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Questions tagged [logic]

Logic is the study of formal systems of reasoning, especially of the deductive variety. It is one of the few fundamental philosophical subdisciplines, along with metaphysics, ontology and aesthetics. Logic has taken on considerable importance in recent mathematical developments, and one of the ...

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Justification for axiom OB-RE in deontic logic

Let OB p denote "p is obligatory". Axiom OB-RE is (p ↔ q) → (OB p ↔ OB q). This axiom seems false to me (under the interpretation of obligation). For example, let p denote "don't lie to me" and q ...
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Grandfather Paradox and Causal Loop

How does the grandfather paradox cause a causal loop (and therefore a bootstrap paradox)? https://en.wikipedia.org/wiki/Grandfather_paradox
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Language Proof and logic problem 16.31

With this problem, I can't seem to figure out why it isn't working out. If anyone has any advise it would be super helpful.
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Is Ross' paradox really a paradox?

Consider the following disjunction introduction: Your room is clean. Therefore, your room is clean or your house is burnt down. Ross' paradox allegedly arises when applying this inference to ...
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Is there anything wrong with this argument?

The Constitution of the Russian Federation says, in Chapter 1, Article 1: The Russian Federation - Russia is a democratic federal law-bound State with a republican form of government. The ...
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proof for relational predicate logic

I have been working on this problem for over an hour and I think I have simply missed something. I need some help. The rules I am allowed to use are the Basic Inference rules (MP, MT, HS, Simp, Conj, ...
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Why can't existence be expressed in linear temporal logic?

In some circumstances, existence cannot be expressed in linear temporal logic. I don't understand why it can't be constructed with negations and global quantifiers. For example, the wikipedia page (...
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What is the difference between inference and deduction?

This question contains my question, but tries to accomplish too much at once; I would like a clear answer to the distinction between inference and deduction. What is the difference between coming to ...
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Language proof and logic 15.16 [duplicate]

I don't know how to make the middle section work out please help
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~(~P&Q) & ~(P&Q) : Prove ~Q

This must be proved using only negation, double neg.Intro, double negation Elimination, indirect proof, conj.Intro, and conj.Elim.
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Language proof and logic Chapter 15 question 21 how?

I'm really not understanding the set up of how to go about solving this problem any help is welcome
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In Fitch, how does one prove ¬(B ∧ C) from two premises (A → ¬B) and (¬A → ¬C) [closed]

Help me out please!! I have been trying to solve it for hours
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Language proof and logic Chapter 15 question 16 help

I'm trying to go about solving this problem but I'm having problems even knowing how to approach it. Can someone help me to set it up? Here is the premise: ∀x∀y(x ⊆ y ↔️ ∀z(z ∈ x ⟶ z ∈ y) Here is ...
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What would be an intuitive understanding of Peirce's law?

Wikipedia describes Peirce's law as In propositional calculus, Peirce's law says that ((P→Q)→P)→P. Written out, this means that P must be true if there is a proposition Q such that the truth of P ...
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language proof and logic chapter 13 question 49 Help

Premises: ∃xP(x) ∀x∀y((P(x)∧P(y)) → x = y) Prove: ∃x(P(x)∧∀y(P(y) → y = x)) I've started it but the end is starting to get super muddy and not work out and I don't know where I went wrong.
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language logic and proof chapter 12 question 49 and question 50

I've been working on this and I can't seem to figure out what exactly is going wrong can anyone help?
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In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?

I can't figure out how to prove that formally. Please, help!!
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What is the best proof that 1+1=2 by a person who was not Bertrand Russell?

The question says it all. Besides Russell and Whitehead, who are the philosophers and mathematicians who demonstrated successfully that 1+1=2? Extra bonus (i.e., a warm feeling inside) awarded for ...
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How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’

What would a formal Fitch proof for this look like? I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it. I started with this, but I don't know if I am doing the right thing, and where to go ...
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Difficulty with understanding the semantics of the following equivalences

I know that the rules for removing quantifiers from the antecedent of a conditional are as follows: (∀x)φ(x) → ψ ⇔ (∃x)(φ(x) → ψ) and (∃x)φ(x) → ψ ⇔ (∀x)(φ(x) → ψ), provided that x is not free in ψ. ...
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Can the conclusion of an inductive argument be that there is only one exception to the list of evidentiary claims?

Can this be an example of an inductive argument? Premise 1: Country A rejected idea Z. Premise 2: Country B rejected idea Z. Premise 3: Country C rejected idea Z. Premise 4: Country D rejected ...
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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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What's wrong with the logic in the followin ''paradox''?

The apparent paradox pertains to the homesteading principle. This isn't a question about the morality/immorality of homesteading, or ownership, or use, etc, just the logic behind it. The concept: ...
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Fitch Proof by Contradiction help

Hi, I'm pretty new to writing formal proofs and I was wondering if I could get some help solving this question. I've set up the problem and I was thinking of perhaps proving it by contradiction that ...
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1answer
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Is there a logical fallacy for rejecting “A not B, because A precludes B?”

