Talk:Mathematical logic

Early history

I reworked some edits to the "Early history" section. Stuff about the 19th century belongs in the following section. In order to have a global viewpoint, and avoid historical myopia, we do need to recognize that non-Western cultures had their own traditions of logic. The dominance of Greek influence in medieval and then 19th century work is, most likely, simply because non-Western work was much less known at the time. The same pattern has repeated itself in many areas of mathematics, where there was much duplication of effort (for example, Pascal's triangle). — Carl (CBM · talk) 19:45, 2 May 2009 (UTC)

We certainly need to have a global viewpoint. However, failing to note the Greek influence in Western cultures is also a mistake. There's a clear historical path from Aristotle, the Stoics, medievals, and through to the logical systems as developed and extended by logicians such as Frege, Peano, and Russell; omitting that omits the key parts of its history. Dwheeler (talk) 19:28, 11 August 2019 (UTC)

Modal logic

Is modal logic really established as part of mathematical logic? Given the ease with which Kripkean modal logics can be expressed in first-order logic, the case for modal logic is not directly one of expressiveness.

In computer science, modal logic is important because of the (relatively) good complexity classes of its various decision procedures. In philosophical logic it is important because of its more natural relationship to natural language. But are there any areas of core mathematical logic where modality is a valuable tool? — Charles Stewart (talk) 14:17, 18 June 2009 (UTC)

Is it a core part of mathematical logic? No, certainly not. But it is important for the more philosophical side, and has the interesting applications to provability logic that are mentioned. So two sentences seems to me like a reasonable amount of time to spend on it, in the spirit of being "just slightly broader than the average mathematical logic textbook". — Carl (CBM · talk) 14:29, 18 June 2009 (UTC)

Modal logic is part of logic. Indeed, a significant part of Aristotle's work on logic is devoted to it. Dwheeler (talk) 19:23, 11 August 2019 (UTC)

Help with term: distinction on Wikidata

I made an initial effort to provide a description and properties of the Wikidata item distinction (Q77227534), but I would appreciate someone with more expertise reviewing this. My initial description is based entirely on the Russian Wikipedia article: "a figure of speech through which the act of cognition is designated, reflecting the objective difference between real objects and elements of consciousness; In formal logic, one of the logical devices that can be used instead of defining". Daask (talk) 20:28, 13 November 2020 (UTC)

formal logic (Q1003009) could also use review. Daask (talk) 20:31, 13 November 2020 (UTC)

Opening sentence

I have read this 10 times over and it still doesn't make sense to me. "Mathematical logic, also called formal logic, is a subfield of mathematics exploring the applications of formal logic to mathematics." This seems like an unnecessary circular definition. I haven't looked at the revision history so I apologise in advance if there is some insight to be found there. Psycho 79 (talk) 23:52, 25 August 2021 (UTC)

I think you're right. Part of the solution is to remove "also called formal logic", which in addition to making the sentence circular, is also wrong. Mathematical logic is the discipline comprising computability theory, proof theory, model theory, and set theory (and I would tend to argue for category theory and perhaps universal algebra, but these are less commonly listed). None of these fields are "called formal logic".

Exactly what these fields have in common is a little hard to put your finger on, but I'm not sure that "applying formal logic to mathematics" is really it. In lots of cases it's actually the reverse, applying mathematics to formal logic.

I think a complete rewrite of the sentence is indicated. We should try to be clear that the boundaries are fuzzy, and avoid trying to capture the essence of mathematical logic by some phrase that sounds more precise than the concept actually is. --Trovatore (talk) 00:23, 26 August 2021 (UTC)

You could have a look at the text over here, both as something to borrow from and perhaps to improve as well! Botterweg14 (talk) 16:11, 27 August 2021 (UTC)

I've gone ahead and rewritten it, using text from the other article. But I'm not at all attached to the new version, so please rewrite it again if you see room for improvement! Botterweg14 (talk) 16:30, 27 August 2021 (UTC)

Hover over Mathematical Logic

When I hover over the Mathematical Logic link to this page from https://en.wikipedia.org/wiki/Peano_axioms (First link in the article), It comes up with disgusting unrelated image attached to the article. Please fix it! I don't know how to sorry. It appears it was griefed or the image was misplaced. Bumv (talk) 11:00, 29 March 2023 (UTC)