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 ...
- 44.2k
14
votes
Why is notation in logic so different from algebra?
The simple answer is that logic has different ideas and needs than mathematics, although, many modern thinkers work with notations of mathematical logic which use both. Symbolic mathematical notation ...
- 35.6k
9
votes
Why is notation in logic so different from algebra?
You are conflating statements and objects.
In your algebra example, you have two statements (2x + y = 5 and x = 3) and from these you derive a third statement (y = -1). Working informally, x is an ...
- 207
8
votes
Accepted
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 ...
- 44.2k
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 ...
- 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 ...
- 41.1k
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 ...
- 31.5k
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. ...
- 41.1k
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 ...
- 44.2k
6
votes
Criticisms of "reductio ad absurdum" argumentation?
See Bouwer's critique:
Brouwer pointed out the validity of the proof method of [the part of the] reductio ad absurdum that can be used to establish negative propositions ¬A. On the other hand, ...
- 41.1k
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 ...
- 855
5
votes
Accepted
In what work did Venn use his diagrams to analyze syllogisms?
John Venn (1834-1923), Symbolic Logic (1881), ch. 5 "Diagrammatic Representation", pp. 100-125.
For an earlier Venn's pubblication, see:
On the diagrammatic and mechanical representation ...
- 41.1k
5
votes
How did C. S. Peirce graphically represent a syllogism?
As is well-known, most of Peirce's studies were either scattered or unpublished (they are reprinted into the 8 vols of Collected Papers).
Peirce deals with syllogism in the fundamental 1885 On the ...
- 41.1k
4
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 ...
- 173
4
votes
Accepted
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 ...
- 44.2k
4
votes
Accepted
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 ...
- 31.5k
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 ...
- 22.6k
4
votes
Why is notation in logic so different from algebra?
The expression A → B means that A → B is true.
The expression 2x + Y = 5 also means that 2x + Y = 5 is true.
If you write A → B = T instead of A → B to mean that A → B is true, then you should write ...
- 9,880
3
votes
Accepted
Reference request for the history of logic
Józef Maria Bocheński, O.P., History of Formal Logic covers logic from the Greeks up to mathematical logic, with a section on Indian logic, too.
- 8,615
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 ...
- 41.1k
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 ...
- 41.1k
3
votes
What is a good history of logic book that covers all logic?
Józef Maria Bocheński, O.P., History of Formal Logic covers logic from the Greeks up to mathematical logic, with a section on Indian logic, too.
- 8,615
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 ...
- 276
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 ...
- 36.1k
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 ...
- 3,734
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 ...
- 221
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 ...
- 1,202
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 ...
- 48.8k
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 ...
- 41.1k
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 (...
- 2,385
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