Questions tagged [history-of-logic]
The history-of-logic tag has no usage guidance.
34
questions
10
votes
4
answers
2k
views
Why is notation in logic so different from algebra?
Introductory courses in philosophical logic that I've seen introduce specialised notation like:
For an outsider, this is highly confusing. I'm sure that everyone studying philosophy has been to high ...
- 429
2
votes
2
answers
95
views
How did C. S. Peirce graphically represent a syllogism?
How did C. S. Peirce graphically represent a syllogism? Analogously to how Venn did?
For example, his Existential Graphs can prove Leibniz's Præclarum Theorema (Splendid Theorem) (source).
- 8,475
3
votes
1
answer
71
views
In what work did Venn use his diagrams to analyze syllogisms?
In what work did Venn first use his diagrams to analyze syllogisms?
cf. the diagrams here
- 8,475
6
votes
3
answers
147
views
What is the first recorded use of the conditional form in human history?
The conditional form, ⟨ IF ϕ, THEN ψ ⟩, seems to have always been with us, but we don't really know.
So, what is the first attested use of the conditional form in human history?
Thank you for any ...
- 9,012
4
votes
0
answers
62
views
Contradictory unprovable statements in Tarski's "The Concept of Truth in Formalized Languages"
In Tarski's "The Concept of Truth in Formalized Languages", he glosses over the proof of a difficult lemma. I am looking for help writing a proof of it. In Tarski's notation, it is:
In ...
- 71
2
votes
0
answers
52
views
Any consensus on Łukasiewicz' idea that Aristotle's syllogisms were systematically misrepresented in the academic literature?
Is there a consensus today on Jan Łukasiewicz' 1957 assertion that Aristotle's syllogisms were systematically misrepresented in the academic literature?
Łukasiewicz, in Aristotle's Syllogistic from ...
- 9,012
0
votes
1
answer
109
views
What are the possible ways to symbolically represent entities, within formal logic?
What are the different solutions proposed in the academic literature to represents symbolically individual entities within formal logic expressions?
One solution I am aware of is to use Latin letters. ...
- 9,012
5
votes
1
answer
350
views
Origins of the syntactic form for rules of inference in modern presentations
I have been wondering where the form
originates from. The turnstile ⊢ famously comes from Frege, but I haven't been able to find where the vertical notation was introduced. In the field of ...
- 153
0
votes
2
answers
170
views
How did Aristotle discover his logic?
Supposedly Euclid employed analysis (conclusions→principles) and not synthesis (principles→conclusions) when he devised his definitions/postulates/axioms in his Elements.
How did Aristotle discover ...
- 8,475
2
votes
3
answers
296
views
What logics/philosophies deny the law of excluded middle (LEM)?
What logics/philosophies deny LEM, the law of excluded middle (tertium non datur)?
This law is expressed as Philosophical Axiom 4.2:
Tertium non datur (Non est medium inter esse et non esse. ‑ ...
- 8,475
4
votes
1
answer
561
views
Advancements in formal logic in the 21st century?
I've recently learned a lot about the history of formal logic, from Frege and Pierce in the late 19th century, to Russell, Hilbert, and Quine (et al)'s development of 1st-order logic, to advances with ...
- 141
2
votes
1
answer
61
views
Reference request for the history of logic
I have lately been interested in the history of logic, specifically, propositional logic and first-order logic. I want to know how those logical systems were first thought of. Can anyone give me some ...
- 8,120
4
votes
1
answer
81
views
Where did De Morgan write the laws that are named for him?
I've been reading through De Morgan's Formal Logic. The book seems more of a combination of an introduction to logic and a grab bag of De Morgan's ideas than a formal system, but I can see why some of ...
- 197
11
votes
5
answers
2k
views
Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?
While reading Logicomix, I came across a scene that I don't quite understand.
Russell: ...Logicians are creating elaborate ways to "say the same things in different words"...this "...
- 413
1
vote
2
answers
94
views
What are some possible motivations for Peirce's use of only one operator(his NAND) to recreate the "and", "or" and "not" operators?
It was found in Peirce's unpublished papers that he defined the NAND operator and discovered that all classical logical operators could be replaced by combinations of NAND.
What are some possible ...
- 572
1
vote
0
answers
59
views
Which unary or binary logical operators existed in logic before 1854 besides 'and', 'or', and 'not'?
Logical operators are a central focus of logicians, and two important books with innovative thoughts on logic include Begriffsschrift (1879) by Gottlob Frege and The Laws of Thought by George Boole in ...
- 572
19
votes
2
answers
2k
views
Why did the mid-19th century and earlier thinkers fixate on one-place predicates?
