Questions and Tasks for Self-Control

1. What is the subject of logic?

2. Distinguish the types of logic.

3. Speak on the general characteristic of formal logic

4. What are the logical laws of thinking?

5. Explain the law of identity.

6. Give an example of the principle of contradiction?

7. What is the main idea of the law of excluded middle?

8. Analyze the logical functions.

9. Differentiate the inductive and deductive reasoning.

Literature

Basic:

The Cambridge Dictionary of Philosophy / Robert Audi. —New York : Cambridge University Press, 1999. — 1001 p.

Supplementary:

Stanford Encyclopedia of Philosophy. — Eelectronic resource : www.stanford.edu

Primary sources:

Aristotle. Metaphysics / Aristotle : [transl. by W. D. Ross]. – Nashotah, Wisconsin : The Classical Library, 2001. — 498 p.

Immanuel Kant. Logic / Immanuel Kant : [transl. by Robert S. Hartman and Wolfgang Schwarz]. — New York : Dover, 1988. — 164 p.

John Stuart Mill. A System of Logic / John Stuart Mill. — London : University Press of the Pacific, 2006. — 604 p.

Unit 20

Logical forms of thinking

The aim of the theme is to observe different types of basic logical forms of thinking such as concepts, propositions and reasoning.

Key words of the theme are: concept, definition, extension of the concept, intension of the concept, proposition, reasoning, deductive reasoning, inductive reasoning.

20.1. Concept as Form of Abstract Thinking

Many philosophers consider concepts to be fundamental ontological categories of being. For example, Kant declared that human minds possess pure or a priori concepts. Instead of being abstracted from individual perceptions, like empirical concepts, they originate in the mind itself. He called these concepts categories, in the sense of the word that means predicate, attribute, characteristic or quality. But these pure categories are predicates of things in general, not of a particular thing. According to Kant, there are 12 categories that constitute the understanding of phenomenal objects.

A concept is a cognitive unit of meaning − an abstract idea or a mental symbol sometimes defined as a "unit of knowledge", built from the other units which act as a concept's characteristics. A concept is typically associated with a corresponding representation in a language or symbology such as a single meaning of a term.

One of the philosophical views maintains that concepts are psychological entities, taking the representational theory of the mind (RTM) as its starting point. According to RTM, thinking occurs in an internal system of representation. So, the representational theory of mind proposes that concepts are mental representations.

The structure of concepts

Since thoughts are composed of more basic, word-sized concepts, so these word-sized concepts − known as lexical concepts − are generally thought to be composed of even more basic concepts. According to the classical theory, a lexical concept C has definitional structure in that it is composed of simpler concepts that express necessary and sufficient conditions for falling under C. The stock example is the concept bachelor, which is traditionally said to have the constituents unmarried and man. If the example is taken at face value, the idea is that something falls under bachelor if it is an unmarried man and only if it is an unmarried man. According to the classical theory, lexical concepts generally will exhibit this same sort of definitional structure. This includes such philosophically interesting concepts as truth, goodness, freedom, and justice.

General structure of the concept consists of two elements: extension and intension.

The extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question. For example, the extension of the word "dog" is the set of all (past, present and future) dogs in the world.

In linguistics, logic, philosophy, and other fields an intension (or concept content) is any property or quality connoted by a word, phrase or other symbol. In the case of a word, it is often implied by the word's definition.

Intension and intensionality (the state of having intension) should not be confused with intention and intentionality, which are pronounced the same and occasionally arise in the same philosophical context.

The classification of concepts

According to the quantity of elements in concept’s extension, all concepts are divided into normal (nonempty) and nonsensical (empty) ones.

