21 votes
Accepted

Why did the mid-19th century and earlier thinkers fixate on one-place predicates?

Because there was a calculus for one-place predicates, Aristotle's syllogistic, roughly equivalent to monadic predicate calculus. Aristotle does discuss "relatives" in Categories, which ...
Conifold's user avatar
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14 votes

What is the origin of the truth table in logic?

You can see: Irving Anellis, The Genesis of the Truth-Table Device (2004) as well as: Irving Anellis, Peirce's Truth-functional Analysis and the Origin of the Truth Table (2012). Before Bertrand ...
Mauro ALLEGRANZA's user avatar
12 votes
Accepted

What is the axiom of reducibility? And what philosophical controversies did it incite?

To put it in simple words we have to describe in a couple of words the project of Principia Mathematica, which Russell inherited from Frege: reconstructing mathematics from logic alone. For a broader ...
Conifold's user avatar
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8 votes
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Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

Wittgenstein was reviving Kant's old view that logical deduction only brings out what is implicitly thought in the premises. Of course, Kant had in mind Aristotle's term logic, which is roughly ...
Conifold's user avatar
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8 votes

Why did the mid-19th century and earlier thinkers fixate on one-place predicates?

An n-ary relation gives rise to parameterized unary predicates if one fixes n-1 arguments. Wilfrid Hodges argues that this is what logicians did before the nineteenth century. (There may be other ...
Pteromys's user avatar
  • 211
7 votes
Accepted

Origins of the syntactic form for rules of inference in modern presentations

As per comments above, the modern use is due to Hilbert's school. Gerhard Gentzen, Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen (1932) derived it from Paul Hertz, Über ...
Mauro ALLEGRANZA's user avatar
7 votes

Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

As a matter of terminology, some logicians use 'tautology' as a synonym for a logical truth, while others restrict it to logical truths of the propositional calculus. I shall use the more general term ...
Bumble's user avatar
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6 votes

Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

This scene seems to imply that Russell didn't view logic as tautologies. Correct. Wittgenstein's view about "logic=tautologies" was grounded on propositional logic and truth table. ...
Mauro ALLEGRANZA's user avatar
6 votes
Accepted

What did the Greeks call the "trial and error" reasoning process?

"Trial and error" applied not to a "reasoning process" but to medical practice, and the name of the practice was derived from Greek ἐμπειρία, experience. The inspiration for the approach apparently ...
Conifold's user avatar
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5 votes

Before Gödel, was undecidability of axiomatic systems an issue at all?

While it’s not quite a perfect parallel, a related concern about decision problems had been phrased some years before Gödel’s work: see https://en.m.wikipedia.org/wiki/Entscheidungsproblem . David ...
Sofie Selnes's user avatar
4 votes
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What is the historical context and what are the philosophical implications of model theory?

Husserl gave an insightful philosophical analysis of the change that occurred in mathematics over the course of 19th and early 20th century, the change some aspects of which he himself foresaw and ...
Conifold's user avatar
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4 votes
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In logic, which came first: the semantic approach or the syntactic approach?

This is something of a chicken and egg problem. In a sense, the circularity is inherent in the very nature of logic. How are we to justify the rules of good reasoning if not by appealing to their ...
Conifold's user avatar
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4 votes
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What are the advantages of Aristotle's term logic over predicate logic?

Gareth Evans is arguing that Aristotelean logic is closer to natural language usage and as such introduces fewer unfamiliar logical devices and has fewer counterintuitive features. This is true, but ...
Bumble's user avatar
  • 25.1k
4 votes

Advancements in formal logic in the 21st century?

Paraconsistent logic has progressed fairly well. A couple of articles in which this logic is applied: Zach Weber, "Transfinite Cardinals in Paraconsistent Set Theory." Goes over a ...
Kristian Berry's user avatar
3 votes
Accepted

Where did De Morgan write the laws that are named for him?

See Formal Logic (1847), page 116: The contrary of PQR is p,q,r. [...] In contraries, conjunction and disjunction change places. And see A.De Morgan's On the Syllogism III (1858), page 182: The ...
Mauro ALLEGRANZA's user avatar
3 votes

What is this snippet from Frege's Begriffsschrift saying?

