19.3. Functions of Logic

1. Cognitive. As any other science logic considers and reveals the objective laws. While physics and chemistry studies the laws of nature, logic tries to find out the laws of thinking. Logic shows us the right forms of thinking and gives the criteria of the truth.

2. Worldview. Logic helps us to comprehend the key philosophical concepts such as consciousness, man, and cognition. It moulds our worldview, and structures it.

3. Methodological. Logical theory is the method of cognition. Logic as a science is methodology of cognition and science.

So, logic influences the development of scientific and cognitive capabilities of man. It also forms the logical culture of our thinking.

Thus, logic is the formal science of using reason. It is considered a branch of both philosophy and mathematics. One of the aims of logic is to identify the correct (or valid) and incorrect (or fallacious) inferences. Logicians study the criteria for the evaluation of arguments. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics, such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality.

Basic concepts and categories:

Logical laws of thought are fundamental axiomatic rules upon which rational discourse itself is based. Aristotle formulated three logical laws: the law of identity, the law of contradiction and the law of excluded middle.

Truth can have a variety of meanings, such as the state of being in accord with a particular fact or reality, or being in accord with the body of real things, real events or actualities. It can also mean having fidelity to an original or to a standard and ideal.

The formal system (also called a logical calculus) consists of a formal language and a set of inference rules, used to derive (to conclude) an expression from one or more other premises that are antecedently supposed (axioms) or derived (theorems).

Logical conjunction is a logical connective (“and”) that has the value of true if both of its operands are true, otherwise a value of false.

Logical disjunction or inclusive disjunction is a logical operator that results in true whenever one or more of its operands are true. For instance in this context, "A or B" is true if A is true, or if B is true, or if both A and B are true.

Entailment (or logical implication) is a relation between sets of sentences and a sentence. Typically entailment is defined in terms of necessary truth preservation: some set T of sentences entails a sentence A if and only if it is necessary that A be true whenever each member of T is true.

Equivalence relation is a relation that specifies how to partition a set such that every element of the set is in exactly one of the blocks in the partition, and the union of all the blocks equals the original set. Two elements of the set are considered equivalent (with respect to the equivalence relation) if and only if they are elements of the same block.

Negation is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified with the truth function that takes truth to falsity and vice versa.