non-monotonic logic is a formal logic whose consequence relation is not monotonic. Most studied formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. A monotonic logic cannot handle various reasoning tasks such as reasoning by default (facts may be known only because of lack of evidence of the contrary), abductive reasoning (facts are only deduced as most likely explanations), reasoning about knowledge (the ignorance of a fact must be retracted when the fact becomes known), and belief revision (new knowledge may contradict old beliefs).
[http://en.wikipedia.org/wiki/Non-monotonic_logic]

DEFINITION

GENERIC

_GENERIC:
* science.logic#cptCore548#

Area-of-study#cptCore406.8#

... informal logic remains an attempt to develop a logic that can be used in everyday reasoning ...
[Groarke, Leo, "Informal Logic", The Stanford Encyclopedia of Philosophy (Summer 2007 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2007/entries/logic-informal/>.]

EVOLUTION#cptCore546.171#

1977: Logical Self-Defense. Johnson and Blair [1977]
The theoretical interests that motivate informal logic are anticipated in Hamblin's Fallacies (Hamblin [1970]) and Toulmin's The Uses of Argument (Toulmin [1964]), but the discipline itself originated in North America in the 1970s. In many ways the work of Johnson and Blair led the way. Their Logical Self-Defense (Johnson and Blair [1977]) was an early attempt to teach the logic of informal reasoning, and their Informal Logic Newsletter (now the journal Informal Logic) established the discipline as a field for discussion, development and research.
[Groarke, Leo, "Informal Logic", The Stanford Encyclopedia of Philosophy (Summer 2007 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2007/entries/logic-informal/>.]

1960s:
Informal logic is a recent discipline. It has some precedents in those nineteenth century works on Logic and Rhetoric which aim to raise general standards of reasoning through public education (see, e.g., Whatley [1830], [1844]). But informal logic is a child of the 1960s. It is ultimately rooted in its social and political movements, which were characterized by a call for an education more "relevant" to the issues of the day.
[Groarke, Leo, "Informal Logic", The Stanford Encyclopedia of Philosophy (Summer 2007 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2007/entries/logic-informal/>.]

wholeNo-relation#cptCore546.15#

DEFINITION

pdl'GENERIC

_GENERIC:
* formal-logic#ql:[Level CONCEPT:rl? conceptCore496]##cptCore496#

pdl'CONSTANT

name::
* McsEngl.pdl'CONSTANT,

The constants are used to express known individuals, for instance
1) The Joe's bar doesn't exist anymore.
...
Variables refer to unknown and constants to known things.

pdl'EVOLUTION#cptCore546.171#

name::
* McsEngl.pdl'EVOLUTION,

The first version of predicate logic was developed by Gottlob Frege (1879), but in a notation that no one else ever used. The more common algebraic notation, which has been presented in this section, was defined by Charles Sanders Peirce (1883, 1885), but with a different choice of symbols for the quantifiers and Boolean operators. Giuseppe Peano (1889) adopted the notation from Peirce and introduced the symbols that are still in use today. That notation is sometimes called Peano-Russell notation, since Alfred North Whitehead and Bertrand Russell popularized it in the Principia Mathematica. But it is more accurate to call it Peirce-Peano notation, since the extensions that Russell and Whitehead added are rarely used today. The notation presented in this section is Peirce's algebraic notation with Peano's choice of symbols. For a survey of other notations for logic, see the examples that compare predicate calculus to conceptual graphs and the Knowledge Interchange Format (KIF). Aristotle presented his original syllogisms in a stylized version of Greek, and modern computer systems sometimes represent predicate calculus in a stylized or controlled natural language.
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

pdl'FORMULA

name::
* McsEngl.pdl'FORMULA,

Following are the formation rules that define the syntax of formulas:
* A term is either a constant like 2, a variable like x, or an n-adic function symbol applied to n arguments, each of which is itself a term.
* An atom is either a single letter like p that represents a proposition or an n-adic predicate symbol applied to n arguments, each of which is a term.
* A formula is either an atom, a formula preceded by ~, any two formulas A and B together with any dyadic Boolean operator ® in the combination (A ® B), or any formula A and any variable x in either of the combinations $xA or "xA.
...
The formation rules of first-order logic are an example of a recursive definition.
...
In propositional logic, the proposition All peaches are fuzzy may be represented by a single symbol p. In predicate logic, however, the fine structure of the proposition is analyzed in detail. Then p would be represented by an entire formula,
#forall x (peach(x)#then fuzzy(x)).
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

pdl'OPERATOR

name::
* McsEngl.pdl'OPERATOR,

functions written with single characters are called operators, but they form terms just like other functions.
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

pdl'PREDICATE

name::
* McsEngl.pdl'PREDICATE,
* McsEngl.pdl'boolean'function,
* McsEngl.pdl'Logical'Predicate,
* McsEngl.pdl'relation,