Nonsensical concepts

The phrase "Colorless green ideas sleep furiously" was coined by Noam Chomsky as an example of nonsense. The individual words make sense and are arranged according to proper grammatical rules, yet the result is nonsense. The inspiration for this attempt at creating verbal nonsense came from the idea of contradiction (for a start, how can a green idea be colorless?) and seemingly irrelevant and/or incompatible characteristics, which conspire to make the phrase meaningless. The phrase "the square root of Tuesday" operates on the latter principle. This principle is behind the inscrutability of the koan "What is the sound of one hand clapping?" where one hand would presumably be insufficient for clapping without the intervention of another.

Nonempty concepts

The concept that contains at least one element in its extension is called nonempty concept. All nonempty concepts can be divided into general and individual (particular). Individual concept is the one that contains only one element in its extension, for example “the founder of logic”. General concept is the one that contains two or /and more elements in its extension (for example “planet”, “criminal”).

General concepts are divided into registered and unregistered. General registered (for example “the state of USA”) contains 51 states in extension and we can count all elements of the extension). In general unregistered notions (for example “oak tree”) we cannot count every element of the extension (it’s hard to say how many oak-trees are in the world).

According to the character of elements in the concept extension, the concepts can be divided into collective and non-collective.

In linguistics and logic, a collective concept (noun) is a word or term used to define a group of objects where objects can be people, animals, emotions, inanimate things, concepts, or other things. For example, in the phrase "a pride of lions," pride is a collective noun. Most collective concepts encountered in everyday speech, such as "group," are mundane and are not specific to one kind of constituent object. For example, the terms "group of people," "group of dogs," and "group of ideas" are all correctly used.

Collective concepts are the ones that refer to groups consisting of more than one individual or entity, even when they are inflected for the singular. Examples include committee, herd, and school (of fish). These concepts have slightly different grammatical properties than other ones. For example, the noun phrases that they head can serve as the subject of a collective predicate, even when they are inflected for the singular. A collective predicate is a predicate that cannot normally take a singular subject.

The concept that generalizes singular objects (“student”, “table”) is called non collective.

According to the types of elements in the concept extension all concepts are divided into abstract and concrete.

Concrete concepts (nouns) refer to physical entities that can, in principle, be observed by at least one of the senses (for instance, chair, apple, Janet or atom).

Abstract concepts (nouns), on the other hand, refer to abstract objects; that is, ideas or concepts (e.g., justice or hatred). While this distinction is sometimes useful, the boundary between concrete and abstract is not always clear; consider, for example, the noun art, which usually refers to a concept (e.g., art is an important element of human culture) but which can refer to a specific artwork in certain contexts (e.g., I put my daughter's art up on the fridge).

According to the characteristic features of concepts they can be divided into positive (contains such characteristic as good, clever, wise) and negative (contains such attributes as awful, ugly, naughty); correlative (the one that has correlation with other concept and has no independent meaning. For instance, such concepts as “cause”, “parents” need to be added with predicate: the “cause of cancer”, “parents of George Washington” and so on); non-correlative (the one that has independent meaning, for instance “the Pacific ocean”, “school”)

According to the relations between concepts, they can be comparable (relative) or incomparable. The incomparable concepts do not have common features between themselves. (For instance “atom” and “joy” as well as basic philosophical categories “being” and “non-being”, “spirit” and “matter” are incomparable).

The comparable concepts have common features in their content (“lion” and “monkey” are comparable because both are living creatures, mammals etc). All comparable concepts can be in the relations of compatibility and incompatibility.

Philosopher Bolzano defined a system of relations between the extensions of ideas. The first relations he defines are compatibility and its negation, incompatibility. Two ideas A and B are compatible if they have (represent) at least one object in common, i.e., if at least one object falls under both A and B. In the case in which not only some, but all objects represented by A are also represented by B, A is included in B. If this relation is reciprocal, i.e., if A is included in B and B included in A, the ideas A and B are equivalent (coextensive). Further, we have two special cases: proper compatibility, i.e., compatibility where neither A is included in B, nor B in A; this relation is called by Bolzano intersection or concatenation. Another is subordination which is proper inclusion, without reciprocity.