A book I'm reading mentions the following:
A major barrier to the development of first-order logic had been the
concentration on one-place predicates to the exclusion of many-place
relational ...
- 491
4
votes
1
answer
526
views
What are the advantages of Aristotle's term logic over predicate logic?
I have read Wikipedia's term logic entry, and the quote by Gareth Evans in the Revival section that's supposed to argue for term logic's advantages over predicate logic:
"I come to semantic ...
- 491
0
votes
1
answer
187
views
What is this snippet from Frege's Begriffsschrift saying?
I have no background knowledge in logic so I am a little lost about where to begin.
This is the photo I am trying to learn about and it is from Frege’s Begriffsschrift.
- 97
6
votes
2
answers
247
views
How were formal systems and notion syntactic consequence (proof) developed?
I've looked at several resources to learn about logic and metalogic, and they first present syntactic consequence and semantic consequence as separate things and then try to show how each implies the ...
- 567
2
votes
3
answers
174
views
Before Gödel, was undecidability of axiomatic systems an issue at all?
Before Gödel, was the issue raised that there may be undecidable statements within axiomatic systems of thought?
Gödel managed to answer affirmatively by proving that the assumption of the ...
- 341
2
votes
0
answers
224
views
What are the eventual purposes of symbolic logic?
What is the teleology of logic? Every body of knowledge has to have a teleology for which it's designed. The body of knowledge in logic doesn't clearly have any teleology or any purpose to which it ...
- 57
3
votes
1
answer
247
views
In logic, which came first: the semantic approach or the syntactic approach?
Logic is today developing in many, very different directions. But the basic distinction between the semantic approach (truth, "⊨") and the syntactic one (provability, "⊢") is still important and ...
- 171
-1
votes
2
answers
136
views
Who first proposed that A → (B ∧ ¬B) ⊢ ¬A was the principle of proof of some theorems?
The proof of various theorems are nowadays routinely described as "proof by contradiction".
For example, the following theorems:
https://en.wikipedia.org/wiki/Proof_by_contradiction
The ...
- 9,012
0
votes
2
answers
238
views
Who first studied asymmetric relations qua relation?
Who first asymmetric relations qua relation, viz., the fact that
A relates to B by some relation
does not always/necessarily imply that
B relates to A by the same relation.
?
- 8,475
3
votes
1
answer
835
views
What is a good history of logic book that covers all logic?
Including inductive, formal and mathematical. I find them separated a lot and I don't know if I have the ability to sit through all the Handbook of the History of Logic series.
- 77
5
votes
2
answers
470
views
What did the Greeks call the "trial and error" reasoning process?
What did the Greeks call the "trial and error" reasoning process?
Bruce Aune's review of Wilson's Peirce's Empiricism: Its Roots and Its Originality claims "The name 'empirici' is in fact traceable ...
- 8,475
10
votes
1
answer
612
views
Why isn't humanistic logic taught in schools any more?
Specifically, I'm curious about the loci or categories that Agricola and later Ramus used extensively. Were they found to be problematic at a later time? If not, why not use them? They're so helpful ...
- 247
1
vote
1
answer
564
views
What is the difference between type–token, genus–species and universal–particular?
Over the course of it's history, western philosophy introduced all these distinctions between an object and it's class. But I'm a bit confused by this, because these all look very much alike. So what ...
- 348
0
votes
2
answers
265
views
Why do both "and" and "or" exist? [duplicate]
In logic, why do both "and" and "or" exist?
"and" is just a change in the argument of "or", and vice versa.
a ∨ b = ¬(¬a ∧ ¬b)
a ∧ b = ¬(¬a ∨ ¬b)
So why do we have both of them? Do they both ...
- 109
13
votes
1
answer
2k
views
What is the axiom of reducibility? And what philosophical controversies did it incite?
Trying to come to terms with basics concerning philosophy of logic, and wish to ask about some particular issue: What is in simple words the axiom of reducibility put forward by Russell? And what is ...
- 2,761
6
votes
1
answer
429
views
What is the historical context and what are the philosophical implications of model theory?
I tried to place Abraham's Robinson non-standard analysis in the thread of history and philosophy of logic, but got confused. I think I miss some background knowledge concerning perhaps the ...
- 2,761
6
votes
1
answer
792
views
What is the origin of the truth table in logic?
Specifically for the material implication if possible. Who was the first to use a truth table for this and justify its validity?
41
votes
3
answers
5k
views
How did first-order logic come to be the dominant formal logic?
Early formal systems like Frege's Begriffsschrift or Peano's work on the axiomatization of the natural numbers used axiom systems with an underlying second-order predicate logic (from today's point of ...
- 4,039