An Introduction to Category Theory by V. Sankrithi Krishnan

By V. Sankrithi Krishnan

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Jr. L. Grover the theory of truth conditions, without our definition, should have our definition as a consequence. 4. Truth and meaning. 3 as giving the meanings of the functors of the language, since it was in terms of these functors that the definition was broken down into its clauses; but lest it be thought this is all there is to meaning in the context of formal languages, or that this is the onZy way of giving the meanings of the functors (and hence of the sentences) of a formal language, we add the following comments.

T l . . ) is true iff [el] (if ‘el’ is a closed M*-term then ‘( . . e l . . >’ is true). Had we conceived of M3 as containing definite descriptions, set abstracts, or other terms containing formulas, the reader would notice that paradox would threaten (think of Richard). But the avoidance would be a straightforward consequence of our limitation of the substitution range of the term variables to terms of M*; hence to terms not containing even bound occurrences of these term variables. Since by assumption the terms of M* are already understood, no vicious circle can develop.

Introduction My aim is to use the techniques of formal semantics to investigate a certain reading of the conditional; in the absence of standard terminology, I shall call it “conditional assertion”. Quine 119501, who credits the idea to Rhinelander, gives the following account: An affirmation of the form ‘if p then (I’ is commonly felt less as an affirmation of a conditional than as a conditional iffirmation of the consequent. If, after we have made such an affirmation, the antecedent turns out true, then we consider ourselves committed to the consequent, and are ready to acknowledge error if it proves false.

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