=== _NOTES: The term predicate is often used as a synonym for relation. Some authors, however, say that relations must have two or more arguments and call a predicate with one argument a property.
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

_DEFINITION:
A relation [logical-predicate] is a function [math-relation] of one or more arguments whose range is the set of truth values {true,false}.
An example of a dyadic or binary relation is the function less than represented by the operator symbol <. Its domain is the set of ordered pairs of real numbers, R?R:
<: RxR ? {true,false}.
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

* In predicate logic, a predicate can take the role as either a property or a relation between entities.
[http://en.wikipedia.org/wiki/Predicate_%28logic%29]

GENERAL:
Math-Relation#ql:[Level CONCEPT:rl? conceptCore77]##cptCore89.14#

pdl'PROOF

name::
* McsEngl.pdl'PROOF,

A proof in predicate logic has much the same form as a proof in propositional logic.
[last modified Jan 17 1996 / Tom LeBlanc / leblanc@cs.rochester.edu ]

pdl'QUANTIFIER

name::
* McsEngl.pdl'QUANTIFIER,

Predicate logic has two additional operators not found in propositional logic (called quantifiers) to express these truth values about predicates.

Existential quantifier E (there exists): (E x) Tall(x) is true if there exists some value for x such that Tall(x) is true.
Universal quantifier A (for all): (A x) Tall(x) is true if Tall(x) is true for all values of x.

ORDER:
The order of quantifiers in predicate logic makes a crucial difference, as it does in English. Consider the sentence Every man in department C99 married a woman who came from Boston, which may be represented by the formula,
"x$y((man(x) Ω dept(x,C99)) Ι (woman(y) Ω hometown(y,Boston) Ω married(x,y))).
This formula says that for every x there exists a y such that if x is a man and x works in department C99, then y is a woman, the home town of y is Boston, and x married y. Since the dyadic predicate married is symmetric, married(Ike,Mamie) is equivalent to married(Mamie,Ike). Interchanging the arguments of that predicate makes no difference, but interchanging the two quantifiers leads to the formula, $y"x((man(x) Ω dept(x,C99)) Ι (woman(y) Ω hometown(y,Boston) Ω married(x,y))).
This formula says that there exists a y such that for every x, if x is a man and x works in department C99, then y is a woman, the home town of y is Boston, and x married y. In ordinary English, that would be the same as saying, A woman who came from Boston married every man in department C99. If there is more than one man in department C99, this sentence has implications that are very different from the preceding one.
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

pdl'VARIABLE

name::
* McsEngl.pdl'VARIABLE,

Variables refer to unknown and constants to known things.

pdl'WholeNo-relation#cptCore546.15#

name::
* McsEngl.pdl'WholeNo-relation,

pdl.SPECIFIC#cptCore546.23#

* First-Order-Predicate-Calculus#cptCore408: attSpe#
* SECOND_ORDER__LOGIC#cptCore510: attSpe#
* Higher-Order Predicate Calculus#cptCoreCR>* INFINITARY_LOGIC

ppl'DEFINITION

This is a technical mathematical article about the area of mathematics known variously as "propositional calculus" or "propositional logic".
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows certain formul[ae] to be established as "theorems".
[http://en.wikipedia.org/wiki/Sentential_logic] 2008-08-30

In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formul? representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows certain formul? to be established as "theorems" of the formal system.
[http://en.wikipedia.org/wiki/Logical_calculus] 2007-08-18

Propositional logic is a mathematical model (or algebra) for reasoning about the truth of logical expressions (propositions).
[last modified Jan 17 1996 / Tom LeBlanc / leblanc@cs.rochester.edu ]

A propositional calculus is a formal system \mathcal{L} = \mathcal{L}\ (\Alpha,\ \Omega,\ \Zeta,\ \Iota), whose formul? are constructed in the following manner:

* The alpha set \Alpha\! is a finite set of elements called proposition symbols or propositional variables. Syntactically speaking, these are the most basic elements of the formal language \mathcal{L}, otherwise referred to as atomic formul? or terminal elements. In the examples to follow, the elements of \Alpha\! are typically the letters p, q, r, and so on.

