Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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How is (A → B) → C different from A → (B → C)?

This question derives from p 322, A Concise Introduction to Logic (12 Ed, 2014), by Patrick Hurley, but I do not quote it because its example presumes knowledge of pharmaceuticals and is too esoteric. ...
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Shouldn't statements be considered equivalent based on their meaning rather than truth tables?

Consider the following truth table, which serves to define the logical connective ⇔, P | Q || P⇔Q T | T || T T | F || F F | T || F F | F || T According to the above truth table, the logical ...
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Can there be a valid argument which has a tautology as a conclusion?

Given this definition: A deduction is valid if and only if its conclusion is true whenever all of its hypotheses are true. Can an argument be valid if it has a tautology as a conclusion? An ...
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How do we separate rules of logic from non-logical constraints?

I think that very often the idea of 'constraint' appears in mathematics. For example, when a triangle is considered, 3 points are constrained not to be co-linear, and then we try to discover the ...
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What are the critiques of the “we might as well assume it” solution to the problem of induction?

I'm curious whether the following proposed solution to the problem of induction has ever been discussed in the literature: Either the future resembles the past or it does not resemble the past. If it ...
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How do I use the “Barbara, Celarent, … etc.” mnemonic?

Medieval logicians memorized this most famous logic mnemonic: Barbara, Celarent, Darii, Ferio ← direct first figure Baralipton, Celantes, Dabitis, Fapesmo, Frisesomorum ← indirect first figure Cesare,...
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Is reductio ad absurdum a valid logical proof?

It strikes me that atheists often in the religion debate will try to characterize religion in a funny or silly way, often comparing religion to belief in fairies or unicorns or flying spaghetti ...
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Is there a deduction analog to the problem of induction?

Aren't deductive and inductive reasoning equally unjustified? So, inductive reasoning is going from specifics to general, whilst deductive reasoning is going from general to specific. But in deductive ...
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Was Kant anticipating Gödel's incompleteness in his antinomies?

Kant's attempts to prove that there's a limit to pure reason based on the existence of antinomies, i.e. pairs of propositions where each one is rational, but the propositions contradict each other. ...
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Why is the darapti syllogism invalid?

I found the following exposition of darapti on wikipedia: All squares are rectangles. (MaP) All squares are rhombuses. (MaS) ∴ Some rhombuses are rectangles. (SiP) As far as I can see, this is ...
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What's the difference among the logical relations :=, =, and ≡?

I understand that ≡ is logical equivalence, "iff". '=' is a symbol for numerical equivalence. And ':=' is an identity claim. I often only see '=' and ':=' used with variables and names, ...
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Do Western logicians have a term for “the five crafts” (الصناعات الخمس)?

My only formal exposure to Logic is from an Arabic text book, where five methods for proving and/or convincing an opponent of your argument was described. These methods are termed "the five crafts" ...
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What's the difference between “not all” and “some” in logic?

We have, not all represented by ~(x) and some represented (∃x) For example if I say, Not all are animals. Some are animals. Because we aren't considering all the animal nor we are disregarding all ...
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Syllogism from Lewis Carroll

I was reading Code by Charles Petzold, and on page 86 he references a syllogism from Lewis Carroll: All philosophers are logical; An illogical man is always obstinate; Therefore, some obstinate ...
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Are there rules for dealing with self-reference “paradoxes” in logic?

My favorite paradox that leads to an endless regress, and also leads to a question: The sentence after this is true. The sentence before this is false. When contradictions appear in proofs, we have ...
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How do I check if two logical expressions are equivalent?

For example: Is (A ∨ B ∨ C) ∧ (D ∨ E ∨ F) the same as (A ∧ D) ∨ (A ∧ E) ∨ (A ∧ F) ∨ (B ∧ D) ∨ (B ∧ E) ∨ ( B ∧ F) ∨ (C ∧ D) ∨ (C &...
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In Gödels Incompleteness theorem what is the notion of truth?

The entry on Gödels Incompletenss theorem in Wikipedia says: Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for ...
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What is Kant's argument about the relationship between logic and reason?

At Wikipedia, I read: Logic arose (see below) from a concern with correctness of argumentation. Modern logicians usually wish to ensure that logic studies just those arguments that arise from ...
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Can one still derive paradoxes from the amended version of Naive Set theory given by Cantor in a letter to Dedekind?

Consider the following definition of set given by Cantor in a letter to Dedekind: If on the other hand the totality of the elements of a multiplicity can be thought of without contradiction as 'being ...
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How does Robert Nozick explain the Gettier problem?

Nozick agrees that the Gettier counterexamples to the JTB analysis of knowledge are cases where someone has a JTB but does not know. What is his explanation of what has gone wrong in those cases? ...
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If logic is based on human reasoning, how can most people be so incoherent?

I believe that our understanding of formal logic is to formalize how a human brain is supposed to work. And this also makes sense when we think of mathematical problems that we only should get the ...
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Can there be an argument without premises?

After a lengthy discussion with WillO here, we can't seem to find a common ground and I am interested in whether there really could be an argument without a single premise. Another question whose ...
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Why bother with anything else besides Aristotle's syllogistic logic?

Disclaimer: this a "devil's advocate's question", meaning I know a lot of the answer, but for the sake of playing the Q&A game, I won't self-answer right away. The main reason I'm ...
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Why is Modus Ponens valid?

I am having trouble understanding what defines Entailment operator. On Mathoverflow I posted this question on what I perceive to be paradox of entailment. Consider: Modus Ponens: P therefore Q P ...
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Is there a logic that takes time into account?

