# Questions tagged [mathematical-logic]

For question regarding the applications of formal logic to mathematics.

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### Did Grothendieck have any thoughts on foundations of mathematics? [closed]

I remember reading that Grothendieck didn't care much about foundational issues and didn't want to be 'stuck all the way down there'. Does anybody know if he ever actually said this? Did he have any ...
1 vote
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### When were Peano axioms formulated purely in first-order logic?

It is mentioned on the Wikipedia article about Peano axioms that: The ninth, final axiom is a second-order statement of the principle of mathematical induction over the natural numbers, which makes ...
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### Universal logicians

Henri Poincaré is often considered to be the last universal mathematician, meaning the last individual who made contributions across all areas of mathematics of his time. Today, even a prodigious ...
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1 vote
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### Role of Alessandro Padoa in the development of modern mathematics

Here is an excerpt from ESSAI D’UNE THÉORIE ALGÉBRIQUE DES NOMBRES ENTIERS, PRÉCÉDÉ D’UNE INTRODUCTION LOGIQUE A UNE THÉORIE DÉDUCTIVE QUELCONQUE from Alessandro Padoa (as can be found here): nous ...
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1 vote
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### Why isn't Boethius's Thesis more commonly accepted in mathematics and logic?

Why isn't Boethius's Thesis, that the negation of an implication is another implication where the consequent is negated, a commonly accepted axiom in mathematics and logic? It is an axiom of connexive ...
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### Medieval Logical Interpretations of the Word "All"

Paraphrasing the Philosopher (Aristotle): Forms of speech are either simple or composite. If expressions are simple, then they are neither true nor false. With this said, did some Medieval logicians ...
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### Who first introduced semantic and syntactic consequence

The relations $A \vdash B$, read "$A$ proves $B$'', and $A\vDash B$, read if $A$ is true then $B$ is true, are referred to as syntactic and semantic consequence, respectively. In the history of ...
1 vote
131 views

### Who first proved that empty set is subset of all sets?

Who is the mathematician who proved that empty set is subset of all sets and made it known to most mathematicians? I looked into the ripple effects in the mathematical world that would occur if the ...
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### When did people first thought of a purely symbolic logic?

In Euclid's Elements, the famous five planar geometry axioms are formulated in common language (ancient greek in this case) and use ambiguous terms. On the other hand, modern theories like ZFC or ...
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### Origin of vacuous truth

I am curious about vacuous truth in logic. I searched Google for various resources, including here. What I could learn from the paper was that I could not know the history or background of vacuous ...
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1 vote
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### Did Dedekind's work directly influence the work of Hilbert?

I am wondering if Dedekind's theory about the structure of deductive science influenced the work of Hilbert. Hilbert obviously favored axioms at the beginnings of a deductive science, whereas Dedekind ...
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### How did Kolmogorov came up with his formalization of intuitionistic logic?

According to this article Kolmogorov published a paper in 1925 in which he attempted to formalize Brouwer’s intuitionistic mathematics. In that paper there are the following logical formulas: \begin{...
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### In which article/book chapter did Cantor, Hilbert, and Poincaré formally define or directly discusse the term “potential infinity”?

Some media sources say that "Cantor claimed that there would only be potential infinity, not actual infinity" In addition, the following link claims that Hilbert, Poincaré, and Cantor were ...
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