* The omega set \Omega\! is a finite set of elements called operator symbols or logical connectives. The set \Omega\! is partitioned into disjoint subsets as follows:
\Omega = \Omega_0 \cup \Omega_1 \cup \ldots \cup \Omega_j \cup \ldots \cup \Omega_m \,.
In this partition, \Omega_j\! is the set of operator symbols of arity j\!.

* The zeta set \Zeta\! is a finite set of transformation rules that are called inference rules when they acquire logical applications.

* The iota set \Iota\! is a finite set of initial points that are called axioms when they receive logical interpretations.

ppl'GENERIC

_GENERIC:
* FORMAL_LOGIC#cptCore496#

ppl'WholeNo-relation#cptCore546.15#

name::
* McsEngl.ppl'WholeNo-relation,

ppl'argument

name::
* McsEngl.ppl'argument,
* McsEngl.argument-of-ppl@cptCore1031,

_DESCRIPTION:
an argument has a conclusion and a number of premises that support that claim.
===
What is interesting about these examples is that they share the same reasoning structure, viz. the pattern shown below.
All x are y. All y are z. Therefore, all x are z.
The existence of such reasoning patterns is fundamental in logic but raises important questions. Which patterns are correct? Are there many such patterns or just a few?
[Genesereth] 1998-05-04

ppl'axiom

name::
* McsEngl.ppl'axiom,
* McsEngl.axiom'in'ppl@cptCore1031,
* McsEngl.distinguished'formula'in'ppl@cptCore1031,

ppl'constant

name::
* McsEngl.ppl'constant,
* McsEngl.logical'constant'in'ppl@cptCore1031,
* McsEngl.constant'in'ppl@cptCore1031,
* McsEngl.constant.ppl,

_DESCRIPTION:
logical constants TRUE and FALSE.

ppl'evaluation

name::
* McsEngl.ppl'evaluation,

_DESCRIPTION:
Propositional logic:
we can only talk about facts and whether or not they are true.
In the worst case, we can use the brute force truth-table method to do inference.
Proof methods such as tableaux are generally more efcient, easier to implement, and easier to understand.
[http://www.inf.unibz.it/~franconi/dl/course/slides/logic/fol/fol-2.pdf]

ppl'inference-rule

name::
* McsEngl.ppl'inference-rule,
* McsEngl.inference'rule'in'ppl@cptCore1031,

ppl'LANGUAGE

name::
* McsEngl.ppl'LANGUAGE,
* McsEngl.language'in'ppl@cptCore1031,

_DEFINITION:
The language of a propositional calculus consists of
(1) a set of primitive symbols, variously referred to as atomic formul?, placeholders, proposition letters, or variables, and
(2) a set of operator symbols, variously interpreted as logical operators or logical connectives. A well-formed formula (wff) is any atomic formula or any formula that can be built up from atomic formul? by means of operator symbols according to the rules of the grammar.

PART:
* OPERATOR_SYMBOL

ppl'LOGICAL-CONNECTIVE

name::
* McsEngl.ppl'LOGICAL-CONNECTIVE,
* McsEngl.ppl'logical'operator,
* McsEngl.ppl'logical'connective,
* McsEngl.ppl'Boolean'Operator,
* McsEngl.operator'symbol'in'ppl@cptCore1031,
* McsEngl.logical'operator'in'ppl@cptCore1031,
* McsEngl.logical'connective'in'ppl@cptCore1031,

=== _NOTES: a set of operator symbols, variously interpreted as logical operators or logical connectives.
[http://en.wikipedia.org/wiki/Propositional_logic]

_DEFINITION:
Besides symbols for propositions, propositional logic also includes Boolean operators that represent logical relations such as and, or, not, and if-then.
[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

SPESIFEPTO:
AND, OR, and NOT are three such operators.

ppl'proposition

name::
* McsEngl.ppl'proposition,
* McsEngl.ppl'LOGICAL'EXPRESSION,
* McsEngl.ppl'proposition,
* McsEngl.ppl'sentence,
* McsEngl.ppl'statement,

_DEFINITION:
We can define logical expressions using a recursive definition:
Propositional variables (whose value is TRUE or FALSE) and the propositional constants TRUE and FALSE are logical expressions.
If LE1 and LE2 are logical expressions, then LE1 AND LE2 is a logical expression, whose value is TRUE if both LE1 and LE2 have the value TRUE, and is FALSE otherwise.
If LE1 and LE2 are logical expressions, then LE1 OR LE2 is a logical expression, whose value is TRUE if either LE1 or LE2 have the value TRUE, and is FALSE otherwise.
If LE1 is a logical expression, then NOT LE1 is a logical expression, whose value is TRUE is LE1 has the value FALSE, and is FALSE otherwise.
[last modified Jan 17 1996 / Tom LeBlanc / leblanc@cs.rochester.edu ]

EXAMPLE:
Examples for statements The following sentences all are statements regardless of its truth value! The moon is made of blue cheese.

