Questions tagged [logic]

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

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118 views

can an argument containing a contradiction be valid argument

I know that validity has nothing with truth of the conclusion or with how good argument is in general, and an argument is valid iff the truth of its premises guarantees the truth of its conclusion. ...
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1answer
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Is my interpretation of “and” correct in these statements?

Let A mean "Equation A has a solution" and B mean "Equation B has no solution." I am a little confused, so I wrote down some possibilities and I wish to see if my interpretation of ...
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2answers
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Question about fitch 6.19 proving A or C from premises A or B and -B or C

How to prove A or C from premises A or B and -B or C. Am using fitch and have been stuck on this for an hour
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1answer
88 views

Does the truth value of a material conditional depend on context?

Suppose the following material conditional "If 1+1=2 then Moon is made of cheese". The antecedent refers to the context of mathematics. In that context "1+1=2" is true. Whereas &...
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1answer
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Requesting help with designing curriculum (Logic)

I am currently a math major in university who wants to design my own area of study/major, specifically in Logic. I was wondering if I could get some help on how Logic sets itself apart from philosophy?...
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68 views

Baconian Logical Fallacy

I have been reading about logical fallacies lately, and I saw the Baconian fallacy listed here (of course on everyone's favorite site, Wikipedia). The description provided reads: "using pieces of ...
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1answer
61 views

What is the difference between these 2 sentences with quantifiers?

I'm practicing writing FOL sentences and I have the following sentences. The first sentence is the solution I provided and the second is the correct solution ( per the solutions manual).The difference ...
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1answer
72 views

Is this a fallacy, and if so which?

Recently, I had this conversation at the workplace: me: I'm calling you because John needs access to this resource. I have access already and we need it to complete our work. her: Why do you have ...
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2answers
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I need help using the rules of implication/inference to construct a proof for the following argument: [closed]

I need help using the rules of implication/inference to construct a proof for the following argument: 1.(A ∨ B) ⊃ (C ∨ D) C ⊃ E C ∨ ~F A ● ~E F ∨ (D ⊃ Z) .: Z KEY: Tilde (~) forms negations (“...
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1answer
102 views

Is logic part of Philosophy or Mathematics?

Is logic part of Philosophy or Mathematics? I asked this question "Does programming use logic more or mathematics more" and users on some site insisted that logic was part of mathematics, I ...
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1answer
44 views

Are actions self-referential? [closed]

Someone recently told me that "actions are self-referential" (which means that we do not have to specify a particular actor to know whether an action is possible or not). He made it sound as ...
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1answer
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Does “business logic” mean formulation of business by logic? [closed]

I have heard that ethics can be formulated by logic. So I guess there are many things which can be formulated by logic. Is it the same case for business? Does "business logic" mean ...
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2answers
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Is a vacuously true argument a valid argument? [duplicate]

From what I know, given some argument, the argument is valid when it has true premises that lead to a true conclusion. Now, what if the premises were false? I mean, the conclusion would be vacuously ...
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170 views

How do we know certain things to be “obvious”, in general?

Sometimes while discussing things, we might come across statements which are pretty obvious to us. And, in English, sometimes we use statements such as -- "It's pretty obvious". But without ...
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Intro Natural Deduction Problem: Given premise (p -> q) -> p show p using deduction

This is from the Daniel Bonevac Deduction text, page 122 #12. Given premise (p -> q) -> p show p using deduction. I can do this using made up rules on steps 4+5, not given in the book. The other ...
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1answer
43 views

Negation of the Rule of Implication proof

tried forever to figure out a solution to this problem. It's based on the rule of Material Implication with a negation in front of both sides. Namely the premise is ~(A>B) with the goal solution ...
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1answer
39 views

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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75 views

Are axioms more important than definitions?

To prove a theorem in mathematics we usually use our axioms, definitions and other already proved theorems. Suppose we wante to prove a specific theorem and we haven't prove any other theorem and also ...
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3answers
143 views

What is the definition of intension?

I have read in philosophy books about intension. But no one has defined it rigorously. What does it actually mean? I asked in a previous question about identity of intension. If this question is ...
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1answer
119 views

Do mathematical objects exist after their definition? [duplicate]

Suppose we have a system with a set of axioms. Now we begined to define new terms. E.g. in maths we have a particular set of axioms and then we define what a function is. But do all the functions ...
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3answers
114 views

A possible formal failure made by Kripke?

In Kripke 's Naming and Necessity, there is a footnote says that "Lewis's elegant paper also suffers from a purely formal difficulty: on his interpretation of quantified modality, the familiar ...
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4answers
151 views

Does truth exist without proof?

When we prove something (e.g. in maths) we show that a particular statement is true. But if we couldn't prove that statement that doesn't mean that the statement would be false right? So is proof a ...
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2answers
66 views

Does the universal quantifier express existence? [duplicate]

Does the universal quantifier express existence? If I say "All dogs are cute", does the truth of that proposition require at least one existent dog? My question is different from the ...
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2answers
65 views

Show that the basic principle for negation (Γ,¬ϕ⊨ iff Γ⊨ϕ) can be deduced from:

I am now reading "Intermediate Logic" by David Bostock. I am stuck by a question. It asks: Show that the basic principle for negation (Γ,¬ϕ⊨ iff Γ⊨ϕ) can in fact be deduced from: If Γ,ϕ⊨ψ ...
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4answers
196 views

What is meant by “assume P”?

The proofs of mathematical statements of the form "If P then Q" usually start with the form: Assume P...then Q. What is meanty by "Assume P"? Should we consider P as a true ...
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1answer
84 views

What is the relationship between the primitive notion and a priori?

The primitive notion is the origin of definition to avoid circularity since definition must be defined by other terminologies which involve new definitions. So in maths we have set, point, space and ...
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31 views

Is the truth table method for valuating 0th order sentences not a proof system in its own right?

