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A proposition is logically true if its truth depends only on the logical vocabulary used in it. This means that it is true in all possible worlds and under all interpretations of its non-logical terms, like the claim "either it is raining, or it is not". [15] These two definitions of formal logic are not identical, but they are closely related.
Forms of logical reasoning can be distinguished based on how the premises support the conclusion. Deductive arguments offer the strongest possible support. Non-deductive arguments are weaker but are nonetheless correct forms of reasoning. [28] [29] The term "proof" is often used for deductive arguments or very strong non-deductive arguments. [30]
The question arises because philosophical writing does more than report results. It is a process of discovery in its own right, and the process unfolds differently in the aphorism than it does in the essay, and differently through irony than through the counter-example.
A logical operation meaning "not and"; it produces a true result for all input combinations except the case where all inputs are true. It is a fundamental operation since any logical function can be constructed using only NAND operations.
As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", [1] while they are rational according to the broader requirement that they are based on reason and knowledge.
A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
Logical, rational or general grammar was the dominant approach to language until it was supplanted by romanticism. [3] Since then, there have been attempts to revive logical grammar. The idea is today at least partially represented by categorial grammar , formal semantics , and transcendental phenomenology ,
In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language. [1] The logical form of an argument is called the argument form of the argument.