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Questions tagged [logic]

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

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Causality: is it possible for one attribute to be found in one node but not the others before it?

This is a rather basic question about causality and logical reasoning, but I'm a bit confused over it (especially in terms of the "first cause" argument). Causality (from Wikipedia): Agency or ...
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3answers
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How does one judge “complexity” of assumptions for the purposes of “best explanation”?

The context for this question is from assessing theological arguments from the point of view of 'inference to the best explanation'. In philosophy (and science), we may wish to argue that some ...
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1answer
51 views

Equivalence of strings of modal operators in modal logic

I'm trying to solve a question which asks me to show that for any two finite strings O₁ and O₂ of □s and ◊s, (e.g. □□◊□◊□), that i) if O₁≡O₂ then OO₁≡OO₂ and ii) if O₁≡O₂ then O₁O≡O₂O where O is ...
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2answers
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Justification of existing methods of formal logic [duplicate]

What is it that mathematicians, and more likely perhaps philosophers, give as an explicit justification that any method of formal logic, which is actually used by mathematicians, or even by automatic ...
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1answer
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What kind of circularity, if any, is it acceptable for a philosophical argument to contain?

I'm studying circularity in arguments and was wondering if there is any acceptable circularity possible in a good philosophical argument. For instance, I gather that some regard rule-circularity as ...
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1answer
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Has there been any philosophical guidance regarding when to use logic vs empirical testing?

One obvious disadvantage of testing a given claim with scientific constraints is that one may never know the number of possible constraints to try, in which combinations, and in which order to modify ...
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10answers
335 views

How is it possible for an infinite number of moments to have elapsed prior to now?

In the context of the cosmological argument: How is it possible for an infinite number of equal length moments to have elapsed prior to now? For more context . . I have read several discussions, ...
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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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1answer
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Why do I doubt my logical reasoning?

I have been wondering for several years why I just can't trust my own proofs in math or when giving some logical arguments. I keep thinking I might be making a mistake at some step of the proof and ...
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1answer
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What does it mean to be a consequence?

A Logical Consequence, in terms for formal language, is derivable from a given set of statements by manipulating symbols according to fixed rules. That I understand, for that is the only way to move ...
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2answers
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Logical expression that non-existent things don't do anything?

How could we express the idea that "something that doesn't exist cannot possibly do anything" using a logical argument? And if so, it is at all possible to prove that kind of proposition?
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1answer
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Finding desirabilities and probabilities in Jeffrey's Logic of Decision

I'm trying to solve problem 16 (Ch. 5) of Jeffrey's Logic of Decision. The problem says: Suppose that A and B are pairwise incompatible propositions, and suppose that the preference ranking is as ...
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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, ...
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Is “(1) All humans are mortal. (2) Socrates is mortal. Conclusion: Socrates is human.” unsound argument?

I am new to a philosophy course and recently learned about validity and soundness of an argument. In this exercise: Premise 1: All humans are mortal. Premise 2: Socrates is mortal. ...
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1answer
167 views

Classical logic, symbolic logic, higher-order logic, First-order logic? Learning from scratch

I'd like to ask you a question about logic. I study philosophy in a Spanish Christian university. In the first year, we study logic but it's the classical one, following Aristotle's Organon, the ...
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Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ ...
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2answers
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How much the world is logical [closed]

In her book The Art of Logic in an Illogical World, Eugenia Cheng writes:"I have already asserted the fact that nothing in the world actually behaves according to logic. So how can we use logic in the ...
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4answers
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How would i go about using natural deduction to prove this argument is valid?

How would I use natural deduction to prove this argument is correct? It's always either night or day. There'd only be a full moon if it were night-time. So, since it's daytime, there's no full moon ...
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1answer
143 views

Questions from a new introduction to modal logic by Hughes and Cresswell

I just want to see if I got this correct. Show that the following wff is valid in every seating arrangement: Mp -> (Lq->Mq). Here's my argument: Assume player A sees at least one player B that ...
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2answers
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What irreducible functions constitute thinking?

Because all new knowledge, to be not illogical, must obey logic i.e. every thinking step must be consistent with rules of logic; so can we write an effective procedure/algorithm which may be followed ...
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3answers
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What are the major research programmes in contemporary logic?

As an interested outsider who is prone to reading about different formulations of logic, I've become interested in better understanding the big picture of what people are trying to accomplish as they ...
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1answer
802 views

Explain Ramsey sentences in simple terms

Can you explain Ramsey sentences in simple terms, maybe giving some concrete examples? I can't seem to understand them (everything about them), no matter how hard I try.
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Validity of a modal argument?

Would you say that the following argument is valid? And if not, why exactly? For all we know, A may be the state of B; What C does is determined by the state of B; Therefore, for all ...
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Is there a natural example of a non-self-referential semantic paradox in philosophy?

A commonly studied paradox is the liar's paradox. The liar's paradox is to determine whether "this statement is false". The usual resolution is to state this the sentence is not actually a statement ...
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1answer
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Is Propositional Logic Sound and Complete

After reading Gödel's incompleteness theorem, I wonder if there are any systems whose axioms are sound and complete. I realize that Gödel's arguments (at least from my sources) only apply to ...
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1answer
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Existential Quantifiers and Modal Logic

I have a question about predicate logic and modal logic. Namely, do any of them overlap with one another? To give an example, does existential quantification apply to counterfactual statements? A ...
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1answer
64 views

What does Tarski mean when he says that truth is a property of sentences?

