Questions tagged [logic]

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

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How pardoxes relate to a theory's decidability and completeness

Would "this sentence is false" make a theory containing it both undecidable & incomplete, while "this sentence is unprovable" make a theory containing it incomplete(syntatically) but not ...
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3answers
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Which fallacy: Thinking everything someone does in a discussion that's wrong is a fallacy?

There are a lot of questions about which fallacy something is on this site. Many times, the argument in the question is not actually a fallacy, but something that the questioner doesn't like/agree ...
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What type of rhetorical device is the offering of a source which is really long and not specifying what part of the source is relevant?

I'm encountering a frequent recurrence of a rhetorical device that seems to me fallacious but I can't figure out what it's called. When making an argument, the person does the following: Makes a ...
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10answers
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Which fallacy: “If white privilege exists, why did Elizabeth Warren pretend to be an Indian?”

I recently came across this meme. It's clearly a logical fallacy (the existence of one use of a socioeconomic tool other than white privilege does not preclude the existence of white privilege), but I'...
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59 views

SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC

Hello can someone explain me exacty how in this fragment of the paper (SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC, RICHARDG.HECK,JR.): (9) Tr(x) ≡∃y(rhs(x,y)∧¬Tr(y)), where rhs(x,y) is a formula ...
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How can I prove the law of excluded third (p ∨ ¬p)) using Fitch?

Good day. I do not quite understand how I can get ~~p after the 11th line. According to the proof of the law itself (and all reasonable logic) I should get it, and then simplify the expression - but ...
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1answer
108 views

Trying to formalize a certain sentence in predicate modal logic

I have the following sentence which I want to formalize in predicate modal logic. The sentence is: What is good for you is not necessarily good for others" My attempt at formalizing this is as ...
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3answers
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Help understanding deductive arguments

I am currently finding it hard to understand deductive arguments. I am taking a module called 'Effective Reasoning'. I've been finding it so hard to understand some things (as simple as this). I ...
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1answer
142 views

Why should a system of set theory represent the following property of x: ((x = h) or (x = k))) using the set that Frege used?

I have been considering the possibility of an approach to set theory that represents the following property of the free variable x, in the terms of parameters h and k: ((x = h) or (x = k))) by means ...
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1answer
86 views

Does everybody have a bias? [closed]

I was in a heated debate with a housemate, and they mentioned that 'Everyone has a bias'. At the time I disagreed, and these were my reasons: To say 'all have a bias' is to then say that I have a ...
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What goes wrong if we explain Russell's paradox as resulting from an overly rigid link between property satisfaction and elementhood?

An excerpt from a question at Math SE (Bounty of 100 available for an answer): What goes wrong if we explain Russell's paradox as resulting from an overly rigid link between property satisfaction and ...
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Thoughts on Open Logic Project?

I'm currently thinking about starting to expand my knowledge of logic beyond what I retain from my previous study of logic by making use of the materials available through: OpenLogicProject (https://...
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1answer
59 views

On the Donald Davidson Discourse of Contradictory Beliefs

The following excerpt is taken from Donald Davidson, Problems of Rationality, Chapter 14, Who is Fooled (1997), page 217: We should not agree that believing the contradictory or the contrary of a ...
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Can knowledge exist without structure?

For reference: https://en.wikipedia.org/wiki/Knowledge https://plato.stanford.edu/entries/knowledge-analysis/ https://plato.stanford.edu/entries/knowledge-how/ https://plato.stanford.edu/...
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4answers
175 views

What Is Critical Thinking, and How Does One Go About Learning It?

I am a freshmen taking an 'Effective/Logical Reasoning' course as an elective. Admittedly, I thought it would be something I could understand easily, but I soon found that this is not something I can ...
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The name for an anticipatory counter-argument?

There's the argument ad absurdum along with several other kind of reasoning. What is the name for a forestalling counter-argument - an argument put forward pre-emptively in anticipation of an ...
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1answer
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What kinds of proofs can be given for axioms, e.g. the modal axiom S5?

From John Bigelow and Robert Pargetter's book, titled, 'Science and Necessity', they assert the following: . . . . The resulting system, S5, contains all the theorems of S4 and all the theorems of ...
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In logic, which came first: the semantic approach or the syntactic approach?

