Tomassi Logic - Chapter 1 Glossary

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argument

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In logic an argument consists of a set of sentences (the premises) which may or may not establish another sentence (the conclusion) as a consequence. Not every set of sentences constitutes an argument in this sense. Premises should be given as reasons for their conclusion and a pattern of inference should be identifiable. Tips: words such as ‘because’, ‘since’ and ‘for’ indicate premises while words such as ‘therefore’, ‘so’, ‘hence’ or ‘thus’ indicate conclusions. Look for words such as these when trying to identify an argument.

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logical consequence

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A sentence is a logical consequence of a set of sentences if the truth of the set of sentences guarantees the truth of the sentence in question.

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necessary truth

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A sentence is a necessary truth if it could not possibly be false. The contrast here is with contingent truth. A sentence is a contingent truth if it is true but could have been false.

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valid

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Validity is that property belonging to arguments whereby if the premises are true then the conclusion must be true, on pain of contradiction. So, if an argument is valid the conclusion of that argument is a logical consequence of its premises.

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invalid

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An argument is invalid if it is possible that its premises be true and its conclusion false.

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sound

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A sound argument is a valid argument with true premises.

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deductive argument

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Here a deductive argument is a valid argument.

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entail

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A set of premises entails a conclusion when the conclusion is a logical consequence of that set of premises.

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imply

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A set of premises implies a conclusion when the conclusion is a logical consequence of that set of premises.

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induction/inductive argument

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Both the premises and the conclusion of an inductive argument concern empirical matters of fact. The premises of an inductive argument at best only support their conclusion, i.e. the premises of such an argument do not entail their conclusion.

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singular sentences

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In effect, any sentence the grammatical subject of which is a single, specific individual.

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logical force

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The logical force of a valid argument derives from the fact that to accept the premises of such an argument while rejecting its conclusion is to contradict oneself.

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empirical

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A philosophical term meaning relating to or derived from experience. Empirical sentences concern experiential matters, worldly matters. An empirical sentence is one whose truth-value is decidable in terms of experience.

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logical form

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The schematic pattern or inferential structure of an argument. Tips: logical form is not really a once-and-for-all matter. Particular arguments can be instances of more than one logical form. Our ability to represent the logical form of an argument is limited by the formal vocabulary available to us.

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formal definition (of validity)

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According to the formal definition an argument is valid if, and only if, it is an instance of a logically valid form of argument.

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modal definition (of validity)

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According to the modal definition an argument is valid if it is such that if the premises are true then the conclusion must be true, on pain of contradiction.

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classical logic

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The system of formal logic designed by Gottlob Frege and Bertrand Russell (as opposed to alternative or ‘deviant’ systems such as relevant logic or intuitionist logic).

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argument-frames

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Schemas or patterns of inference with gaps which (in PL) are plugged by sentential variables or sentence-letters.

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place-markers

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Symbols which mark gaps in argument-frames.

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variable (QL)

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Intuitively, a symbol which marks a place for an unnamed thing (an element of the domain). In QL, the symbols ‘x’, ‘y’, ‘z’ are variables. Tips: read each such symbol as meaning ‘thing’. If more than one variable is involved in a formula as in ∀x [∃y [Rxy]] read the formula as meaning ‘Consider every thing, x, there is some thing, y, such that…’. Any variable which occurs within the scope of a quantifier is said to be a bound variable (bound by the quantifier). A variable which does not occur within the scope of a quantifier is a free variable. Note very carefully that in QL no variable may occur free, i.e. without a quantifier to bind it.

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proposition

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Intuitively, the meaning or sense of a declarative sentence. Many philosophers believe that propositions are the real bearers of truth-values.

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sentential variables

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Symbols which mark gaps which may be plugged by sentences.

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substitutional criterion of validity (for logical forms of argument)

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The criterion that a form of argument is valid if, and only if, every substitution-instance of that form is itself a valid argument.

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substitution-instance (of a particular logical form)

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Any particular natural language argument which instantiates or exemplifies the logical form in question.

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counterexample (to a logical form)

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Any substitution-instance of that form which has true premises and a false conclusion.

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refutation by counterexample

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The method of proving invalidity by means of a counterexample.

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quantifier switch/quantifier shift fallacy

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Fallacious reasoning which can be formally represented by the reversal of the order of quantifiers across the inference from premises to conclusion.

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general sentences

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Sentences involving terms such as ‘all’ and ‘some’, ‘most’ and ‘many’.

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quantificational logic (QL)

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Intuitively, the logic of general sentences and the arguments they compose.