This might sound a bit opinionated or a bit too pedantic, but in every book (that I've looked at) about propositional logic, usually this chain of events happens: Discuss the alphabet and grammar of ...
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Could the axiom of infinity be in itself inconsistent?

I've seen several threads discussing the axiom of infinity but I wasn't able to find a discussion on this particular aspect. And recent conversations with some people have led me to wonder if it is ...
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95 views

Do all paradoxes of naive set theory have something in common?

If P(x) is the formula "x ∉ x", then ... the assumption that a set h has P(x) purity ... (i.e. the assumption that for all t, if t∈h then P(t)) ... implies that there exists a set k, where ...
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52 views

Play by these rules, however broken, or create new ones

Example, A: The rules are unfair, you see, only privileged few are getting the benefit. B: I don't see anything wrong with that. Either create new rules, or hustle through these and be like them. What ...
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4answers
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Is tautology for logic what theorems are for mathematics?

Consider the following statements. "If x is an integer then 3+2=5" and "If x is not integer then 3+2=5". Constructing truth tables for the above statements show that there is no ...
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1answer
121 views

Does Godel's second incompleteness theorem mean it's impossible to know whether a proven statement cannot also be disproven?

I am trying to understand Godel's Second Incompleteness Theorem which says that any formal system cannot prove itself consistent. In math, we have axiomatic systems like ZFC, which could ultimately ...
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One-paragraph explanation of the principle the counterexample by modern logicians? [closed]

Is there any good, one-paragraph explanation of the principle and importance of the counterexample in logic by a modern logician (19th to 21st century)?
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Why law of identity is formulated in terms of “things” and not statements?

The law of non-contradiction (LNC) and law of excluded middle (LEM) are both formulated in terms of statements. That is "A and not A" is always false and "A or not A" is always ...
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23 views

How to symbolize the following sentence

I need some help with the following: It is from the Logic book (4th Ed) Let A:Albert jogs regularly H: Albert is healthy B:Bob jogs regularly Given this sentence: If Albert is healthy,he jogs ...
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108 views

The concept of infinite past [closed]

Is it possible to give an a priori answer to whether or not an infinite past is possible?
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71 views

H{+}: “absence of evidence = evidence of absence?” — Is it necessarily informally logically fallacious to claim H{+}? Or are there exceptions? [duplicate]

Absence of Evidence =|= Evidence of Absence Does this proposition always hold (true), or are there exceptions? Is it a logical fallacy to claim: “absence of evidence is evidence of absence”? How is ...
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1answer
524 views

Why does Gensler's Star Test not work on some syllogisms? [duplicate]

All teachers are intelligent. All teachers are well-paid. From the Star Test, we can deduce that the argument must be invalid with whatever conclusion (according to the classical syllogism figures), ...
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6answers
373 views

Is atheism the null hypothesis on god's existence? Can the null hypothesis be accepted? Is the proposition “god does not exist” falsifiable?

 Is Atheism the Null Hypothesis?  Is Atheism Falsifiable?  Does Atheism Carry the Burden of Proof? Atheism has distinct definitions which can be categorized as follows: • Weak/Soft ...
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Help with Circular Reasoning example and whether this example is fallacious

I thought of a scenario that raised some question for me, consider you: [A] Face prejudice because of X --> [B] Makes you more inclined to assume the next person who mistreats you is doing so ...
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Has any physicist advocate for both Putnam's thesis of “Logic is Empirical” and the Multiverse?

Philosopher Hilary Putnam proposed a very interesting thesis 1, advocating that Logic itself may be empirical. I have found another interesting article 2 by the physicist Matthew S Leifer where he ...
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2answers
60 views

Do mathematicicans care about implications where the hypothesis is always false?

Suppose we want to prove the implication P implies Q. Now we can use proof by contradiction and show that there is no case were P is true and not Q is true. But this does not imply that there is a ...
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82 views

Are there famous unsolved problems in logic akin to the Millenium Prize problems?

Are there major theorems that logicians have yet to tackle? And I don't mean any problems that pertain to the philosophy of logic (i.e. logical pluralism, the nature of logical consequence, etc), but ...
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1answer
54 views

Counterfactuals in Premises for Arguments

Can counterfactuals in premises make an argument sound and valid? I understand that soundness requires both validity and true premises whilst validity requires the premises to follow to the conclusion....
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Can god violate the laws of thought (i.e., the logical absolutes)? If so, can such a god be ruled out of existence? [duplicate]

**The Laws of Thought** Laws of Identity, Non-Contradiction, Excluded Middle Something is what it is, ...
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141 views

How to contradict a general statement?

Consider the statement, "All the geometrical shapes on the screen have radius equal to 6". Suppose on the screen we have 6 circles with radius equal to 6 and also 1 triangle. In order to ...
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Does modus tollens capture the essence of “necessary condition”?

Does modus tollens capture the essence of "necessary condition"? (1) P → Q, ¬Q, … so ¬P. (2) So Q is a necessary condition of P. Is (1) the inner structure of (2)? Are any of these true: The ...
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Are these two propositions equivalent?

Are the propositions "Everything happens for a reason", and "Nothing happens without a reason" logically equivalent?
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48 views

Explanation of a quote from Spinoza

Notandum, dari necessario unius cujusque rei existentis certam aliquam CAUSAM, propter quam existit. Et notandum, hanc causam, propter quart aliqua res existit, vel debere contineri in ipsa natura et ...
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Can’t we assume that the Boltzmann Brain scenario can be cognitively stable?

In the Boltzmann Brain scenario, we are all brains produced by random fluctuations within a high entropy universe. The argument which I had accepted before was that our very reasoning can not be ...

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