Comments on: Correspondence Theory and Paradoxes

By: jon

jon — Tue, 01 Dec 2009 17:05:36 +0000

Brian,
If we have Tp -> p and necessitation (for T), then our theory of truth is inconsistent. So the correspondence theorist probably shouldn’t be too worried that there are truths which don’t correspond to reality.

However, do you really need a truth-predicate to run your argument? If the correspondence theorist agrees to “If p corresponds to reality, then p” (for all p), you can run the first part of your argument and conclude that (Co) does not correspond to reality, and hence that (Co). This seems pretty embarrassing: the correspondence theorist is committed to asserting (Co) (on the basis of proof) but also committed to saying that (Co) doesn’t correspond to reality.

By: Brian Weatherson

Brian Weatherson — Tue, 01 Dec 2009 16:59:44 +0000

The problem is that the reasoning looks a bit like reasoning that leads to paradox, and a bit like unproblematic reasoning we use all the time. So I’m not sure that we should reject the reasoning just because of the first analogy.

Here’s a slightly more substantive way of putting the point. Correspondence theories of truth are committed to the solution to the Liar paradox generalising to explain what’s going on with (Co). That might be right, but I don’t know why I should believe it is right, or what grounds correspondence theorists have given me to believe it is right.

By: djc

djc — Tue, 01 Dec 2009 16:53:38 +0000

Andrew: Indeed. Brian: The observation that analogous reasoning refutes tautologies as well as substantive theories might be taken to suggest that the problem lies with the reasoning, not with the theories. (Cue: solution to the Liar paradox, which alas I don’t have.)

By: Brian Weatherson

Brian Weatherson — Tue, 01 Dec 2009 15:31:05 +0000

Good point Andrew, this is a weaker rule than I was suggesting. So it’s unlikely the proof fails there.

Dave, doesn’t this suggest there is no such thing as a theory of truth?

By: Andrew Bacon

Andrew Bacon — Tue, 01 Dec 2009 14:33:06 +0000

“[…] That contradicts our original assumption. So© does not correspond to reality. And that’s what it says, so presumably it is true. (Though this step does require a p, therefore p is true inference, which some might find problematic.)”

That last step seems to be more like an application of necessitation (if |- p then |- T(“p”)). Necessitation is much weaker than the axiom (p->T(“p”)) or the rule p |- T(“p”) both of which I’m much less inclined to believe than the principle that you can’t prove untrue things.

@djc: you can’t get a contradiction from “S is true iff S is true” without some extra assumptions which are already contradictory (as it’s already a theorem of propositional logic.)

By: djc

djc — Tue, 01 Dec 2009 14:12:11 +0000

Ah, the universal refutation of all theories of truth. To refute “For all S, S is true iff S has phi”, consider D: “D does not have phi”. One can even refute the theory that holds that S is true iff S is true this way!