Questions tagged [logic]

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

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2answers
550 views

What are the conditions for RAA?

My textbook states that: In this case, however, what about situations where we can get Q ^ ~Q (sorry, unfamiliar with this formatting) without depending on P? For instance, the proof of EFQ: 1 (1) ...
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3answers
167 views

Aristotle's Logic and Human Thought

Is Aristotle's logic sufficient to model human reasoning? If not, why not? Are there counter-examples, certain cases where we reason differently? Let's assume we're talking about sound reasoning,...
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1answer
52 views

Negation of equality in FOL

I am unsure if there is a rule in FOL that allows me to make this derivation ¬(a = b) Assumption a ≠ b ??? Is this derivation allowed, and if so what notation should I use to justify it?
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2answers
52 views

Solving a proof in which the goal is the negation of a variable in Fitch

I'm working on an assignment and I'm stuck on this proof. I feel like I'm on the right track but I can't find the way to prove the goal. A ^ B (A ^ ~C) --> ~D A -> ~C (B ^ E) --> (C v D) ~E I ...
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1answer
92 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 ...
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1answer
70 views

Can a different universe be built with three dimensions? [closed]

Can you theoretically create a universe that will have the same dimensions but will look different? For example, a paper that has a limit, or another similar dimension can it be different?
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4answers
105 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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2answers
2k views

Fitch Proof - LPL Exercise 8.17

I am currently finding the third part of this exercise (Conditional 3) difficult to prove. I was sure that my proof was correct, but the Fitch program is saying otherwise. I am finding it ...
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3answers
201 views

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

Note: There is a lack of consistency regarding symbols for modal operators. Hughes and Cresswell use a different symbolization schema than many and a comment about L & M may provide clarity ...
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1answer
244 views

How to prove □Q from P→Q and □P?

Given P→Q, and □P, in what systems can we conclude □Q? I want to know in which system the consequent is derivable from the premises and in which it is axiomatic (or perhaps we can include it as an ...
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1answer
111 views

What argument styles have only recently been labelled fallacies?

While reading Douglas Walton's "Historical Origins of Argumentum ad Consequentiam", I realized there is at least one argument style that appears reasonable but which has been labelled as a logical ...
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1answer
93 views

What kind of fallacy or false logic is this?

I got into an argument with a friend on MMA fighters and said that any fighter that gets caught PEDs should probably have an asterisk by his record. His defence was that could I say for sure that ...
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5answers
225 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 ...
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1answer
542 views

Why is the statement false: If (A⊃B)∨(A⊃C) is true, then A implies either B or C

I'm reviewing my previous exams for the final, and the only two true or false questions that confuse me are: If (A⊃B)∨(A⊃C) is true, then A implies either B or C. (P⊃Q)∨(P⊃~Q) means P⊃(Q∨~Q). The ...
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1answer
79 views

Is there inherent selfishness within altruism? [closed]

Recently I have been noticing a theme on my social media. There is a post of someone passing away. Within that post the comment section is filled with comments such as: "I lost my mother 4 years ago. ...
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2answers
104 views

‘The claim that I had an affair with Miss A and that I didn’t father her child is false’

The prosecutor asks, ‘Did you father the child of the murdered victim Miss A?’. Mr. N replies, ‘The claim that I had an affair with Miss A and that I didn’t father her child is false’. In response ...
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2answers
55 views

Recursive definitions (a couple questions based on them)

From the book Logic, laws of truth, by Nicholas J.J Smith: What does Smith mean by recursive definitions? Why does it matter? How do you make recursive definitions for something such as: a) the set ...
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2answers
277 views

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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8answers
286 views

Does believing in a Christian God logically imply believing in miracles?

Assume you are a Christian and you believe that the descriptions of the life of Jesus are facts. Things like turning water into wine magically, walking on water and other miracles seem to be ...
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1answer
68 views

Boolean equation Indexing exercise

By the method of indexing, prove the following Boolean equation to be valid: (A ∪ B)′ ∩ C = (C ∩ A′) ∪ (C ∩ B′) What I tried to do - but somehow it doesn't go right, where did I made a mistake, ...
4
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1answer
210 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 ...
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4answers
311 views

How should we understand the oracle's dilemma in making a prediction?

Let's look at a thought experiment: There is an oracle who has exact knowledge of the state of a deterministic universe, so her predictions about the universe's future have always turned out to be ...
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1answer
178 views

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 ...
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5answers
631 views

Must infinity involve repetitions?

Infinity for Nietzsche in at least one line of argument involves the eternal return; he refers to it in the Die fröhliche Wissenschaft and Also sprach Zarathustra; most completely in his Notes on the ...
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1answer
45 views

Is infinity possible [duplicate]

Can there be such a thing as infinity if the universe isn't growing constantly? Or is it a finite universe? I tried to ask myself this but is it really possible to understand?
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6answers
6k views

If everything is possible, is it possible for something to be impossible?

