Questions tagged [logic]

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

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Why are there two fundamental laws of logic?

We have the law of non-contradiction and the law of excluded middle, but looking at it, it seems that both of them are the same thing, or at least one of them logically implies the other. Is there a ...
66 views

Which is the correct/better way to represent the following argument?

p1. If an omni-god exists, then evil cannot exist p2. evil exists c. an omni-god does not exist I'm pretty sure its modus tollens and is represented as follows, p -> q ¬q ¬p But my friend is ...
31 views

Logic terminology: does “conditional” etc refer to the operator or the WFF?

To be precise.... Do the terms we use to talk about the truth-functional operators (conditional, negation, conjunction, disjunction, biconditional) refer to the operator in isolation, or the WFF that ...
85 views

What paradoxes arise from quantifying over EVERYTHING?

This question is in context of the umbrella view of objects, that there exists a general category that everything falls under. Here are the quote and link that peaked my curiosity. Finally, note ...
44 views

Correct way to Interpret statements not containing Quantifiers

What's the correct interpretation of "seemingly universal" statements that do not use quantifiers? For example, p:"Roses are red". Is this equivalent to q:"All roses are red."? What's the correct ...
279 views

Can all formal systems be generalized as specified relations between finite strings? [closed]

https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics) In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be ...
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A Paradox for Anti-Realism?

Semantic Anti-Realists hold that a claim has a (constructive) proof if the claim is true. I wonder whether this position runs into a version of Yablo's supposedly non-circular version of the liar ...
96 views

Suppose ‘Some S are P’ is true. Determine the truth-values of the following (if possible)

I just want hints to make sure I'm going in the right direction. All S are ~ P. I got true Some S are not ~ P. I got false No P are S. I got false Some P are ~ S. I got true No S are ~ P. I got false
108 views

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 ...
131 views

Finite Alphabets

This is a question based on section 2.5.6 from the book Logic, laws of truth, by Nicholas J.J Smith, page 48. What does Nicholas mean when he says: Note that we can further specify exactly what we ...
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Determining the validity of the arguments in the exercises of The Norton Introduction to Philosophy

The first exercise is "Spot the valid argument(s)." The following are the arguments. I think all of these arguments are valid. Am I right? (i) If abortion is permissible, infanticide is ...
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Material vs formal logic?

I would like to know how material logic differs from formal logic. From the little that I'm aware of, it is apparently the case that material logic concerns itself with the truth of the content of an ...
272 views

Is there a generally agreed upon solution to Bradley's Infinite Regress without appeal to Paraconsistent Logic?

I'm interested in Priest's solution using paraconsistent logic, but before I embark on that, I wanted to know if there was a generally agreed upon solution in more "classical" schools of thought. ...
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Are accurate statements about fictional entities false?

"Homer Simpson is Marge Simpson's husband." Is this a true statement since it accurately describes the fictional character, Homer Simpson, or is it false since there is no Homer Simpson in reality to ...
187 views

A comprehensive introduction to relationship between math and experience

I am a mathematician with interest in physics and pure logic and exists one problem: the connection between math and physics. Math concerned on pure universal truths and physics concerned on ...
313 views

Why does the Principle of Explosion not make Mathematical Logic inconsistent?

In Reductio ad Absurdum (RAA), we determine that a proposition P is false when it derives a contradiction. If we use this same derived contradiction as the premises to the Principle of Explosion (POE),...
276 views

Noam Chomsky vs 9/11 Truth movement. Is Noam's Logic legit?

When Noam Chomsky was asked about what he thought about the collapse of building 7 at the University of Florida in 2013, he replied that only a minuscule part of the scientific community backed up the ...
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What is the difference between logic and reasoning?

What is the difference between logic and reasoning? I can makes sense of what logic is about. But when it comes to reasoning what does it do more than logic does? Can you give an example which shows ...
164 views

How to denote the idea of nothingness in formal terms?

I was thinking about the question "Why is there something rather than nothing?" , and have read about some theories that existence is the case because non-existence is logically impossible So, I ...
264 views

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 ...
100 views

What are the problems with Tractatus?

Tractatus, in a way, says World isn't what is out there, but is the world you imagine. World is what you would tell another person when you will recount this world. (It is what you would 'know' of the ...
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Is there a difference in the definition of “some” between Aristotelian and modern logic?

My logic prof told me that "some are" does NOT necessarily mean "some are not".... Ie. it could possibly mean "ALL are", but not necessarily (ie. we are not certain that all are) However, recently I ...
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Suppose you know the premises of an argument are inconsistent. Do you have to do a truth table to know whether it is valid or invalid?

Suppose you know the premises of an argument are inconsistent. Do you have to do a truth table to know whether it is valid or invalid?
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Is double negation always applicable to commitments?

If I commit to X, am I always committing to not ~X? In classical propositional logic, double negation always the same as not negating at all. I'm curious if this principle applies to commitments. ...
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What is the difference between the resolution rule and the elimination in natural deduction?

I understand that elimination is: p v q ¬q then p and resolution is: q1 v q2 v q3...qn ¬q1 v q2 v q3...qn then q2 v q3...qn I see no difference, but my teacher is telling us don't use the ...
430 views

Is there anyone who believes that all modal statements are meaningless or trivial?

