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Questions tagged [philosophy-of-logic]

Philosophy of logic is a branch of philosophy concerned with investigating the nature, scope and role of logic.

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How do skeptics explain axioms not being arbitrary?

I get infinite regress but surely the axioms of ZFC or arithmetic were not so much chosen as discovered and intuited and thought about. They certainly didn't just grab whatever was around them and say ...
Ehudjd Ejeijr's user avatar
1 vote
4 answers
191 views

How can objects be nonexisting?

A square circle. Obviously, this is contradictory, but i feel odd saying it doesnt exist as well. thats not the bestw ay to say it. but, then again, whatg do we even mean in mathematics or logic by ...
Lawrence Lee's user avatar
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What did Bradley mean that it "may be true" that all trespassers will be prosecuted?

What exactly did F. H. Bradley mean when he wrote in his 1883 Principles of Logic that the statement that all trespassers will be prosecuted "may be true"? Did he mean that the statement is ...
Speakpigeon's user avatar
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In the Contingency argumemt it is referenced that alternative having things can not be necessary, whats the alternative in here can be considered as?

In the Argument of Contingency there is referenced that if something has alternatives, that thing can't be necessary because of it could be something different than what it is, so is this information ...
Hido's user avatar
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3 answers
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Statement Vs Proposition Vs Premise Vs Assertion

I have spent a few days running around the internet trying to find a distinct and simple explanation of how all of these terms fit together. I'm aware it is quite nuanced. Could someone help me ...
surbjit singh's user avatar
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Which is correct, "the implication A → B" or "the implication ‘A → B’"?

Which is correct? The true (or false) implication A → B. The true (or false) implication ‘A → B’. What are the arguments for saying that it is wrong to say: the implication A → B and the we should ...
Speakpigeon's user avatar
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-1 votes
2 answers
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What difference between the truth of a conditional* and its logical validity?

I am confused . . . Here is a remark on the "classical analysis" of the implication: On the classical analysis, logical implication is the same, not as the truth of a conditional statement, ...
Speakpigeon's user avatar
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On why the phenomenal world can be presumed to "comply" with standard/classical logic in a classical (not quantum) physics experiment

In order to be able to employ the scientific method, we rely on the phenomenal world remaining consistent enough that if we run the same experiment tomorrow that we ran today then the observed results ...
Simon M's user avatar
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2 answers
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Are all languages universal?

I am reading the book titled 'A Companion to Philosophical Logic,' where I gained insight into how logic serves as a tool for representing our thoughts, which are expressed in natural language. In my ...
HAMDI ABDERRAHMENE's user avatar
1 vote
1 answer
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Theory build on the top of a Logic

Could somebody elaborate the meaning of following statement from wikipedia concerning intrinsical differences between set theory and type theory: Unlike set theories, type theories are not built on ...
user267839's user avatar
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1 answer
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All syllogism is addressed to that within the soul: Did Aristotle really said that?

All syllogism and therefore a fortiori demonstration, is addressed not to outward speech but to that within the soul. Did Aristotle really said that, and if so, where? The claim that he did is in I. ...
Speakpigeon's user avatar
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Why not just give up on the idea of truth-functionality?

I understand that today only a minority of academics who are specialised in formal logic accept the horseshoe (aka "Classical Logic" or "First-Order Logic") as an accurate, or even ...
Speakpigeon's user avatar
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1 answer
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Which author(s) first talked of Aristotle's syllogistic as a logic of terms?

Which author(s) first talked of Aristotle's syllogistic as a logic of terms? Thank you for any scholarly references. Aristotle does defines the notion of "term" in Prior Analytics: I call a ...
Speakpigeon's user avatar
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6 votes
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Who coined the use of the word "entailment" in the logical sense?

Who coined the use of the word entailment in the logical sense? And to mean what exactly? Thank you for any scholarly reference. EDIT For example, there is a definition of "semantic entailment&...
Speakpigeon's user avatar
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8 votes
3 answers
350 views

Can the law of non-contradiction exist without the law of identity?

Lately I've been reading about Quentin Meillassoux, and it seems that the only law of logic he doesn't see as contingent is the law of non-contradiction, because if the world is what it is not, then ...
edelex's user avatar
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What are some cases in which we can use reason but not logic?

I am curious whether there have been philosophers arguing that there are contexts in which we can use reason, but not logic. For example, some authors might say that logic cannot be used in the very ...
lfba's user avatar
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Is it possible to stick to one of these viewpoints of variables?

