Questions tagged [logic]

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

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25
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15answers
2k views

Is the claim “this coin is fair” falsifiable?

Wikipedia says, The claim "No human lives forever" is not falsifiable since one would have to observe a human living forever to falsify that claim. Thinking on similar lines, even if the ...
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7answers
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Has quantum mechanics destroyed the fundaments of logical reasoning?

In quantum mechanics it is thought to be possible that something could be at two places at the same time. But if that is really the case then perhaps law of non-contradiction is no longer valid. So ...
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10answers
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Are different values of nothing equivalent?

Are different values of nothing equivalent? Is 'no tigers' the same as 'no zebras'?
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5answers
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Can a lack of knowledge or understanding invalidate a positive claim?

Consider the example of causal determinism. It can be phrased in many ways, all with identical meaning: - The idea that "every event, including human cognition and behavior, decision and action, is ...
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1answer
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When it is correct to use Tarski's undefinability theorem versus Gödel's incompleteness theorem?

Smullyan (1991, 2001) has argued forcefully that Tarski's undefinability theorem deserves much of the attention garnered by Gödel's incompleteness theorems. That the latter theorems have much to say ...
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2answers
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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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4answers
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Do “if everybody did it” arguments commit a fallacy?

Who is committing a fallacy in this discussion, and what kind of fallacy is it? A: There's nothing wrong with killing people at random B: If everybody did it, you would too most likely be a random ...
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7answers
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What are the practical applications of modal logic?

I'm a computer science and philosophy double major. I know logic is paramount in computer science, but what about modal logic? Are there any practical applications in computer science and perhaps even ...
13
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3answers
554 views

Are systems of logic that don't follow or extend garden-variety FOL possible?

As I know all humans share a unique logic and even less-educated people uses same common sense in their statements. For example, it is rational for anybody that if P is correct then P or Q is correct ...
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16answers
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Does the notion of an all-powerful God conflict with the idea of free will?

In Abrahamic religions, God is often believed to be wholly omnipotent. People also seem to believe that humans have "free will", especially insofar that they feel they are in control of their own ...
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7answers
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Why did we define vacuous statements as true rather than false?

I have been trying to understand why implications about the empty set are treated as "true". It seems to me intuitively that vacuous statements should be false. For example consider the sentence: ...
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10answers
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Why can't humans believe contradictions?

I'm reading something on the topic of logic and one of the exercises asked me to convince myself that a contradictory statement was true. I could not convince myself of this and now I am curious about ...
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10answers
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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 ...
6
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6answers
572 views

Is the space we live in continuous (as mathematically defined) or quantized?

Let me start with stating my definitions in measuring the length of objects: The way to measure an object properly is to measure it when it's static. So take the ultra resolution (which can describe ...
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6answers
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What is the philosophical equivalent of mathematical proofs?

In mathematics, there seem to be five standard methods of proving or refuting an argument: a proof by induction, contradiction, counter example etc. Are there some typical proof methods that exist in ...
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4answers
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Is Galileo's argument about falling bodies logically flawed?

Galileo's famous argument against the Aristotle's theory of falling bodies goes like this. "Let's say heavy objects do fall faster than light ones. Then it seems the heavier weight will fall with the ...
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5answers
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What's an intuition for material implication?

The paradoxes of material implication show that the usual interpretation of implication as "if ... then" statements leads to counter-intuitive results. For example, from (P & Q) -> R we can ...
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8answers
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What is the truth value of the proposition 'All unicorns are beautiful'?

If we let Fx denotes that which has the property of being a unicorn, and Gx denotes that which has the property of being beautiful, then this proposition would be signified by the following: ∀x(Fx→Gx)...
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3answers
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What is the philosophical problem with Skolem's Paradox?

I guess there are two questions here. QUESTION 1: Skolem's Paradox shows that countability is relative in first-order logic, but where is the relativity? In this first question, I will do the ...
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8answers
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Are all non self-referential statements true or false?

It is well known that there exists self-referential statements which are neither true or false, such as "I am lying". Is it possible to have statements neither true or false which are not self-...
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7answers
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Why does the material conditional have the truth table it does?

Can someone provide me with the simplest possible argument for why the material conditional has the truth table it does? Googling doesn't help at all, providing only flimsy and clumsy arguments. I ...
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4answers
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Difference between logic and mathematics

I’ve read the article in the SEP about the philosophy of mathematics. I believe I follow most of it. However, I am a bit puzzled by something that may be due to some basic misunderstanding on my part....
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4answers
388 views

Is existence a feature of life? Can a stone exist without life to recognize it?

First of all I would like to make clear I am not an expert in philosophy. With the question "Is existence a feature of life?" I mean the following: Could something exist without the presence of an ...
15
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6answers
961 views

When given limited information, is the simplest solution that matches that information most likely correct?

