About the concept of logical truth

Question

From Frege and Russell to modern mathematical logic textbooks, there were a "shift" of focus from the concept of logical truth, through that of valid formula, to the current concepts of logical consequence and valid argument.

Are there available some recent logico-philosophical reflections on the concept of logical truth ?

Note. Please, this is not a "reference request* : I'm not searching for "classic". I personally think that the "mainstream" view about mathematical logic as abandoned the concept of "logical truth" (see this post ).

I'm not advocating for myself some new "brilliant" insight: I'm simply asking myself (and to the "community") if there is some new research (historical or philosophical) about this idea that at the begin of math log (Frege and Russell) was fundamentale and now - at least, it seems to me - is hardly cited anymore.

Thanks !

Answer 1

There's plenty of logico-philosophical research concerning logical truth. Just to name some recent articles:

• H. Wansing: A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and Falsity. Topoi 31 (2012), 93-100.

• W. H. Hanson: Actuality, Necessity, and Logical Truth. Philosophical Studies 130 (2006), 437 - 459.

• M. Bremer: Do Logical Truths Carry Information? Minds and Machines 13 (2003), 567-575.

• M. Gómez-Torrente: Logical Truth and Tarskian Logical Truth. Synthese 117 (1998), 375-408.

Answer 2

I'm not sure if this relates to your question.

In propositional logic, for example, a truth valuation is a function $v$ from sentences to the boolean algebra $\{ T, F \}$ satisfying the obvious properties, such as $v(P \wedge Q) = v(P) \wedge v(Q)$.

Truth valuations (often seen as rows of "truth tables") are often used in propositional logic; e.g. one can prove some proposition is a tautology if and only if every truth valuation maps it to T.

For first-order logic in general, semantics is usually based on interpretations rather than truth valuations, but any interpretation does have an associated truth valuation; i.e. "is the sentence $P$ true in the interpretation?".

Formal logic is not purely about syntax; semantics is very important as well. However, the emphasis on semantics is not about trying to capture some nebulous notion of Platonic ideals, but instead on concrete things like interpreting logical sentences as talking about sets or arrows in a category or somesuch.

However, we do need to keep syntax and semantics separate, so that we know what we're actually saying when we talk about formal logic, and it may be this separation that you've keyed in upon, and misinterpreted the study of syntax as an abandonment of semantics.