It has been a struggle to find a precise account of the concept of variables. There are however two viewpoints that I've seen authors convey in several logic textbooks. Variables as placeholders for ...
Harshit Rajput's user avatar
6 votes
8 answers
2k views

Does the PSR violate Occam’s razor?

The principle of sufficient reason (PSR) in a nutshell says that things happen for a reason. Occam’s razor suggests to not postulate things that bring in additional assumptions without doing any ...
Baby_philosopher's user avatar
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4 answers
457 views

Is there any logical operator that indicates tautology (in the form of truth table)? And, if so what could be it's possible significance be?

I got to this question because I was trying to see the inconsistencies that could arise if I would approach every informal logic in a formal way, that is when I start to break down what the difference ...
How why e's user avatar
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Is it true that no philosopher disagrees that everything exists?

I am baffled by what Quine claims here: A curious thing about the ontological problem is its simplicity. It can be put in three Anglo-Saxon monosyllables: 'What is there?' It can be answered, ...
Speakpigeon's user avatar
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Why is the lack of sound proof theory fatal for Second-Order Logic but the practical lack of sound proof theory for FOL benign?

Received orthodoxy says, among the community of logicians, that first-order logic (with predicates, connectives, and variables) is good because it has a sound proof theory and second-order logic (with ...
Fomalhaut's user avatar
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2 votes
2 answers
289 views

What is the modality of a statement that follows from a necessary statement?

Let □P. Suppose □P => Q. What can be said about the modality of Q? □P <=> P holds in every possible world. Thus it is available as a premise to derive Q in every possible world. Suppose Q is ...
Wowser's user avatar
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What did Bertrand Russell mean exactly when he said that *such that*, while fundamental both to formal logic and to mathematics, is "undefinable"?

Bertrand Russell in Principles of mathematics (1903) presents the notion of such that as fundamental to logic and mathematics, and states that it is “undefinable”: The Indefinables of Mathematics ...
Speakpigeon's user avatar
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Treating truth as a predicate

It is interesting to me that in some conventions of logic I have seen (generally, common ones), the form of logical language is designed to make “truth” implicit. For example, merely to write: P(x) is ...
Julius Hamilton's user avatar
4 votes
1 answer
104 views

Demonstrate that a term cannot be well-typed?

This problem is coming from Exercise 3.3 in Bacon's A Philosophical Introduction to Higher-order Logics. I am trying to do my due-diligence here and not skip problems, but this one stuck out to me. ...
C D's user avatar
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4 answers
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Has Münchhausen's trilemma been solved?

I believe that the classic argument that conceptual regress goes back forever may be wrong. For instance, if I try to infinitely regress on concepts, I actually end up at a point where I can't go on ...
Lawrence Lee's user avatar
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1 answer
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What is the first recorded, explicit and articulated, logical argument in the history of humanity?

What is the first historical record of an explicit and articulated logical argument in the history of humanity? Is it Xenophanes (presumably around 540 BC)? But if cattle and horses or lions had ...
Speakpigeon's user avatar
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5 votes
4 answers
540 views

What is reason, and where does it come from?

It seems odd to me, to reflect that things in the world are the way they are, but not some other way. Maybe ‘reason’ tells us why things are a certain way. By structuring thinking, ‘reason’ lets us ...
Lawrence Lee's user avatar
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1 answer
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What are the arguments for innatism, essentialism, and rationalism?

How do people justify some existents being absolutely necessary. Why cant it just be against a backdrop of a relative nothingness? How can someone justify certain ideas being absolutely essential and ...
Gerald Robertson's user avatar
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2 answers
156 views

Do all theories require frameworks or assumptions to be supplied? If so, why?

In a philosophy class, particularly in Epistemology, the professors seem to have the assumption that to conceive the concept of anything at all, including even this very sentence, require us to have ...
Gerald Robertson's user avatar
1 vote
1 answer
126 views

Do Gödel's incompleteness theorems and Tarski's theorem of indefinability of truth show we can never discover and prove every truth?

I thought I had a grasp on this. Do Gödel's apply to just math; logic, too; or more, and what does its applicability entail? If it applies to math, does it apply to physics? Similarly with Tarski: can ...
Sayetsu's user avatar
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3 answers
286 views

How universal is logic? [closed]

There is what seems to me an inconclusive debate in the academic literature concerning the idea that logic is universal, but in what sense exactly would logic be universal? One example of a claim that ...
Speakpigeon's user avatar
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2 votes
4 answers
947 views

Is Fermat's last theorem a logical necessity or a different kind of necessary truth?

Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The question was, is this a logically necessary ...
Vihan 's user avatar
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0 answers
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Question about a presentation on substructural logic (negation modulo two kinds of residuation)

I've been reading through this slide-based presentation on substructural logic and I'm delightfully perplexed by the following section: What is the use to which the two given flavors of negation can ...
Kristian Berry's user avatar
1 vote
0 answers
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Missing two syntactical expressions of rules of inference in sentential logic

I have a table of the rules of inference in propositional logic. Among the entries are an Associative and a Commutative. The Associative rule is expressed with disjunction, but the commutative is ...
J D's user avatar
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3 votes
3 answers
107 views

Does logical pluralism imply conceptual pluralism?

By "conceptual pluralism," I mean something like, "Multiple conceptual analyses of the same concept are true." The example for the sake of which this question occurred to me is the ...
Kristian Berry's user avatar
2 votes
0 answers
54 views

Has anyone studied the beings of logic from Heidegger's "Time & being" perspective?

The nature of the word 'logic' differs according to the context where it is used (i.e., Aristotle and Socrates, boolean algebra, symbolic logic, propositional logic, etc.) Has any philosopher focussed ...
Jérôme Verstrynge's user avatar
2 votes
0 answers
69 views

Propositions vs sentence types and tokens and the context insensitivity of PL

I came across the following explanation for the context insensitivity of the language of propositiional logic (PL) on page 34 of The Laws of Truth by Nicholas Smith: Because glossary entries pair ...
user51462's user avatar
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4 votes
5 answers
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Is the Law of Excluded Middle an allowed argument in court?

Is the Law of Excluded Middle a valid deduction rule in court? If not, is it reasonable to say that all arguments in court must be "constructive in nature"? As an example, consider this ...
CatProgrammer's user avatar
2 votes
4 answers
302 views

Is mathematics based on formal logic, or vice versa?

Math is obviously based on logic in a heirarchical sense, but what about the historical sense? Is there any historical evidence of a "transition" from first order logic to mathematics? All ...
Steven Harder's user avatar
3 votes
6 answers
1k views

Who ever argued that natural languages have an exact logic?

Peter F. Strawson famously concluded his 1950 critique of Bertrand Russell's theory of descriptions by the somewhat irrelevant remark that ordinary language has "no exact logic". Russell, in ...
Speakpigeon's user avatar
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Could a quantum computer simulate any system based on different types of logic?

Quantum computing is based on quantum mechanics (obviously) which has different logical rules than classical/Boolean logic. However, does this mean that a quantum computer could simulate or process ...
vengaq's user avatar
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0 votes
1 answer
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Trivialism vs Alethic Nihlism

What are the similiarities and differences between the two theories (as well as arguments for and counterarguments against). From what I know, trivialism states that everything is true (and I believe ...
HelpMePlease's user avatar
0 votes
2 answers
106 views

What is logic in the context of Classical Logic?

How mathematicians define the concept of logic for the purposes of Classical Logic? Also, how do philosophers and mathematicians at different period in history defined the word "logic", if ...
Speakpigeon's user avatar
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1 vote
1 answer
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Conjunction with questions: an issue more of logic or of language (if not both)?

Assume that questions can be conjoined with other questions, e.g.: Who is Shawn Balt? What is prawn salt? Who is Shawn Balt and what is prawn salt? Assume that wh-terms are (plurally) agglomerative ...
Kristian Berry's user avatar
1 vote
1 answer
449 views

How is the completeness of first order logic reconciled with the incompleteness of set theory?

First Order Logic (FOL) is complete in the sense that: there is a proof procedure for FOL such that just the statements(/wffs) of FOL that are true and remain true under any re-interpretation of their ...
Surprised's user avatar
1 vote
2 answers
95 views

What does it mean "to provide semantics" in the context of formal logic?

When reading some SEP articles, this is a phrase I commonly came across, "this provides a semantics for this logic". But what does it mean?
Babu's user avatar
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2 votes
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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. ‑ ...
Geremia's user avatar
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9 votes
3 answers
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Is there a system of logic which denies DNI?

From what I know, the law of double negation is often simplified as p <=> ~~p. Intuitionist logic splits the biconditional into DNI and DNE. DNI: p -> ~~p DNE: ~~p -> p and denies DNE ...
Kelvin Chan's user avatar
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0 answers
58 views

Were there any logicians in the past who argued that the Liar was logical, and so either true or false?

The Liar seems to have been universally regarded as paradoxical from the moment philosophers started to discuss its logic. Is that really the case, though? My question is as follows: Outside ...
Speakpigeon's user avatar
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