Talk:Mathematical logic

I made an initial effort to provide a description and properties of the Wikidata item {{Q|Q77227534}}, but I would appreciate someone with more expertise reviewing this. My initial description is based entirely on the Russian Wikipedia article: {{tqi|"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)

: {{Q|Q1003009}} could also use review. Daask (talk) 20:31, 13 November 2020 (UTC)

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)

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)

"Mathematical logic is the study of formal logic within mathematics" and "Formal logic (also known as symbolic logic) is widely used in mathematical logic" (on "logic" page).

To me it sounds like a circular definition. Human 7000000000 (talk) 09:48, 17 May 2025 (UTC)

:If you want to see logic defined, go to propositional calculus, first-order logic, Hilbert system, and the other pages to which they refer. "Mathematical logic is the study of formal logic within mathematics" is at best an overview of a definition. "Formal logic (also known as symbolic logic) is widely used in mathematical logic" is not a definition at all; it merely acknowledges that the "formal logic" page is referred to by the "mathematical logic" page. JRSpriggs (talk) 13:03, 17 May 2025 (UTC)

::ok. I don't see how the definition of logic comes in to what i said though. I wasn't talking about how logic is defined by the logic page, only how it defines "formal logic", which paragraph, whith mathematical logic, link to one another. Human 7000000000 (talk) 15:14, 17 May 2025 (UTC)

:::To my way of thinking "logic" and "formal logic" mean the same thing. Informal logic or philosophical logic are not really logic at all. Fuzzy logic is even worse. JRSpriggs (talk) 16:38, 17 May 2025 (UTC)