Paris is the capital of France.
Mice chase cats.
He is older than she is.
--------------------------------------------------------------------------------
Counter examples --------------------------------------------------------------------------------
To understand what a statement or proposition is, it is may be a good way to show which kinds of sentences do not count as a statement.
1. A question is definitely not a statement How old are you?
Do you love me?
In some cases perhaps it is possible to answer the question with YES or No, but it makes no sense to speak of any truth value. Both examples are not statements which can be TRUE or FALSE.

--------------------------------------------------------------------------------
2. Commands do not count as a statement! Shut the window!
Please turn right!

--------------------------------------------------------------------------------
3. Wishes cannot be a statement If only I hadn't said her that I'm rich.
Merry Christmas and a Happy New Year!

ppl'proof

name::
* McsEngl.ppl'proof,
* McsEngl.proof'in'ppl@cptCore1031,

_DESCRIPTION:
a proof, i.e. a record of the key steps in the process of deriving a conclusion from a set of premises in which each step is immediately obvious.
[Genesereth] 1998-05-04

ppl'reasoning

name::
* McsEngl.ppl'reasoning,
* McsEngl.inferencing.ppl,
* McsEngl.reasoning.ppl,

_DESCRIPTION:
We are interested in the questions:
* when is a statement logically implied by a set of statements,
* can we dene deduction in such a way that deduction and entailment
coincide?
[http://www.inf.unibz.it/~franconi/dl/course/slides/logic/propositional/prop-logic-1.pdf]

_GENERIC:
* REASONING_IN_FORMAL_LOGIC#ql:reasoning'IN'FO*###

ppl'relation-to-other-logics

name::
* McsEngl.ppl'relation-to-other-logics,
* McsEngl.ppl'AND'OTHER'LOGICS,

Other logical calculi

Propositional calculus is about the simplest kind of logical calculus in any current use. (Aristotelian "syllogistic" calculus, which is largely supplanted in modern logic, is in some ways simpler — but in other ways more complex — than propositional calculus.) It can be extended in several ways.

The most immediate way to develop a more complex logical calculus is to introduce rules that are sensitive to more fine-grained details of the sentences being used. When the "atomic sentences" of propositional logic are broken up into terms, variables, predicates, and quantifiers, they yield first-order logic, or first-order predicate logic, which keeps all the rules of propositional logic and adds some new ones. (For example, from "All dogs are mammals" we may infer "If Rover is a dog then Rover is a mammal".)

With the tools of first-order logic it is possible to formulate a number of theories, either with explicit axioms or by rules of inference, that can themselves be treated as logical calculi. Arithmetic is the best known of these; others include set theory and mereology.

Modal logic also offers a variety of inferences that cannot be captured in propositional calculus. For example, from "Necessarily p" we may infer that p. From p we may infer "It is possible that p". The translation between modal logics and algebraic logics is as for classical and intuitionistic logics but with the introduction of a unary operator on Boolean or Heyting algebras, different from the Boolean operations, interpreting the possibility modality, and in the case of Heyting algebra a second operator interpreting necessity (for Boolean algebra this is redundant since necessity is the De Morgan dual of possibility). The first operator preserves 0 and disjunction while the second preserves 1 and conjunction.

Many-valued logics are those allowing sentences to have values other than true and false. (For example, neither and both are standard "extra values"; "continuum logic" allows each sentence to have any of an infinite number of "degrees of truth" between true and false.) These logics often require calculational devices quite distinct from propositional calculus. When the values form a Boolean algebra (which may have more than two or even infinitely many values), many-valued logic reduces to classical logic; many-valued logics are therefore only of independent interest when the values form an algebra that is not Boolean.
[http://en.wikipedia.org/wiki/Propositional_logic]

ppl'resourceInfHmn#cptResource843#

name::
* McsEngl.ppl'resourceInfHmn,

[Sowa, http://www.bestweb.net/~sowa/misc/mathw.htm, (2000-07-30)]