A fundamental statement of Tarski's Theory of Truth is that truth is a property of sentences. What does this statement mean? What kind of Truth is it referring to? What is the formal definition of '...
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1answer
141 views

Negation of a E quantifier in a Modal Logic T System?

In System T its possible to conclude: (1) □Ex->Ex Therefore its possible to conclude: (2) Ex->◊Ex But whats the result, if I negate the existence quantifier? Is it: (3) ~Ex->~◊Ex or is it: (4) ~Ex->◊~...
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1answer
66 views

John Earman and Time Travel

Time travel and grandfather paradox: Earman suggests in his 1995 paper that physical possibility should be considered similarly with the laws of nature (i.e. logical possibility). Does this mean that ...
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1answer
82 views

What is the difference between depth and surface information?

I was looking for an answer to this question: Was Euclid's method of proof axiomatic? While doing so I ran across an abstract of Jaakko Hintikka for an article "What is the axiomatic method?" ...
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1answer
74 views

What fallacy is this?

I am curious about what fallacy the following kind of reasoning represents. Let's say we are questioning if something is true. I would argue that in order for us to question if something is true we ...
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Is this an example of Undistributed Middle?

Is this an example of Undistributed Middle? John is not a teenager, since all teenagers are impulsive, and John is not impulsive.
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3answers
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Interpretation and symbolic notations of operations in mathematics

As we know a mathematical operation is a function. And a function is a special type of relation. Ultimately a relation is a set of ordered pairs. For example, what is addition of natural numbers? At ...
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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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2answers
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How to get the refutation of (OP ⊃ OQ) ∴ O(P ⊃ Q) in Deontic Logic

In Deontic Logic, one could easily infer "If it is obligatory that P, then it is Obligatory that Q", from "It is obligatory that if P then Q" O(P ⊃ Q) ∴ (OP ⊃ OQ) Where the ⊃ is an implication (...
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1answer
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Descartes on Llull's logic

I recall from readng long ago that Descartes described Llull's logic as something that would allow one to speak on many subjects without knowing any of them That quote from Bonner, Art and logic ...
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Is this an example of Denying the Antecedent?

Is this an example of Denying the Antecedent? Harry is not an inexperienced driver, and thus must not be irrational, seeing as all inexperienced drivers are irrational. At first, I thought it was ...
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Negation of a statement

The question asks us to negate the following statement. Jackie eats sweets, if she is not hungry. This is a basic if (p), then (q) statement whose negation will simply be p and ~q, but the solution ...
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Why do the professional mathematicians believe blindly in so meaningless concepts as Infinity? [closed]

To refute such a concept as Infinity (or many infinities) in mathematics doesn't at all require all that big efforts mainly from its own definition in mathematics. To explain this very simple fiction ...
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Name of Principle Giving Precedence to a More General Hypothesis

As far as I know, there is a principle that gives precedence to a theory that is more general than a more specific one, i.e the more general one is more acceptable. What is the name of that principle?
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60 views

Correct Way of Handling A Corollary of A Corollary?

I have a conclusion S that is moderately interesting. While the corollary of S is more interesting, the corollary of the corollary of S is extremely interesting. Should I just label them corollary 1 ...
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Is God either immoral or not omnipotent?

The usual (Christian) justification for suffering/evil in the world created by a benevolent God is freedom of the will. However, the more interesting question is not about the source of evil (which ...
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Is deduction based on induction?

I'm wondering if deduction is in the end based on induction. The problem of induction discovered by the Scottish philosopher David Hume is quite well known. On the other hand, it's commonly supported ...
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Axioms for modal logics based upon counterfactuals

Suppose we have a logic for counterfactuals as with David Lewis. I here use ⇛ for the counterfactual conditional. So suppose we have: Rules: (1) If A and A→B are theorems, then B is a theorem. (2)...
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1answer
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Conditional logic - how to apply a conditional with complex antecedent in tableaux?

I'm referring to the conditional logic of C+ as described Graham Priest in "An introduction to non-classical logic" chapter 5, where the strict conditional is enhanced with ceteris paribus, and a ...
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1answer
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Are there logicians who argue that knowing and believing are NOT amenable to formal study via modal logics?

Vincent Hendricks and John Symons notes the following about epistemic logic: Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have ...
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Is the sentence, 'God exists', a logical statement?

According to wikipedia a statement is either (a) a meaningful declarative sentence that is either true or false, or (b) that which a true or false declarative sentence asserts. Is the sentence God ...
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How to prove : P v ( P → Q ) by Natural Deduction

Another of Tomassi's exercises I can't solve (Logic, page 109, Revision exercise III, 9) : P v ( P → Q ) I have to use natural deduction and the only rules I know are: • assumptions, • modus ...
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4answers
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How to prove : (( P → Q ) ∨ ( Q → R )) by natural deduction

Here's another of Tomassi's exercises I can't solve (Logic, page 106): : (( P → Q ) ∨ ( Q → R )) I have to use natural deduction and the only rules I know are: • assumptions, • modus ponendo ...