Questions tagged [logic]

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

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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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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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55 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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26 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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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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38 views

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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26 views

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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57 views

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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48 views

Validity/Soundness of an argument from R. Carrier

This is about training in argumentation. I use a text from R. Carrier: https://www.richardcarrier.info/archives/468, where he claims that from nothing everything follows. (Don't get shocked, the ...
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50 views

Difference between a law of logic and a logical principle

The traditional notion of logic, broadly speaking) is that it is a system of laws and principles governing valid inferential reasoning (i.e. laws of logic logical principles). But what precisely ...
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Fallacy and guilt by discussion?

I recently encountered a discussion that went along the lines of: A: Pedophiles are not just old men touching little kids. They're also 23 year olds going out with 16 year olds. B: Pedophilia ...
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57 views

Life as a formal system

I am curious if there is some existing work on viewing life as a formal system. In formal system we have: axioms and rules of logic (like in math AND, OR) then we derive and prove theorems I see ...
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36 views

Set of all hidden assumptions in a statement

Imagine a person "A" who says to a person "B" the following statement: "It is true that the house in front of me has three windows". If you think about it, this statement is true for a person "B" only ...
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53 views

Does the conditional statement “If not-p then p” have a name?

For there to be not-p it is necessary that there be p. It is easy to show that "If not-p then p" is true, and conversely "If p then not-p" is false. Further the contra-positive of "If not-p then p" ...
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53 views

What is a logical ground?

I've been stumbling upon the expression and am now asking myself what it's meaning is. What does mentioning a logical ground refer to? Perhaps anyone could try to break down the possibly multilayered ...
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80 views

The Concept of Trivialism

I understand trivialism is the position that everything is true, but I don't understand how it arrives there conceptually. The trivialist realizes that our natural (L)anguage (combined with our ...
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52 views

Why do we call the axiom Br in modal logic “Platonic Thesis”?

The Axiom Br (or B) in modal logic is sometimes called "Platonic Thesis", I wonder it is because of its semantical property (being symmetrical) but I couldn't find anything related.
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I know that he knows that I know that he knows

Not sure if this is the right place for this question but here goes... Some time in the past I've stumbled upon some site/article/post/etc that discussed the issue of 2 parties having (or not) some ...
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31 views

Is it reasonable to conflate being and truth?

Let x be something that exists unequivocally. Then "x exists" is true, but does it make sense to say x itself is true? And vice versa - the proposition "x exists" is true, but is there a sense in ...
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fitch arrow proof

using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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Alphabetic Substitution, Barcan, and Strict Implication

Context: I'm stuck on Axiom 8 from the introduction to Barcan 1946, "A Functional Calculus of First Order Based on Strict Implication." My instinct is that I'm missing a basic, perhaps obvious concept-...
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120 views

Analogy of Set and Subset and Contracts in abstracto and Marriage in concreto/in particular

I had a talk with a professor of family law and we are frequently told that there are general ordinances for contracts in general and particular ordinances for marriage. I am problematised by the ...
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110 views

What ifluences whether a formula of a predicate logic is true/false in some particular interpretation of a language L?

It is not clear to me, what influences whether a formula in a predicate logic is true/false in some particular interpretation of the language L. In propositional logic we valuate every atomic formula ...
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71 views

Question about an argument with a conflicting premises and conclusion

I have a homework problem where I have to state if an argument is valid, conclusive or neither. However I am struggling to wrap my head around this one. The argument goes: Generally, a flood ...
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29 views

Is this the correct way to phrase a logical argument with multiple syllogisms?

I'm not familiar with phrasing arguments in the form of traditional logical syllogisms, so I'd like to ask if this formulation is correct, or if it can be expressed more concisely. Note, I'm not ...
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What is the meaning of Principle C'' in Hartry Field's 'Science Without Numbers'?

For Field, the following is 'perfectly obvious', but I would like confirmation that I understand it completely. Let A be a nominalistically statable assertion. Let A* be the assertion that results by ...
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133 views

What is an enumerative definition?

W. Kent Wilson in his book argues for developing an enumerative definition of concepts. An enumerative definition formulates its meaning by enumerating the objects or phenomena that fall under the ...
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121 views

Bibliography about non-mathematical applications of logic:

I have been recently playing with modal and temporal modal logics in the context of "organisms" (mostly after some study of entelechy in Aristotle and relatedly, some ideas of current biology). I have ...
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28 views

When thinning on the right how is it correct that the number of formulae on the right can be increased from zero to one?