ppl'SYNTAX

name::
* McsEngl.ppl'SYNTAX,

Syntax -- Expressions in the language
Semantics -- meaning of expressions

ppl'STRUCTURE

name::
* McsEngl.ppl'STRUCTURE,

The following outlines a standard propositional calculus. Many different formulations exist which are all more or less equivalent but differ in the details of
(1) their language, that is, the particular collection of primitive symbols and operator symbols,
(2) the set of axioms, or distinguished formul?, and
(3) the set of inference rules.
[http://en.wikipedia.org/wiki/Propositional_logic]

ppl'tautology

name::
* McsEngl.ppl'tautology,
* McsEngl.tautology'in'ppl@cptCore1031,

_DESCRIPTION:
A tautology is a logical expression that is always TRUE, regardless of the assignment of truth values to the variables in the expressions.
Examples of tautologies:
TRUE
TRUE OR p
p OR NOT p
NOT (p AND NOT p)
p == p
(p OR q) == p OR (NOT p AND q)
(p == q) -> (p -> q)
If we can establish that "LE1 == LE2" is a tautology, then no matter what values we assign to the variables in LE1 and LE2, we know that "LE1 == LE2" has the value TRUE.
If "LE1 == LE2" is a tautology, then we can substitute LE2 for LE1 (or vice versa) in any expression, without changing the value of the expression.

--------------------------------------------------------------------------------
The Tautology Problem
It is an interesting question to ask whether a given logical expression is a tautology. This question is known as the "tautology problem."
To solve the tautology problem, we need only construct the truth table for the logical expression. If the expression has the value TRUE for all possible assignment values for the variables in the expression (that is, if the entire column for the expression in the truth table is TRUE), then the expression is a tautology.
Note that the truth table will have 2^k rows and n columns, where the original expression has k variables and n operators. Thus, this algorithm requires O(2^kn) time, ie. exponential time.
There is no known algorithm for the tautology problem that takes less than exponential time. Such problems are called "intractable" because large instances of the these problems cannot be solved in a reasonable amount of time.
Another such intractable problem is the "satisfiability problem" which asks whether there is an assignment of truth values to variables in a logical expression that makes the expression TRUE. There is no known algorithm for this problem that is more efficient than cycling through all possible combinations of truth assignments for the variables.

ppl'truth-table

name::
* McsEngl.ppl'truth-table,
* McsEngl.truth'table'in'ppl@cptCore1031,

_DESCRIPTION:
Example: given the expression "(p AND q) OR r", we can describe the Boolean function that determines the value of the expression by considering all combinations of value assignments for p, q, and r.
p   q  r (p AND q) OR r
------------------------------
T   T  T T
T   T  F T
T   F  T T
T   F  F F
F   T  T T
F   T  F F
F   F  T T
F   F  F F
The above table describing the Boolean function "(p AND q) OR r" is called a truth table. In a truth table, there is a column for each variable in the expression, and each row in the table corresponds to an assignment of values to variables. The final column gives the value of the expression for the particular set of variable assignments given in the row.

ppl'variable

name::
* McsEngl.ppl'variable,
* McsEngl.variable'in'ppl@cptCore1031,
* McsEngl.propositional'variable@cptCore1031,
* McsEngl.primitive'symbol'in'ppl@cptCore1031,
* McsEngl.atomic'formula'in'ppl@cptCore1031,
* McsEngl.placeholder'in'ppl@cptCore1031,
* McsEngl.proposition'letter'in'ppl@cptCore1031,

=== _NOTES: The language of a propositional calculus consists of (1) a set of primitive symbols, variously referred to as atomic formul?, placeholders, proposition letters, or variables,
[http://en.wikipedia.org/wiki/Propositional_logic]

_DEFINITION:
A variable in propositional logic (a propositional variable) is any statement that can have one of the truth values, TRUE of FALSE.
[internet] 1998-05-02

DEFINITION

DEFINITION

EVOLUTION#cptCore546.171#

PROPOSITION

name::
* McsEngl.proposition'in'traditional'logic@cptCore530,

_DEFINITION:
The proposition consists of two terms, in which one term (the "predicate") is "affirmed" or "denied" of the other (the "subject"), and which is capable of truth or falsity.
[http://en.wikipedia.org/wiki/Term_Logic]