I'm not sure if I'm asking the right question here, but I'm wondering if there is an actual fallacy to describe this situation.
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Fitch Biconditional Proof Help?

Hi, I'm starting to learn formal proofs using Fitch, but I'm having a bit of trouble figuring out my arguments. I've generally mapped out the subproofs I was considering to use, but I'm unsure how to ...
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Informally explain the proof of the diagonal lemma

I am reading this proof of the diagonal lemma and I do not understand what is happening here. Could you informally explain what is the strategy here? I would appreciate it if you went step by step. I ...
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1answer
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Does following logic necessarily require one to conclude that they are objective and have no bias?

In social psychology, naïve realism is the human tendency to believe that we see the world around us objectively, and that people who disagree with us must be uninformed, irrational, or biased. It is ...
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888 views

Is there a concept that relates to the idea of a “snuck premise”?

In this video around 6:00 into it, Charisma on Command channel, "7 Reasons Ben Shapiro Is So Dominant in Debates" https://www.youtube.com/watch?v=JY5t6iUzajk the concept of a "snuck premise" is ...
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2answers
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Can something proved by contradiction always be proved without a proof by contradiction?

Proof by contradictions work by assuming that something is true, and then using logic (along with other assumptions which you know are true) to show that that leads to a contradiction, thus proving ...
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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 ...
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Does Tegmark himself include paraconsistent mathematical structures in his mathematical multiverse hypothesis?

Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like ...
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Do mathematicians use logic when adding things up?

I asked a similar question recently, and it was closed. So, bear with me. When two things are materially equivalent we don't add anything to work out how much we have of both together, right? If ...
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How to solve the derivation?

Derive the following without assumptions: ¬∃xFx↔∀x¬Fx How do I solve this derivation?
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Is there a summary of Russell’s Principia Mathematica?

Perhaps better, is there an accessible version of the Principia? I am looking for a summary that would summarize and clarify Russell’s reasoning behind his famous conclusion that 1 + 1 = 2.
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Is this an Affirming the Consequent fallacy?

If a Company doctor is competent, then he or she has completed the Company's "Fitness-for-Duty Examiner" certification training. [If P then Q] Company doctors are all Certified Fitness-for-Duty ...
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Is logic a consequence of structure of language i.e. syntax?

I was reading the paper An elucidatory reading of the Tractatus and in page-3 section- Ineffabilist Readings, it was written "The order in our propositions, which renders them capable of thus ...
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Are there “partially explosive” logics?

Roughly speaking, I'm wondering if it's possible to meaningfully grade different systems on how explosion-tolerant they are. In classical sentential logic and intuitionistic sentential logic, a ...
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How do you prove law of excluded middle using tertium non datur?

I’m in my second year of an undergraduate philosophy degree. Last year we did classical logic (TFL and FOL truth tables and fitch style natural deductions). This year, one of the topics we are ...
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Can “free will is an illusion” be proven logically? [closed]

What is your view or argument?
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132 views

What is the subject of Tractatus by Wittgenstein?

Is Tractatus about the Philosophy of language or Philosophy of logic. I was hearing John Searle's lecture and he said there are two strands in Philosophy of language :- 1. Logical theory of language 2....
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Completeness/Soundess of Second Order Logic

I recently read that Gödel's incompleteness theorem entails that second order logic cannot simultaneously hold the traits of: (i) completeness, (ii) soundness, and (iii) effectiveness. However, I saw ...
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What criteria does Frank Jackson give in order to assert the negation of a conditional?

In Frank Jackson's paper, On Assertion and Indicative Conditionals he gives a criteria for when one should assert a conditional (material conditional). This criteria is given in terms of conditional ...
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Can we define this set?

Given an infinite set S in some universe U, construct the set of complementary pairs C: {{A,Ac}} where A,Ac∈P(U), the power set of U, and A or Ac is contained in S, not necessarily a proper subset ...
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What is compactness?

The proof, formal definition and academic explanations are easy to find but hard to understand. Can you please explain it in ordinary language with clear examples? See the following references: ...
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How does one prove ‘(B→C)→¬A’ from ‘(A→B)∨C’ and ‘(A→¬C)’ in Fitch?

I am trying to work my way through this Fitch proof, and I am not sure what I am doing wrong, but I keep getting stuck no matter what I try. First attempt: Second attempt:
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Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?

Tegmark's mathematical multiverse hypothesis assumes that all mathematical structures exist as universes But do you know whether his hypothesis also allows/accept universes described by other types ...
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How are the assumptions underlying logic chosen?

Logic works based on certain assumptions about its rules. How are these axiomatic assumptions selected in the first place, given that a system of logic does not exist prior to the point of selection? ...
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Recommendation: Second Order Logic textbook

I'm looking into Universalist Realism, Nominalism, Trope theory and the application of Second Order logic to each of them, however I have little/no experience with Second Order logic. Please let me ...
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Is complete isolation possible?

Imagine an ideal box, whose contents are perfectly isolated. Whatever is inside it, it has not, has had or will have any relations with the rest of the universe. We could say that its content does not ...