The Truth According To Martin Prior
I have often understood that truth is that which corresponds to the facts, though then we must address what we mean by facts and most importantly, what we mean by ‘corresponds (to)’. According to Wikipedia, “Truth is most often used to mean in accord with fact or reality, or fidelity to an original or to a standard or ideal.” In effect, ‘correspond’ suggests some kind of semantic or semiotic analysis.
In formal logic, with our system of axioms, we understand that each statement or line is true, so it is embedded within our formal logical analysis. In attempts to capture language as forms of mathematics, some philosophers feel that such analyses must include a definition of truth. This was the view of Richard Montague, but not I understand of Arthur Prior. In a tentative analysis long ago, I was considering a semantic model. It was not my intention to provide a definition of truth, but it emerged. It accorded an approach, but did not really accord with either Montague or Prior:
truth'{a} ≡ a
The expression truth'{ a } treats ‘truth’ as a niladic operator: an operator with the output or result a, but lacking an input or what are often called parameters. In fact the expression represents a statement defining that output a. We might define 5 as follows:
5'{a} ≡ ( a=5)
On some other occasion I might use this format to outline truth-conditional semantics, devised by Donald Davidson on the basis of work by Alfred Tarski. But in the above expression, truth'{a} ≡ a, the definition of that output a is a itself.
And this approach only works if you can produce expressions that include (a ≡ a ), i.e. a is equivalent to itself. Where in fact you need say nothing about a, but just as with correspondence you need to say something about equivalence.
Martin Prior
The Philosophy Takeaway 'Truth' Issue 42