Is there any basis in philosophy for the idea that when given limited information, the simplest solution that matches that information should be presumed correct or most likely to be correct? For ...
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1answer
336 views

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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3answers
796 views

Are there kinds of arithmetic that are decidable despite the Gödel theorem?

A proposition p in a consistent formal language is decidable when we can assert either the truth of p or the truth of not p (But not both, for then it would be inconsistent and we have already said ...
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11answers
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What is the logical distinction between “the same” and “equal to?”

We all understand that Given A = C, and B = C, Then A = B. However, A is not “the same as” B. Example: A is the question, “What animals have feathers and can fly?” B is the question, “What was the ...
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1answer
397 views

Is Tarski's derivation of the Liar paradox valid?

First a link to his derivation: http://www.jfsowa.com/logic/tarski.htm Its a famous essay so you really should read all of it but at the moment its enough if you read section 7 where Tarski derives ...
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3answers
898 views

How do mathematical objects relate to the real world?

I am just going to give an example of what I mean using Skolem's Paradox. I DO NOT want to get into Skolem's Paradox itself or its "resolution." Skolem's showed that countability is relative in ...
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1answer
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What are the truth tables for “necessary” and “sufficient”?

Here he says that: If you have A is sufficient for B it means that every time you have A you will have B, without exception: A -> B If you have A is necessary for B it means that every ...
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4answers
904 views

Does Wittgenstein's Tractatus establish serious bounds for discussions of the supernatural from a modern point of view?

In today's mathematics, we have many variants of logic (propositional, first order, higher order, fuzzy logic, etc.). These are all self-consistent formal systems that are based on some set of axioms. ...
12
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6answers
916 views

Are there degrees of truth ?

I do not assume bivalence - that every proposition or declarative statement - is either true or false but not both. I do not raise the issue of 3-valued logics or offer or invite any theory of truth. ...
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4answers
513 views

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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1answer
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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 ...
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5answers
579 views

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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4answers
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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 ...
9
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2answers
628 views

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 ...
8
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5answers
341 views

What logical systems categorize A->~A as a contradiction.?

In the basic propositional logic I learned in school A->~A is not a contradiction because it is not false when ~A is true. What logical systems would hold this statement to always be false?
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8answers
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What's the word for anything is true if the antecedent is false?

(1) If A then B. (2) A is false. Then B can be anything (true or false) and (1) remains true. So B is true by __. What's the word or words in the blank?
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5answers
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Are “If P then Q” and “Q only if P” equivalent?

My textbook says "If P then Q" and "Q only if P" are logically equivalent, but consider this: "If it's green, it's poisonous." "It's poisonous only if it's green." Now say there's a purple ...
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3answers
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What is the meaning of “predicate” in this definition?

I have trouble understanding the article on existence in this Philosophy dictionary. Instantiation in reality, or actual being. Kant pointed out that existence is not a predicate. What is the ...
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1answer
471 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?
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1answer
307 views

Is Belnap's four-valued logic technically a relevance logic?

Belnap, the American Logician, constructed a four-valued logic which is a form of relavance logic; interestingly the truth-values it takes are: true false both true & false neither ...
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5answers
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What is the difference between the “is” of predication and the “is” of identity?

What is the difference between these, the "is" of predication and the "is" of identity? For example, when I say, "my pet is a cat", am I using "is" as an identity or as a predicate?
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1answer
261 views

Why is a predicate of 0-arity considered as a sentence letter?

I often find that nullary functions are considered constants and 0-arity predicates are considered sentence letters. What is the intuition behind that notation?
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4answers
304 views

Is there any reason for the heavy focus on binary relations in formal logic?

As a fan of C. S. Peirce, I'm surprised that, at least triadic relations, aren't investigated as much as binary relations are. What I mean is that with binary relations, they have already been ...
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3answers
884 views

Inference rules for quantifiers in logic

I have come across an inference rule that if I had statements like: Not all are birds which translates to ~(x)Bx, is equivalent to, Some are not birds which translates to (∃x)~Bx. According to this ...
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3answers
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If the premises of an argument CANNOT all be true, then said argument is valid

Based on the fact that a deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false, I am ...
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2answers
337 views

Step by step natural deduction: (T > E) ^ (A > L) /… (T v A) > (E v L)

I'm having trouble proving the following using natural deduction: (T > E) ^ (A > L) /... (T v A) > (E v L) I checked the answer but I didn't quite understanding the reason why the proof progressed ...
3
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2answers
260 views

References for the Realism/Anti-Realism debate in Logic

The concept of anti-realism in logic seems to be an interesting and growing idea. I'm looking for references (papers, books, authors...) regarding the debate between realism and anti-realism but ...