I understood there being no formulae to the right of the turnstile as meaning that the formulae on the left was inconsistent. However, my textbook writes that there is a special case of thinning on ...
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24 views

Can these selfreferential statements be rewritten as such?

This statement is a paradox = this statement is both true and false this statement is a hypodox = this statement is either true or false this statement is a contradiction/always false = this ...
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51 views

Logical Notation in Anscombe's “Causality and Extensionality”

In "Causality and Extensionality," Anscombe writes thus: Our argument uses the description of a class—say x̂(Gx · p), assuming G to be a respectable class-forming predicate. Let G be such that x̂(Gx) ...
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The nature of truth and logical connectives

I think most would agree that: P or !P !(P and !P) are always true. This allows us to have certainty no matter what we're talking about. Does that make the logical connectives the most fundamental ...
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why are ∀x(P(x)→ ∃y(Q(y)∧R(x,y))) and ∃y(Q(y)∧∀x(P(x)→(R(x,y))) not logically equivalent?

been sitting here for hours and still can't figure this out. is the order of ∀x and ∃y important in this case? all I can think of now is "all P is R of some Q", but I don't think this is right.
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386 views

LPL Predicate Logic Translations Exercise 11.20.7

I have this one question (Part 7) in exercise 11.20 that I can't seem to get the answer from. I tried ∀x∀y ((x ≠ y ∧ Larger(x,y)) → Dodec(x)) and ∀x∀y (Larger(x,y) → Dodec(x)), as well as many other ...
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48 views

Was Russell's purpose in Principia Mathematica to formalize all the possible constructions of logic?

In writing Principia Mathematica, was one Russell's purposes to formally describe all the possible variations of logical concepts and reasoning that can be used in mathematics? For example, suppose ...
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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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An erotetic argument about the liar paradox

I noticed something about the liar paradox, when the liar sentences are taken as questions. Let’s start with the liar index, “This sentence is false.” Allow this to be questioned: “Is this sentence ...
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86 views

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 name of the fallacy where acknowledging an issue is confused with actually addressing the issue?

A few days ago an artist came to present his work to our class. At the beginning of his presentation he said "I know cultural appropriation is a very loaded topic, and it occupies my mind often" as ...
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What falls under Hegel's concept of “absolute knowledge”: does that include deductive logic and scientific explanation?

In the wikipedia page for Hegel's Science of Logic, it states: According to Hegel, logic is the form taken by the science of thinking in general. He thought that, as it had hitherto been ...
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Can a solipsist doubt?

I've been thinking about epistemological solipsism, which seemingly necessarily follows from metaphysical solipsism. Namely, that the "world" of the solipsist is one and the same with the self of the ...
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Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
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86 views

Why do there exist “logical fallacies” that are not really consistent logical fallacies?

Why do there exist "logical fallacies" that are not really consistent logical fallacies? By logical fallacy, consider e.g. ad hominem. By consistent logical fallacy I refer to a type of logical ...
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113 views

Is the following considered an argument or just a set of statements? If it is an argument what would be the premises and conclusion?

In every age, philosophers have compared the human mind to the latest technological gizmo. Currently we use computers as models of our minds. Seventy-five years ago, our minds were compared to ...
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231 views

The sea battle paradox and the soundness criterion

Again a short look at Aristotle's resolution (one of many) of the sea battle paradox: In one famous example about a hypothetical sea battle, [Aristotle] observes that the necessary truth of a mere ...
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134 views

What are the Limitations and Vulnerabilities of Objectivity Biases?

How reliable is a "Logic / Objectivity" Bias when it comes to reasoning? Or, What are the potential limitations or vulnerabilities of relying solely on these bases of reasoning? Note 1: &...
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141 views

In the context of debate centred on a statement, how to validate arguments given to confirm or disconfirm that statement in a logical manner?

Let's say we have the following statement to serve as a starting point around which a debate can be centerd. Man is immortal Someone could say that man is mortal according to accepted scientific ...
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146 views

Concerning the integrity of some logical syllogisms on moral subjectivism and ice-cream

I understand moral subjectivism to be the meta-ethical idea that all moral statements are merely expressions of the individual and thus that there are no moral statements that are implicitly (...
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60 views

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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103 views

Difference between non-sequitur fallacy and post hoc fallacy?

What is the difference between post hoc fallacy and non sequitur fallacy?