So be honest. When you say, "This sentence is true/false," do you think you are saying something meaningful? Would you actually use that phrase, speak it aloud, and expect to have said something meaningful? — Leontiskos
A sentence says something if it presents a comprehensible assertion. It says something if its claim is intelligible. — Leontiskos
Now when you say, "X is false," I can think of X's that fit the bill. I might ask what you mean by X, and you might say, "2+2=5." That's fine. "...is false" applies to claims or assertions. If there is no claim or assertion then there is no place for "...is false." For example, "Duck is false," "2+3+4+5 is false," "This sentence is false."
Not all paraconsistent logics accept dialetheism, but dialethiests are pretty much obligated to accept paraconsistent logic. — Banno
What is wrong with the standard answer? Even if ‘the Goldbach Disjunction is a logical truth’ is determinately and unambiguously true out of our mouths, it is not true out of another possible community’s mouth.6 They may use ‘logical truth’ to mean, say, intuitionistic validity. Goldbach’s Disjunction is not an intuitionistic validity. So, there are two relations: validity Us and validity Intuitionistic.
There is no dispute that both relations ‘exist’ if either does.7 The only dispute is about which of these we happen to pick out with ‘logical truth’ (or about what is packed into the concept of logical truth that we happen to employ). The monist and the pluralist, understood in the standard way, agree on the non-semantic world. (Indeed, one could make classical logic the One True Logic, in the standard sense, by indoctrinating children with the classical truth tables!)8
Of course, it is often of metaphysical and methodological import what a sentence is about. The fact that another possible community means ether by ‘dark matter’ hardly undercuts the interest of the debate over dark matter. But the logical case is not like this. It is more like the case of pure (rather than applied) geometry. Hyperbolic lines exist if Euclidean lines do, qua pure mathematical entities. So, all we would learn in deciding ‘’whether the…relations so defined agree…with the pre-theoretic notions’ would be something about ourselves. We would just learn which line-like things we happened to refer to with ‘line’... The only factual question at stake is what we happen to mean by ‘valid’. If there were a (meta)logical analog to the question of which geometry is true of physical spacetime, then the logical case might be like the dark matter case...
...But the choice of (meta)logic under which to close cannot itself be made on the basis of the physical facts. We need a metalogic to state them in the first place! For instance, do they include that either there are gravitons or that it is not the case that there are gravitons (or the denial of the 15 claim that there both are gravitons and are not gravitons)? It depends on whether the Law of the Excluded Middle (or Noncontradiction) is valid
As you may have gathered by now, it is not hard to design a new logic. You
too can create your own a syntax, make up a deductive system, and fashion
a semantics to go with it. You might have to be a bit clever if you want the
derivation system to be complete for the semantics, and it might take some
effort to convince the world at large that your logic is truly interesting. But, in
return, you can enjoy hours of good, clean fun, exploring your logic’s mathe-
matical and computational properties.
Recent decades have witnessed a veritable explosion of formal logics. Fuzzy
logic is designed to model reasoning about vague properties. Probabilistic
logic is designed to model reasoning about uncertainty. Default logics and
nonmonotonic logics are designed to model defeasible forms of reasoning,
which is to say, “reasonable” inferences that can later be overturned in the face
of new information. There are epistemic logics, designed to model reasoning
about knowledge; causal logics, designed to model reasoning about causal re-
lationships; and even “deontic” logics, which are designed to model reason-
ing about moral and ethical obligations. Depending on whether the primary
motivation for introducing these systems is philosophical, mathematical, or
computational, you may find such creatures studies under the rubric of math-
ematical logic, philosophical logic, artificial intelligence, cognitive science, or
elsewhere.
The list goes on and on, and the possibilities seem endless. We may never
attain Leibniz’ dream of reducing all of human reason to calculation—but that
can’t stop us from trying.
I've seen that paper before. I give it credit for at least addressing the issue of metaphysical truth, but it is a prime example of implicit question begging re the deflation of truth. Truth just is something to do with formalism, and how can you pick between formalisms? According to which one is true? Well, you have to use a formalism to discuss truth, and different formalisms say different things. — Count Timothy von Icarus
The answers seem to be, respectively, "Who knows?" and "The other guy!" :lol: — Leontiskos
I guess the obvious question is, if you know what truth is, apart from formal systems, then tell us. Otherwise, it seems to me that we could do far worse than Tarski's account of truth in terms of satisfaction.
On deflationary accounts, “all that can be significantly said about truth is exhausted by an account of the role of the expression ‘true’... in our [speech] or thought,” and we might add formal systems here. Thus, notions of truth are neither “metaphysically substantive nor explanatory.” — Count Timothy von Icarus
That's were I came across the Clarke-Doane article and the discussion of approaching the issue as one of attitude.One option available to the monist is to interpret the claim that there is one and only one correct logic noncognitively. Clarke-Doane, after finding no satisfying factualist construal of monism, interprets the claim as expressing an attitude. Perhaps this strategy could be extended to the debate between monists and pluralists more broadly.
Return to the basic principle things ought to make sense. How that is accomplished may vary. — Cheshire
The story at least since Russell's paradox and Gödel seems to indicate that this is not what happens. — Banno
If I am candid, it seems to me that your fears are ill conceived and unfounded
If we accept this, not as a useful tool, but as a claim about truth tout court, what exactly makes STT a better theory of truth than any other? Can it be truly better? True relative to what, itself? — Count Timothy von Icarus
what exactly makes STT a better theory of truth than any other? — Count Timothy von Icarus
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