SPESIFEPTO:
A proposition may be universal or particular, and it may be affirmative or negative. Thus there are just four kinds of propositions:
* A-type: Universal and affirmative or ("All men are mortal")
* I-type: Particular and affirmative ("Some men are philosophers")
* E-type: Universal and negative ("No philosophers are rich")
* O-type: Particular and negative ("Some men are not philosophers").
This was called the fourfold scheme of propositions. (The origin of the letters A, I, E, and O are explained below in the section on syllogistic maxims.) Aristotle summarised the logical relationship between four types of propositions with his square of oppositions. The syllogistic is a formal theory explaining which combinations of true premises yield true conclusions.
[http://en.wikipedia.org/wiki/Term_Logic]

SYLLOGISM

name::
* McsEngl.syllogism'in'traditional'logic@cptCore530,

_DEFINITION:
The syllogism is an inference in which one proposition (the "conclusion") follows of necessity from two others (the "premises").
[http://en.wikipedia.org/wiki/Term_Logic]

NAME

name::
* McsEngl.term'in'traditional'logic@cptCore530,

_DEFINITION:
The term is a part of speech representing something, but which is not true or false in its own right, such as "man" or "mortal".
[http://en.wikipedia.org/wiki/Term_Logic]

_DESCRIPTION:
A term (Greek horos) is the basic component of the proposition. The original meaning of the horos (and also of the Latin terminus) is "extreme" or "boundary". The two terms lie on the outside of the proposition, joined by the act of affirmation or denial.
For Aristotle, a term is simply a "thing", a part of a proposition. For early modern logicians like Arnauld (whose Port-Royal Logic was the best-known text of his day), it is a psychological entity like an "idea" or "concept". Mill considers it a word. None of these interpretations are quite satisfactory. In asserting that something is a unicorn, we are not asserting anything of anything. Nor does "all Greeks are men" say that the ideas of Greeks are ideas of men, or that word "Greeks" is the word "men". A proposition cannot be built from real things or ideas, but it is not just meaningless words either. This is a problem about the meaning of language that is still not entirely resolved. (See the book by Prior below for an excellent discussion of the problem).
[http://en.wikipedia.org/wiki/Term_Logic]

FvMcs.science.logic.SECOND-ORDER-(sologic)

_CREATED: {2007-08-18}

name::
* McsEngl.conceptCore510,
* McsEngl.science.logic.SECOND-ORDER-(sologic),
* McsEngl.FvMcs.science.logic.SECOND-ORDER-(sologic),
* McsEngl.second-order-logic,
* McsEngl.second'order'logic@cptCore510,
* McsEngl.science.second-order-logic,

FvMcs.science.MATHEMATICS

name::
* McsEngl.conceptCore89,
* McsEngl.science.MATHEMATICS,
* McsEngl.FvMcs.science.MATHEMATICS,
* McsEngl.mathematics@cptCore89,
* McsEngl.science.mathematics@cptCore89,
* McsEngl.sciMath@cptCore89, {2012-05-18}
* McsEngl.maths,
* McsEngl.math@cptCore89,
* McsEngl.sciMth@cptCore89, {2012-04-26}
====== lagoGreek:
* McsElln.ΕΠΙΣΤΗΜΗ'ΜΑΘΗΜΑΤΙΚΗ@cptCore89,
* McsElln.ΜΑΘΗΜΑΤΙΚΑ@cptCore89,
* McsElln.ΜΑΘΗΜΑΤΙΚΗ-ΕΠΙΣΤΗΜΗ,
====== lagoEsperanto:
* McsEngl.matematiko@lagoEspo,
* McsEspo.matematiko,
====== lagoChinese:
shu4xue2 (mathematic; mathematics) [count+learn]

Etymology

The word "mathematics" (Greek: μαθηματικά or mathe-matika') comes from the Greek μάθημα (ma'the-ma), which means learning, study, science, and additionally came to have the narrower and more technical meaning "mathematical study", even in Classical times. Its adjective is μαθηματικός (mathe-matiko's), related to learning, or studious, which likewise further came to mean mathematical. In particular, μαθηματικ? τέχνη (mathe-matike-' te'khne-), in Latin ars mathematica, meant the mathematical art.

The apparent plural form in English, like the French plural form les mathe'matiques (and the less commonly used singular derivative la mathe'matique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural τα μαθηματικά (ta mathe-matika'), used by Aristotle, and meaning roughly "all things mathematical".[8] In English, however, mathematics is a singular noun, often shortened to math in English-speaking North America and maths elsewhere.
[http://en.wikipedia.org/wiki/Mathematics]