Questions tagged [logic]

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

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Trying to understand the fallacy in my inductive reasoning regarding this conclusion?

Consider the following statements: Anna told you she failed her physics midterm. Anna hasn't been in physics class since the teacher graded the exams. Anna has been in sociology class, which meets ...
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Is this a fallacy?

Julie wrote in her diary. At the end of his life, James asked God to forgive him for his sins. There is further historical evidence to show that James performed various public welfare activities ...
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Do you know any Fitch proof for ~p=>(p=>q)?

Please, somebody know A FITCH proof for this tautologu?
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Logic problem about user objects

You have 100 user objects, 20 contains age, 35 contains gender and 15 contains both . How many have no property set ?
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Approximately directed graph of logic types

I'm not sure if this is the right stack to post this question. Given there are many types of logic; Syllogistic, Symbolic, Modal, Deontic, Temporal, Epistemic, (non)monotonic, formal, informal, FOL, ...
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How can I prove A(x) from ¬∀x(Q(x) → x 6= a)? [closed]

I am trying to study for my exam Monday, and I was doing some exercises but I got to this one and I can't figure out how to get to A(X) from the premise ¬∀x(Q(x) → x 6= a) using Fitch proof system, ...
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Did Zeno of Sidon really write that any geometrical system must have some unstated assumptions?

According to this site Zeno of Sidon argued that even if we admit the fundamental principles of geometry, the deductions from them cannot be proved without the admission of something else as well ...
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Why is the class of basic statements permitted by “p” a subclass of the class of basic statement permitted by “q”?

Excerpt from section 37 "Logical Ranges. Notes on the Theory of Measurement" of "The Logic of Scientific Discovery": If a statement "p" is more easy to falsify than a ...
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Understanding [(a→b).(c→d)] formula in section 36 of The Logic of Scientific Discovery

Excerpt from footnote 1 in section 36 of Popper's "The Logic of Scientific Discovery": In the present section, the arrow is used to express a conditional rather than the entailment relation....
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How to prove (∀x)(∀y)(Fx⇒Gy) form (∀x)(Fx⇒(∀y)Gy)? [closed]

I wrote this. Is it a correct answer? 1 (1) (∀x)(Fx⇒(∀y)Gy) A 1 (2) Fa⇒(∀y)Gy 1 ∀E 1 (3) Fa⇒Gb 2 ∀E 1 (4) (∀x)(Fx⇒Gb) 3 ∀I 1 (5) (∀x)(∀y)(Fx⇒Gy) 4 ∀I
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What is 'expendable' in logic and how to explain 'tautology' given this image?

This image is from http://www.nfillion.com/index.php/teaching/9-logic-112. According to this, a proposition can have 4 basic properties: (1) necessarily, (2) not possibly, (3) missing, and (4) ...
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Is it consistent to say “X is possible but false”?

Is it consistent to say something like "Possibly there is a cat in my room, but in fact there is not"? Basically, is it consistent to assert that something is possible but in fact not the ...
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Difference between Tautology and Circular Reasoning

Often it is considered that a tautology is the same as a circular reasoning. However, in the Wikipedia entry of Tautology (language), it mentioned that circular reasoning and tautology are different....
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Structure of a deductive argument

I wonder if this is true for all deductive arguments, a deductive argument must have at least one premise where the term "ALL" or "NONE" or an equivalent word appears Is it true? ...
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Does philosophy fall apart without the law of identity?

What would happen to all of philosophical thinking if the law of identity, i.e. 'each thing is the same with itself and different from another', were false?
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2answers
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How do I prove ∀x(A(x) -> B(x)) from ~∃x(A(x) ^ ~B(x)) using a fitch proof?

What would the formal fitch proof for this be? This question came up in my practice problems and I'm really stuck on how to proceed. I'm assuming that you start with an assumption, but I can't figure ...
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Is it possible and meaningful to substitute the Laws of Identity into the variables of the Laws recursively?

Normally when working with logical formulae, we can substitute other formulae into the variables. For instance: Let p≡avb, q≡m∧n, then (p⊻q)↔(avb)⊻(m∧n). This ability to perform substitution is a ...
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Principle of Parsimony and Epistemological Economy

Why aren't definitions in other sciences (especially humanities) parsimonious in that they word themselves so as to provide the least necessary&sufficient logical conditions? The Principle of ...
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Looking for the correct english term for

I just remembered a conversation I had (in german) about 18 years ago and the other person used the (german) term "All Theorie", which in this context was not related to the theory of ...
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Is perspective a human limitation or a property of reality?

This might be an unremarkable observation but the further away someone is to an object the smaller it becomes and vice-versa. From an evolutionary standpoint it doesn't seem to be any type of benefit ...
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Why is it that the statement “All goblins are yellow” does not contradict the statement “All goblins are pink?”

From what I know, I think it has something to do with vacuous truths, but my understanding is not quite there yet.
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1answer
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Non-equivalence of `i`-form and a claim of existence

What's the difference in meaning between an i-sentence and its corresponding existential claim? In traditional logic, the following inference is valid All As are Bs. AaB ----------------- --...
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Does it hold that everything exists necessarily?