It is often useful to interpret statements in various modal logics using possible-world semantics. For instance "it is necessary that P" means "P is true in all possible worlds", "it is possible that ...
76 views

What to read for an introduction on the epistemology of logic?

I would like to read about the epistemology of logic, preferably at a undergraduate level (not being a philosopher myself). What (text)book should I read for a good introduction on these topics? The ...
107 views

Why is Math not Logic? [duplicate]

So I've heard, "Math is not logic," because logic has no notion of order. However, consider the following argument: There once was a man on a mountaintop. He came down, murdered a villager's cat, and ...
320 views

Observing a zero probability event

I am not a philosopher. Just curious. From a philosophical point of view, if one observes an event with zero probability, does this immediately lead to a contradiction? For example, if you have a ...
605 views

Is the real number line actually real when we construct it?

Intuitionism is akin to constructivism in mathematics but not quite the same from what I can tell. In the usual treatment of the real line, the additional numbers are found between the rationals by ...
163 views

Mathematical proof of a philosophical theory

Can I prove a philosophical theory mathematically? If yes? How? For example, can the theory of materialism be proved mathematically?
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Multiple connectives using atomic sentences?

Can you use multiple connectives in atomic sentences? For example, consider the following transcription guide: A. The New England Patriots are the best team in the NFL. B. The New England Patriots ...
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How does one differentiate between premise and proposition?

I find it difficult to differentiate between premises and propositions. Given these statements: "If men evolved from apes then there wouldn't be any ape nowadays." "There are apes nowadays." ...
119 views

Why is Law of Large Numbers a Law and Central Limit Theorem a Theorem… when they look like the opposites?

In probabilities, the Law of Large Numbers (which has a "weak" and a "strong" version) tells that the more samples you take of a fact (under a model you state), the closer you are to the actual mean ...
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Contradictory statements with Nested Quantifiers

Edit: Thanks very much to everyone for the answers! As a follow-up question, I'm curious if there are Aristotelian methods for finding contradictories to statements with nested quantifiers. As, thanks ...
175 views

What is the difference between Herbrand Logic, Relational Logic and Predicate Logic?

I am learning a course from Stanford University, and it introduces the notion of Herbrand Logic. However in Wikipedia I cannot find a definition specifically for "Herbrand Logic", only for Herbrand ...
209 views

Why do we need Aristotle's theory of predication?

My question is about Aristotle's theory of predication. Why do we need it at all? I know it's intuitive to pick up something and say something about it like "S is P", but doesn't this lead us to ...
78 views

Are verb tenses actually irrelevant in logic?

In my Introduction to Logic course, we learned that verb tenses are irrelevant when symbolizing and deducing arguments. However, it seems to me that the verb tenses could sometimes choose whether or ...
131 views

Checking the validity of the logical conclusion gleaned from a heated conversation

I have two friends - call them John and Jane. I was recently privy to an argument concerning a book between John and Jane that went like this: John: This book did not make a single coherent, ...
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What are some benefits of a second order logic?

I have read that a second-order logic can help one define equality by quantifying over all predicates such as what is done in the following definition: (x=y):⟺[∀P:P(x)⟺P(y)] By contrast a first-...
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Does intuitionistic negation of A mean that there does not exist a proof of A?

Section 13 of Kleene's Intoduction to Metamathematics introduces briefly Brouwer's informal intuitionistic school of thought. There he writes that the interpretation of not A is meant to be taken as ...
269 views

In fitch, S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)

Construct a proof for the argument: S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R) I have gotten to the point in the illustration, but I am unable to figure out where to go from here. I get tricked up on ...
79 views

Help with an existential natural deduction proof

From the assumption ∃x∃y R(x, y) I need to derive the conclusion ∃y∃x R(x, y) From the comments: I tried to use Existential Elimination but I can't figure out how to do it properly.
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How disjunction works with the conditional excluded middle

I'm studying the semantics for counterfactuals, and I'm slightly confused about how certain inferences supposedly make the Conditional Excluded Middle (CXM) fail. Formally, we can write the ...
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A deontic premise that leads to a necessity from a permission

I wanted to devise some rules for myself, then formulate those rules using formal symbolic logic, and one of the rules that I have set for myself is : "Do not say what is unnecessary", in other words :...
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What is Robert Nozick alluding to by a “vast generalization” of Feynman’s path integral?

I was reading a book from the philosopher Robert Nozick (Invariances: The Structure of the Objective World), and there was something that confused me. Around page 159 he argues that every logically ...
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Clarifications on 1) Modus Ponens, 2) Modus Tollens, 3) Inductive, 4) Incomplete based on examples

My second lecture on Hypothetico-Deductive methods (based on Popper's falsification theory). In the class, we were given the following examples. We had to classify which examples belong to 1) Modus ...
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Does the Law Of Excluded Middle Apply to the Principle Of Identity and Non Contradiction? [closed]

This argument will seem confusing, precisely because it observes the laws of identity being subject to equivocation. If this is kept in mind, the following should make more sense and explain why the ...