The formula is used into the third part of Begriffsschrift (1879), regarding the General theory of sequences, not translated in modern symbols by Mendelsohn. You have to look at: G.Landini, Frege’s ...
Mauro ALLEGRANZA's user avatar
3 votes

How did first-order logic come to be the dominant formal logic?

First-order logic came to be the dominant formal logic because it is fundamental to all logic. Any departure from FOL creates ambiguities which must be resolved. For example, the second-order ...
rgfuller's user avatar
  • 101
3 votes

What is the difference between type–token, genus–species and universal–particular?

The type-token and universal-particular distinctions are probably isomorphic in meaning, but they are used in different domains. Type-token is used in linguistic problems like "They drive the same ...
Allen More's user avatar
2 votes

What did the Greeks call the "trial and error" reasoning process?

The Greeks understood the process of trial and error. You try one way, then you try another. But there is no evidence of which I'm aware that the Greeks elevated trial and error into a methodology of ...
Geoffrey Thomas's user avatar
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2 votes

How were formal systems and notion syntactic consequence (proof) developed?

You wrote... But how did humans develop formal systems and the notion of syntactic consequence in the first place? Wouldn't they have had to develop such systems based on what semantic consequences ...
dwolfeu's user avatar
  • 147
2 votes

Before Gödel, was undecidability of axiomatic systems an issue at all?

Before Frege, axiomatic systems were not a focus of philosophy, and Goedel is pursuing the immediate upshot of Frege's failure. So, in some sense, no. Nobody cared. Mathematics was grounded in some ...
hide_in_plain_sight's user avatar
2 votes
Accepted

Before Gödel, was undecidability of axiomatic systems an issue at all?

Godel himself said that all he did was formalise the Cretan liar paradox into a formal system. So the idea or notion of undecidable statements was already apparent a long time before Godel but ...
Mozibur Ullah's user avatar
2 votes
Accepted

What are some possible motivations for Peirce's use of only one operator(his NAND) to recreate the "and", "or" and "not" operators?

See Charles Sanders Peirce, Collected Papers : Volume 4. The Simplest Mathematics (1933), page 13: [4.12] A Boolian Algebra with One Constant [untitled paper c.1880] Every logical notation hitherto ...
Mauro ALLEGRANZA's user avatar
2 votes
Accepted

Who first studied asymmetric relations qua relation?

The Categories, chap.7 /On Relatives/ contains a remarkable discussion in just a few pages and its author, supposedly Aristotle, might well be the first to have 'studied' asymmetric relations. So ...
sand1's user avatar
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2 votes

What are the possible ways to symbolically represent entities, within formal logic?

The sense of idea of ἄτομον, translated into Latin as individuum, that is, what we get by individuation is so primordial for us that it is uniformly an invariable constituent of thought and language (...
Tankut Beygu's user avatar
  • 2,135
1 vote

What logics/philosophies deny the law of excluded middle (LEM)?

Beyond True and False - Graham Priest The Logic of Buddhist Philosophy https://aeon.co/essays/the-logic-of-buddhist-philosophy-goes-beyond-simple-truth Let’s start by turning back the clock. It is ...
SystemTheory's user avatar
  • 1,669
1 vote

Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

There's an element of truth and of dramatic license in the graphic novel. It is, after all, a work of literature rather than reportage. Russell had lost the Christian faith he was brought up in as a ...
Mozibur Ullah's user avatar
1 vote

Who first studied asymmetric relations qua relation?

William Rowan Hamilton's discovery of quaternions in the 19th century may be the first studied non-commutative relations. Here is Wikipedia: In mathematics, the quaternions are a number system ...
Frank Hubeny's user avatar
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1 vote

Who first proposed that A → (B ∧ ¬B) ⊢ ¬A was the principle of proof of some theorems?

Euclid's Proposition 20 in Book IX of the Elements claim Prime numbers are more than any assigned multitude of prime numbers. David E. Joyce provides the following outline of the proof: Suppose ...
Frank Hubeny's user avatar
  • 19.4k
1 vote

Who first proposed that A → (B ∧ ¬B) ⊢ ¬A was the principle of proof of some theorems?

For sure, we can find it in Aristotle : In the proofs for imperfect deductions [the syllogistic figures different from the fist one], Aristotle says that he “reduces” (anagein) each case to one of ...
Mauro ALLEGRANZA's user avatar

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