Given $\phi$ one may infer $T\ulcorner \phi \urcorner$or

$\forall x \in Sent(L_T) (T neg(x) \leftrightarrow \neg Tx)$etc.

But I don't, because I think of them as being about the formal behaviour of a truth

*predicate*, and not about

*truth*.

Instead, I'd prefer this more

*representationalist*view:

1. There are these things, calledThat's my theory of truth!strings: they are sequences (usually finite) drawn from an alphabet.

2. There issyntax, which specifies that some of these syntactical strings aresentences(of some language $\mathcal{L}$).

3. And there are $\mathcal{L}$-interpretations, $\mathcal{I}$.

4. Then there is a semanticrelation, written

$\mathcal{I} \models \phi$which means "the sentence $\phi$ is true in the interpretation $\mathcal{I}$".

(And for my non-causal theory of reference, replace "sentence $\phi$" by "term $t$" and replace "$\mathcal{I} \models \phi$" by "$t^{\mathcal{I}} = a$").

But there are several objections:

1. (Non-classicist)My response is: yes, entirely agree. The interpretations can be anything you find in a logic (or formal semantics) textbook: $n$-valued, $2^{\aleph_0}$-valued, supervaluational, Kripke frames, etc.

By an "interpretation" you mean a classical one? What if we want to discuss $n$-valued logic or truth in some Kripke frames or something exotic?

2. (Sentential deflationist)My response is: I don't agree. Truth for linguistic entities is a binary relation, relating a string and an interpretation $\mathcal{I}$ (or an interpreted language $\mathbf{L} = (\mathcal{L}, \mathcal{I})$). The function of any unary truth predicate one studies is to denote some class of truths in an interpreted language, or to denotes some class of true propositions. For example, given $\mathbb{N}$, then define

Surely truth is a unary predicate, $Tx$, applicable to sentences. The function of $T$ is logical, to express schematic generalizations, which must satisfy disquotation/transparency?

$E = Th_{L}(\mathbb{N})$,i.e., true arithmetic (well, codes of). Then, if the symbol $T$ is interpreted as $E$, we get,

$(\mathbb{N}, E) \models T\ulcorner \phi \urcorner \leftrightarrow \phi$,for each $\phi \in L$. So, each T-sentence (so long as $\phi \in L$) comes out true in $(\mathbb{N}, E)$.

3. (Minimalist)My response is: I'm not sure. I do tend to think that propositional truth is more basic somehow. But then no one has a good theory of propositions (for example, it's unclear how diagonalization and self-reference works for propositions).

Yes, ok: truth for sentences is binary, not unary. Sentential deflationists are mistaken. But surely the primary notion of truth is forpropositions; then it really is expressed by a unary predicate, $Tx$. The function of $T$ as applied to propositions is logical, to express generalizations, which must satisfy disquotation/transparency?

[I am being a bit sneaky: my favourite

*formal*theory of truth is KF, the Kripke-Feferman theory of truth.]

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