In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor. Here’s a quick sketch of one such argument. First, the following seems to be a logical truth: ...
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Optimal truth assignments for minimizing variation from credences

Suppose I have a set of propositions and "exogenous" credence levels for each proposition i.e. how likely I think it is to be true. Then suppose Ι know that certain logical relations hold ...
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How are objective probabilites and statistics (frequency in the world) of groups related to individual cases?

I'm a bit confused about why frequentist measures of probability based on groups are relevant to individual cases. It seems that moving from the group to the individual is somehow a violation of the ...
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67 views

an argument that is clearly valid but invalid in a sentence logic

I was reading these paper(dont really remember the title) it stated that there are simple arguments that are clearly valid but would be counted as invalid in the sentence logic system it was using. i ...
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List of books which teaches historical Aristotelian logic

Background: I want to study philosophy and I think a good way is to first learn logic, so I tried reading The Categories. But even after trying so hard, I didn't understand it. The writing is very ...
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Good (intro) textbook for deontic logic

I've read 90% of Sider's Logic for Philosophy and thought it was great - very lucid. Assuming I am more or less familiar with what's introduced there, are there any great resources out there for ...
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Is 1=2 a logical contradiction, or merely a false statement?

I know that (1=2 AND NOT 1=2) is a logical contradiction, but what about 1=2 by itself? Is it a logical contradiction, or merely a false statement? And what about something like NOT 1=1?
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2answers
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Formal Proof and Russell's paradox?

I am a little thrown off with this. Can we express Russell’s paradox as "A dog chases all and only those dogs that don’t chase themselves"? What is a formal proof showing that it is ...
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Term Logic Paraconsistency — Is it just a meta-level manifestation of existential import?

This lecture by Graham Priest contains an interesting claim, namely that term logic is paraconsistent. I have two questions about this: Is paraconsistency in this context ever considered a meta-level ...
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What type of logical fallacy happens here?

This has been going on a lot lately in my country. Usually, in a discussion where some antisocial behavior of an organization is being criticized, a supporter of the organization, usually a member of ...
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Same vs identical vs equal objects

1st case Consider two objects made from the same factory without any difference (an ideal scenario). Can we say that the two objects are the same? I would say no because one may be produced earlier ...
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Is the material implication the correct model of conditional reasoning in mathematics?

Question: Do you believe that the material implication correctly models the kind of conditional reasoning necessary in mathematics to prove a theorem? Example: If x > y and y > 0, then x > ...
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How does Consequentialism handle uncertainty?

E.g. Suppose you are a Consequentialist faced with a variation of the trolley car problem. Your options are to save five people with a 20% likelihood or one person with a 100% likelihood. Which option,...
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Is there an issue with the Socratic method arguing against points?

So, I've noticed something, looking at the classic example: Do the gods know everything? Yes. Do some gods disagree with others? Yes. So gods disagree about what is true? I suppose they must. So gods ...
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How to prove (A v B), (A → C), (B → D) therefore (C v D)

Obviously since A → C and B → D then if A v B one of C or D must be true. My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
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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 ...
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Derivation using inference rules

Suppose I have the premise: ~(AvB).(Negation A or B) How can I get to the conclusion: A<=>B (A if and only if B) using inference rules like introduction or elimination and also ...
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Hypothetical syllogism

So hypothetical syllogism is: if a then b if b then c so, if a then c . According to wikipedia, "In short, it states that if one thing happens, another will as well. If that second thing happens, ...
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What relationship exists between logical and. material Implication (Conditional)? Can you please represent both conditionals in a truth table?

Can someone help me derive the truth table of the logical conditional from the material conditional? Given the argument: S:= {A1, A2, ..., An |= C}, where A1 through An are premises and C is the ...
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Why is the definition of the real numbers not contradictory? [closed]

I understand that a set whose members can, in principle, be enumerated (by having a formula) can be considered as a well-defined set. Therefore, set of all even numbers, multiples of 3, and so on ...
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“This sentence is true”. Is there a word for this class of statement?

Is there a term that means "A self referential statement which is true if (and because) it is true and false if (and because) it is false"? "This sentence is a lie" is a paradox in ...
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How to get proof using proof editor and checker

How can I use Natural deduction proof editor and checker or The Logic Daemon to derive the given conclusion from the given premise: (∃x) ( Fx ∙ (y) (Fy → y = x) ) / (∃x) (y) (Fy ≡ y = x) It tells me ...
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Do contemporary logicians generally claim that classical logic can be simply reduced to these 5 logic principles?

Do contemporary logicians generally claim, as Wikipedia does, that classical logic can be simply reduced to the 5 logical principles below? Or is it more complex than that and are there principles not ...
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Having trouble paraphrasing sentence

F: French wins gold medal G: Germans win gold medal D: Danish win gold medal I have to use truth connectives to paraphrase: They will not all win gold medals I am thinking when paraphrasing it , one ...
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What are some logic rules that are true for every kind of logic?

What are some logic rules that are true for every kind of logic? Some rules from conventional logic are ignored like in paraconsistent logic, but I am wondering if there are logic rules that are true ...
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What is the relation between a priori and tautologies?

I have just started learning Epistemology. I am not sure about the relation between a priori and tautologies. My textbook has given definitions for a priori and tautology. A priori: knowledge which is ...
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What does it mean for two distinct people to know a fact?

Let there be two people A and B. They both encounter a strange object O. What do they know about each others knowledge about O? More strictly, we are speaking of a situation where, say, you and me ...

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