Yes, logic has a stubborn scientific base. Otherwise we say there is no logic. Some of them already proven, but some of them need validation.

Dear Juan-Esteban, the question is to be framed within the distinction between classical logic and non-classical logics. Roughly said, one reason for the origins of NCL is that classical formal logic was either too loose or else too strict.

As you know, one antecedent for the question is precisely Putnam's question: Is logic empirical? We already know the answer.

Such a question can and should linked to Quine's discovery of the question regarding the (in)fallibility of logic. However, at the very origin stand out Gödel's schism when he "accused" logic's tautology.

Agree with you C. Lewis, that's why we have precisely work on a difficult problem, which is the demarcation between formal classical logis and NCLs. Most of NCLs are devoted exactly to overcome those pitfalls in language. Much progress ha been done, thanks to free logics, or to epistemic logics, or also via some work on labelled logics.

I add some idea with a little different with Carlos Eduardo Maldonado: Logic is actually empirical, no matter it blong to classical or non-classical, even Gödel's schism (when he "accused" logic's tautology) exists as Mr.Carlos Eduardo Maldonado said. Schism does not reject empirical resolusion. That is , Schism should not be regarded as an empirical failure.

The question is extremely general and there are a lot of easy examples that show the empirical character of logic, or at least the possibility to check it by practice. So I decided to concentrate on a less easy example. It is Gödel's Uncompleteness Theorem, adressed in the last post by Zhang. It can be formulated as follows: there is no recursive axiomatization for the whole theory of N. Every recursive consistent axiomatization would be only for a Fragment of the theory, and there remains at least a Statement A such that neither A nore \not A are provable from the given axiomatization. Well, this highly non-trivial statement is checked since humans practice number theory. Every number theorist with experience knows that one needs an infinity of non-trivial Independent ideas in order to prove all things that are true in arithmetics. The Point is, that every recursive axiomatization - even an infnte one - contains only finitely many sxiom schemes, so a finite number of ideas. [Equivalently, it contains a finitary method to generate all axioms, so roughly speaking only one idea...] So Gödel's Uncompleteness Theorem has been empirically verified Long before it has been formulated. That is why it has been accepted so easily. In conclusion - yes - logic is not so different from (other) natural sciences, and has in important empirical side, which is exactly so important as for physics or chemistry. But like there, one cannot reduce a whole science to empirism.

Logic like other mathematical disciplines, for instance algebra, began to be used in practice, but then by abstraction, became a formal discipline. Algebra developed in ocident from the preliminary studies in the muslim world and now is behind category theory, which was called "abstract nonsense" by its detractors.

Great, Graham!!!!!

Vrey cleevr!!!

I think that logic is to be an experimental science, hence the truthfulness of its laws are assumed because they work fine in real world applications. Otherwise, to show its laws, we have to apply them before proving its suitability. In other words, logic cannot prove to itself. Consequently only the successfulness of its applications can support it.

Dear Graham,

Very illustrative your message. Logic laws should be included among human rights.

Dear Juan

Analytic logic is an empirical science.  Analytic logic is one's and for all decomposed by Ludwig Wittgenstein(1) as he stated  in his Tractatus logico-phylosophicus. For me as humble  analyser, I could not find anything better to understand anaytic logic (as long as meta physic logic is kept out of the way)

Greetings

Ad Vermijs

www.adels-it.nl

I appreciate your interesting answer. I also think logic to be empirical science. Nevertheless, I think that it's high abstraction level makes it a very tested doctrine.

Let me explain the idea. If we test, say by abacus, the sums 2+3=5 and 4+5=9, each of them is tested once. However, their abstractions "even+odd = odd" and "even + odd = odd" are tested twice. Likewise, logical laws are tested with every of their concretions. Since logic laws lie in the most abstract level, they are tested more than the laws of any other empiric science. Thus, we can trust in them a lot.

But what is the basic nature of logic, what is its ontology - does it exist in our minds with collective agreement but grounded in our ordinary experiences of life (in Lifeworld in Husserlian terms) or it has its own independent existence not parasitic on our experiences of the world (and would exist if all of us die...), or say existing in a priori manner...?

I think about this in terms of Kripke's argument that all true identity statements involving rigid designators are necessary truths, yet discovering such truths (and thereby acquiring knowledge of them) can be an empirical enterprise. Knowing the truth of The Morning Star = The Morning Star was not empirical knowledge, but knowing the truth of The Morning Star = The Evening Star was empirical; it required astronomical observations to establish its truth. I think logic can be like that: logical truths are necessarily true, but coming to know some of them involves squaring them with linguistic and other facts, which is empirical trial-and-error activity.

Here is Kripke's argument for the necessity of identity:

‘Already when I worked on modal logic it had seemed to me ... that the Leibnitzian principle of the indiscernibility of identicals was as self-evident as the law of contradiction. That some philosophers could have doubted it always seemed to me bizarre. ...Waiving fussy considerations ... it was clear from (x) □ (x = x) and Leibnitz’s law that identity is an ‘internal’ relation: (x)(y) (x = y ⊃ □ x = y). (What pairs (x, y) could be counterexamples? Not pairs of distinct objects, for then the antecedent is false; nor any pair of an object and itself, for then the consequent is true.)’ -- Naming and Necessity, p. 3.

This is of course a metaphysical, not an empirical question. Do reason and logic come from matter or are they immaterial reality in their own right? Some materialists who often consider themselves 'rationalists' do not like the second, 'platonic', option. Rémi Brague writes about them [ in his book "Modérément moderne"]: "Those who like to pretend to be 'rationalists' are not really so. For them, reason is something secondary: reason arose from unreason [ dead matter ], like a kind of habit left over from the struggle for survival of the fittest..."

I agree with Brague, this is actually not very convincing: In fact, it is easy to imagine a world without people, and even a world without stars is conceivable, but no world can be consistently thought of in which, for instance, the laws of logic or mathematics do not apply. That alone shows that they exist in some kind of immaterial and intangible manner and that they precede in a sense every material world.

Leibniz saw it that way. In a note of 1677 [1] he wrote for example: "It is true, and even necessary, that the circle is the largest isoperimetric figure, even if no circle ever existed in reality. Likewise, even if neither I nor you nor any other human being ever existed."

And for him the existence of such 'eternal truths' is an argument for the Logos God; cf. https://drive.google.com/file/d/1gzCbFNFM62_v3QV0ErEcAqZCgNlioRfg

[1] G. W. Leibniz, Sämtliche Schriften und Briefe. Ed. Academy of Sciences of Berlin. Series VI, philosophische Schriften, 4,18. Darmstadt, Leipzig, and Berlin, 1923 ff.