If everything is possible, is it possible for something to be impossible? Possibility and impossibility are modal notions; and are dual in the usual formulation; the SEP remarks: It would seem to ...
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2answers
152 views

Do α and β entail each other?

Show whether the following is true or false: α |= β or β |= α, for any two formulas α and β I'm assuming here that α and β are formulas, not a set of formulas. My thought is that I can prove that ...
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5answers
238 views

What CAN a sentence say about itself? Can a sentence say about itself that it is false?

Lets attack the easier part first: If a sentence can say that it is false then there is a sentence x such that 1) x = "x is false". But according to Leibniz law we then have that 2) x is true IFF ...
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3answers
2k views

Multiple quantifiers and negation

In a formula of the form ~ for all x, for all y (l(x,y) -> r(x,y)) how do we apply negation to the formula "(l(x,y) -> r(x,y))" ? And similarly if we have a formula with different quantifiers, such ...
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6answers
1k views

What is the philosophical study of classification called?

What is the philosophical study of classification called? Taxonomy? Taxology? "Category theory"? "Classificology"? Logic? And which philosopher(s) studied exactly what it means to classify? How we ...
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6answers
1k views

Why are homologies evidence for evolution instead of common design?

I have seen some creationists arguing that when evolutionary biologists use homologies (anatomical or genetic) as evidence for evolution, they are committing the fallacy of affirming the consequent. ...
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1answer
401 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 ...
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3answers
174 views

New riddle of induction; does the observer know the arbitrary time t?

Wikipedia, in "New riddle of induction", sets out Nelson Goodman's paradox as follows: Goodman defined grue relative to an arbitrary but fixed time t as follows: An object is grue if and only if ...
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1answer
71 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 ...
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2answers
24 views

How do I prove ~(A & B) therefore ~A V ~B using natural deduction? [duplicate]

Been trying to prove this one for a while now and can't crack it. Assume ¬(A ∧ B) Derive ¬A ∨ ¬B
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2answers
154 views

How do I solve this formalized argument by drawing conclusions from inference rules?

I am given a conclusion and three premises, but I have to draw more inference rules from the three premises in order to prove the conclusion is in fact true. How do I draw the conclusion from the ...
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1answer
92 views

Problematic conditional argument: what is the logical form and is it valid?

I'm trying to reconstruct an argument. The argument is not about what should or shouldn't be done. As you can see the antecedent is never being picked up in the next premise. So it's just a sequence ...
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3answers
74 views

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 ...
2
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1answer
258 views

How does a truth tree provide positive and negative effect tests for implication?

I'm trying to prove that the truth-tree method can be used to give a positive effect test for implication, and a negative effect test for non-implication. I've been given the fact that The truth-tree ...
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1answer
69 views

Please what do we call this type of hypothetical statement?:

"It is certain you have a nose when you can smell but not everyone with a nose can smell". Or "It is certain you have a brain when you can think. But not everyone with a brain can think" Note: As I ...
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0answers
50 views

Some examples of philosophies that consider nonexistence the same as existence?

Can you give me some examples of philosophies that consider nonexistence the same as existence? I thought that maybe some paraconsistent systems (https://en.wikipedia.org/wiki/Paraconsistent_logic) ...
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1answer
88 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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1answer
136 views

Do you know of any mathematical theorem whose proof relies on the use of the principle of explosion (ECQ)?

Ex contradictione (sequitur) quodlibet (ECQ) is almost universally recognised in mathematical logic as a valid inference. In symbolic logic, this inference is usually expressed in the following way: ...
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2answers
52 views

Structure of an if and only if proof

I am trying to get this proof to work out and so far I feel like I have the first part right but I'm stuck on how to get the A→B part.
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1answer
118 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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0answers
70 views

Is there an Abstract/Concrete Gray Area?

In natural language and daily life, it has become prevalent there is a class of entities which do not follow the abstract concrete distinction. Many people refer to abstractions that exist in time. (...
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15answers
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Does a negative claimant have a burden of proof?

I have often heard it said that the burden of proof is on the positive claimant but not on the one making a negative claim. A person claiming, "God exists" has a burden of proof but not a person ...
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3answers
292 views

Fitch Proof Question

I'm having trouble with a proof and I'm not sure if it's valid or not. If it appears to be invalid, we are supposed to assign names to the letters in the proof and check it in a World, but when I do ...
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3answers
20k views

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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0answers
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Traditional beginner's commentary on Aristotle's categories [duplicate]

I am looking for a traditional beginner's commentary on Aristotle's categories in order to start learning Aristotle's system of logic. Even better would be a "road map" for studying Aristotle's logic ...