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22 votes
Accepted

What is the origin of the negation ( ¬ ) operator from logic?

If vague resemblance is enough, then "$¬$" resembles "$-$", which denotes negation in arithmetic. Lambert in Sechs Versuche einer Zeichenkunst in der Vernunftlehre (1782) and Boole ...
Conifold's user avatar
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14 votes

How did the notion of rigour in Euclid’s time differ from that in the 1920 revolution of Math?

For example, the very first proposition: Construct an equilateral triangle $ABC$, where one side $AB$ is given. Euclid says Draw a circle with center $A$ and radius $AB$. [By Postulate 1] Draw the ...
Gerald Edgar's user avatar
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10 votes

How did the notion of rigour in Euclid’s time differ from that in the 1920 revolution of Math?

The main difference is that Mathematical logic and set theory did not exist at the time of Euclid. (The Logic of Aristoteles is still very far from mathematical logic created in 19th century). As a ...
Alexandre Eremenko's user avatar
10 votes
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Where does the material implication come from, if not from George Boole?

It may be surprising, but the material implication does not come from truth tables, the truth table definition is a late development. Neither de Morgan, nor Peirce, nor Frege, nor even Russell came up ...
Conifold's user avatar
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9 votes
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Why is the existential quantifier symbol ∃ a backwards "E"?

When introducing the older terminology in the previous sentence, Peano describes it thus: ... signifie "il y a des a", "les a existent"... It seems likely this is the source of the inverted "E".
iacob's user avatar
  • 400
8 votes

How many important logicians did NOT receive doctoral degrees?

Thoralf Skolem could perhaps be counted as a quasi example of that. He did not enroll as a PhD candidate before becoming a docent and a member of the Norwegian Academy of Science and Letters, and it ...
J Marcos's user avatar
  • 181
7 votes

Who was the first to write proofs in this manner?

Whitehead & Russel, Principia Mathematica (1910) is pretty much like this. The justifications are on the left, and only certain lines are numbered. But I doubt it is the first. Compare Frege's ...
Gerald Edgar's user avatar
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6 votes

Earliest proof of the soundness of first order predicate logic

See D.Hilbert & W.Ackermann, Principles of Mathematical Logic: the 1950 American translation of the 1938 second edition of Grundzüge der theoretischen Logik. The 1928 first edition is considered ...
Mauro ALLEGRANZA's user avatar
6 votes
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When was compactness theorem for propositional logic first proven?

For a general overview of the history of first order logic see SEP, The Emergence of First-Order Logic. On the history of compactness theorem more specifically see Dawson, The compactness of first-...
Conifold's user avatar
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5 votes

Where does the material implication come from, if not from George Boole?

Charles Sanders Peirce is credited with the introduction of truth tables in an unpublished manuscript dated 1893. This includes a truth table for what we now call material implication. A detailed ...
nwr's user avatar
  • 6,879
4 votes

Where does the material implication come from, if not from George Boole?

The "discoverer" of what we call today material conditional, i.e. the truth-functional definition of "if ... then", is Philo the Dialectician (ca.300 BCE). See Ancient Logic : A conditional was ...
Mauro ALLEGRANZA's user avatar
4 votes

How did people realize they could do logic with electronics?

I think the resources listed above are good background references but if you want to know how logic was introduced to actual electronic equipment then consider Claude Shannon. At the age of 21, ...
K7PEH's user avatar
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4 votes

When was compactness theorem for propositional logic first proven?

See John Dawson, The Compactness of First-order Logic From Gödel to Lindström (HPL,1993), page 18: After 1934, [...] the only person who seems to have recognized the importance of compactness was the ...
Mauro ALLEGRANZA's user avatar
4 votes
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Is there any English translation of this Gergonne paper?

Because I'm fond of translating old math and science papers, particularly from French and Latin, I decided to start a new translation project for this work into English. You can check the progress at ...
Sam Gallagher's user avatar
4 votes

Is there any English translation of this Gergonne paper?

I doubt that there is an English traslation, and old papers that quote it are in French (e.g. Peano, Origine du signe $\subset$ in L'Intermédiaire des Mathématiciens, 1903, or Giard, La « dialectique ...
user6530's user avatar
  • 3,870
3 votes

How did the notion of rigour in Euclid’s time differ from that in the 1920 revolution of Math?

The hope of Hilbert was that once correctly formalized, it would be possible to show that mathematics was sound and that any statement has a proof. Godel's incompleteness results put an end to that ...
coudy's user avatar
  • 233
3 votes

Does Hadamard claim that Pascal could have discovered non-Euclidean geometry?

Hadamard's proposes that if Pascal juxtaposed two of his ideas he could have confronted the "great problem of logic" and understood the "true meaning" of the parallel postulate, i....
Conifold's user avatar
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2 votes
Accepted

Could someone explain Vives logical notation?

Juan Luis Vives (1493–1540) was a Spanish humanist and (like other Humanists : Valla, Ramus) was a harsh critic of medieval formal logic. Some of his works, relevant for the history of logic are : ...
Mauro ALLEGRANZA's user avatar
2 votes
Accepted

What are the paradoxes of which Russell is talking about in the following?

Eames discusses this issue in Bertrand Russell's Theory of Knowledge, pp.151-154. The targets are Dewey's theory of warranted assertibility and Reichenbach's theory of verifiability, which both tie ...
Conifold's user avatar
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2 votes

How many important logicians did NOT receive doctoral degrees?

Regarding "logicians or mathematicians", Karl Weierstrass made it "into the academy while skipping over the PhD", though he did eventually receive an honorary doctorate. From ...
nwr's user avatar
  • 6,879
1 vote

Mathematics involved in "Jabberwocky"

Another source is: Martin Gardner, The Annotated Alice with extensive commentary on both Alice books.
Gerald Edgar's user avatar
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1 vote
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The status of Tarski's theory of truth

EDIT 07/07/21 I thought I would add more detail to my overly simplistic and perhaps somewhat misleading account of the philosophical criticism of Tarski’s theory of truth. There is criticism of Tarski’...
nwr's user avatar
  • 6,879
1 vote

Earliest proof of the soundness of first order predicate logic

Gödel first proved the soundness theorem in his completeness theorem in 1930 based on proof theory ("Die Vollständigkeit der Axiome des logischen Funktionenkalküls"). The model-theoretic ...
Eugene Zhang's user avatar
1 vote
Accepted

After the invention of Boolean algebra, why did it take so long for the existential and universal quantifiers to become formalized into symbols?

This is likely to be for the same reason as to why arithmetic wasn't formalised until long after arithmetic was discovered: there was no point to it. Peano Arithmetic was formalised when the question ...
Mozibur Ullah's user avatar
1 vote

Do units in physics have any link to the origins of type theory in logic?

And even before units were introduced in physics, people knew, for example, not to add oranges to say, apples. At least this is what I was taught in primary school, and I imagine that this goes back a ...
Mozibur Ullah's user avatar
1 vote

Where does the material implication come from, if not from George Boole?

Here we find a quote from Dorothy Edgington, The Stanford Encyclopedia of Philosophy, "Conditionals": The truth-functional theory of the conditional was integral to Frege's new logic (1879)....
Gerald Edgar's user avatar
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1 vote
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Where can I find sources for Gergonne's research on the fundamental relations among classes?

See Essai de dialectique rationnelle (1816-17). A brief description can be found in Leila Haaparanta (editor), The Development of Modern Logic (2009), Ch.3 : Logic from Humanism to Kant.
Mauro ALLEGRANZA's user avatar

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