I hope this is neither too simple nor off-topic; I apologize if so. I have just noticed that standard sentence logic seems to make assumptions about time in determining the truth/falsity of a ...
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What's the name for an argument that “this book or this person says P is true, therefore P must be true”?

People often claim P is true because a single book or person says P is true. This is most often the case when the book or the person is said to be divine. So is it a fallacy when people theorise the ...
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Are there any resources for teaching young children philosophy and logic?

My oldest child is nearly six years old and will be starting his first level of formal schooling in a few weeks. I don't believe he will be taught philosophy and logic in the classroom, so I would ...
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Why would definition not be proposition?

I've read in one mathematics book that any definition is not a proposition. Why is it so? What definition of proposition makes the former into the latter? EDIT: There is well-known analytic-syntactic ...
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Is the argument that a claim is “too strange to be made up” an appeal to logos or pathos?

When someone tries to persuade you of the truth of something they said and they use the argument that it is too strange to be made up (or any variations of this, such as "too complicated to be fiction"...
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What exactly is informal logic and is this what I'm looking for?

I've been reading and researching about formal and symbolic logic for some time now, mainly out of interest in rationality. But I've come to a point where the various logical systems seem more like ...
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Asking a genie for more wishes [closed]

I just saw this SMBC comic. The second picture looked really promising, but as far as I see it, this attorney screwed up. With his second wish it doesn't matter whether you say wish or splork, so ...
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Does the phrase “vacuous tautology” have specific meaning?

I just came across a use of the phrase "vacuous tautology" used in a piece of writing. Now, based on my understanding, by definition a tautology has no content and is therefore always vacuous. This ...
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Possible worlds in logic

In modern logic there is often talked about possible worlds. I understand this idea in this way: Every proposition may be true or false. Possible world W is a set of all propositions where there is ...
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Why don't we have consensus in more complicated areas of logic?

When I once realised I don't really understand how and why proof by contradiction works, I started reading about it. And apparently I wasn't the only one who felt there's something wrong about it - ...
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What are the practical applications of formal logic, outside of math and computer programming?

I am studying a bit of this and so far it seems that, apart from math and computer science, the discipline of Logic is very inward-facing...with logicians proving things for other logicians. This may ...
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A Question Regarding Russell's Paradox

Consider the 'set' behind Russell's Paradox: R = { x | x is a set and x ∉ x } in light of Cantor's definition of set ("aggregate"/Menge) in his CONTRIBUTIONS TO ...
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Why can't an algorithm understand incompleteness?

I've heard a lot of people say that Gödel's proof shows that human intelligence somehow goes beyond what a computer could ever do. It's only ever been articulated to me very badly, though not for want ...
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Do I need to read The Organon to understand Aristotle's philosophy?

I recently read through the collected works of Plato and really enjoyed learning about his philosophy and ideas. I'd like to do the same for Aristotle and have started reading through his works as ...
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What are the more complex/interesting examples of synthetic a priori statements?

The usual examples of synthetic a priori statements are – it seems at least since Kant: "Nothing can be simultaneously red and green all over" 7 + 5 = 12 (or any other basic arithmetic statements). ...
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What are the differences between philosophies presupposing one Logic versus many logics?

I was wondering in light of the historical developments of logic since ancient Greeks and well into the nineteenth and twentieth centuries: What kind of a philosophy assumes only one Logic, and what ...
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Where did Gödel write that first-order logic is the “true” logic?

In "On How Logic Became First-Order" Matti Eklund writes (p. 2/148): It appears to be widely held today that arguments from Skolem and Kurt Gödel, both alleged proponents of the thesis that ...
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Supervaluationism and Theories of Truth

How does the supervaluationalist defend his/her theory of truth since the correspondence theory of truth seems to presuppose bivalence? It would seem then that the only truth is Super-Truth. And, the ...
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Causality vs. implication

Implication is said to be more general than causality since, for example, being a dog implies being a mammal but it doesn't cause it. Is there a formalization of the difference between implication and ...
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Understanding Grice's Theory of (Non-Natural) Meaning

I am trying to understand Paul Grice's famous essay "Meaning". So consider a computer system which is fed a dictionary of every English word in existence. The computer system then randomly spits out ...
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What are free variables and what does it mean for a statement to contain one?

I am puzzled a bit. I read the wiki page and an introductory book on logics, but I can't quite grasp it yet. The place where i came across them is Van Inwagens 'Material Beings'. Consider the ...
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What is Quine's response to Parmenides's argument against change?

I was recently reading Russell's chapter on Parmenides in The History of Western Philosophy, and I came across a fun little argument for the absence of change. Essentially, it says that word meaning ...
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Does fictional discourse pose special difficulties for logic?

Natural language is context-dependent, like the statement “My uncle is a plumber”, which is true or false depending on who asserts it. There has been lots of discussion about fictional entities and ...
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Does a philosopher need much knowledge of mathematical/formal logic?

I am not a philosopher but I would like to ask this question. I know that there are philosophers like Hobbes, Locke or Foucault, who excel in the areas of ethics, political philosophy and aesthetics. ...
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Can a “real” paradox exist?

Given a statement, S: "S is not true." We arrive at a paradoxical solution whether or not we assume S to be true or false. Does this automatically imply that we have made an error in logic, ...
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What would you call a counterfactual theory of Justified True Belief?

Ever since I heard the characterization of knowledge as justified true belief, the proper meaning of the word "justified" has always seemed clear to me: it should mean that you acquired the belief in ...

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