Logic is today developing in many, very different directions. But the basic distinction between the semantic approach (truth, "⊨") and the syntactic one (provability, "⊢") is still important and ...
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1answer
90 views

Aristotelian vs Boolean, trying to determine the exact difference [duplicate]

Good afternoon, I've looked at some other answers and I feel those don't quite answer what I'm trying to ask, so I'll just ask it here. I'm in a logic course and I'm either misunderstanding ...
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Logic Philosophy question

I am looking for help in answering the full question with a full conditional proof (cp). This will help me understand this question and others that I am trying to understand. Thank you. Would ...
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1answer
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Help with a Predicate Logic homework proof

I have a Predicate Logic argument I need to translate into the symbolism of predicate logic first and then I need to construct a proof in CP. The argument is "Some wars are just. No war of ...
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Rhetoric: How to frame redundancy in an argument as deficiency?

How can we categorize redundancy in an argument as deficiency? That is, weaken the argument because of its redundancy? Suppose X is an argument that boasts coherence and clarity, but it has various ...
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1answer
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Did William of Soissons prove the law of explosion in the 12th century?

In the 12th century, William of Soissons attempted to prove that any proposition can be inferred from a contradiction. I've adapted his proof into a logical system I'm more familiar with: Let E ...
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1answer
82 views

Does a pattern constitute evidence, logic or something else? [closed]

Powerful groups (e.g. tribes and states) often exploit or attack weaker groups. That's a historical pattern suggesting that people will continue to prey on each other. Many wars have begun with ...
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What counts as a logically necessarily true statement and what is not?

"If an existing population contains both mortal and immortal beings, some members of that population are not subject to death." Is this statement considered logically necessarily true? I personally ...
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108 views

Infinity - Sizes vs Types

Suppose there is a line, infinitely long in both directions. Make arbitrarily "uniform" cuts or "integers". Obviously there are infinitely many of these. And there are arbitrary "lengths" BETWEEN ...
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Could philosophers via Logic prove the validity of some holy books, then use them as a source of trustful knowledge?

Could philosophy or philosophers or some philosophers prove the validity of the text of a holy book, e.g: Qur'an or the Bible, or some holy books, using logic and philosophical means, then use these ...
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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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How to derive P > (Q > R) from (P > Q) > R in Fitch?

I am having a little bit of difficulty coming up with a Fitch-style natural deduction proof. Presumably, I need to use a few conditional introduction rules, but I am not sure what I can get out of ...
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3answers
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What is the justification for the claim that observing something that is both a raven and black increases the likelihood that all ravens are black?

Suppose that I have access to a machine that allows me to input a positive integer (perhaps up to ten decimal digits) and the machine will -- depending only on the input -- output a statement. If the ...
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How would I go about proving P>Q from the premise (notP v Q)? [duplicate]

A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules. Here is ...
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156 views

Fitch Proof - Logic LPL 6.31

I am trying to complete the following proof in Fitch but am completely clueless on how to approach it. Any help would be appreciated! Thanks
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How can a undecidable theory be complete?

I don't understand how a theory can be undecidable (there is no effective procedure for determining if a sentence of the language is a theorem) and also be complete. How do we know all sentences are ...
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Is Herbrand semantics a kind of term formalism?

Michael Genesereth and Eric Kao describe Herbrand semantics as follows: Herbrand semantics is an alternative semantics for First Order Logic based on truth assignments for ground sentences rather ...
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Why doesn't one assert in metamathematics that a sentence S is a logical consequence of the conjunction of a set of sentences?

In other words, why isn't there -- at least in standard textbook presentations of things like the deduction theorem and the compactness theorem -- a conjunction connective that is applied to sets of ...
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Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
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2answers
151 views

To connect or to disconnect mathematics and platonism?

How [do philosophers] strongly support or refute the view that: mathematics is a bag of tricks for real-world problem solving; undecidable statements are an irrelevant and harmless side-effect of an ...
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Complement of “at least two people share the same birthday”

Suppose a room contains 𝑛 people. What is the probability that at least two people share the same birthday? So this is actually a question on probability, but I'm really confused in the logic and ...
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Is every reason reducible to a sequence of tautological statements? [closed]

I think of tautological statements as those statements which when explained should repeat themselves, and should intuitively explain the reason. For example, A = A because 'A is equal to A'; Dog is ...
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Do Aristotle's three laws of logic apply to statements about the future?

I have just read about Aristotle's Three Laws of Logic. I was wondering if statements such as "There is a chance of it raining in the next hour" can be evaluated using the three laws. Can you apply ...
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Logic Question in a fitch style system - disjunction elimination

I am having difficulty in formally proving two arguments. Firstly, given the premises A ∨ (B∧C) ¬B∨¬C∨ D derive A v D. I can see why it has to be either A or D, because if it's B and C, ...
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293 views

Proof Using Model Universe

Suppose I am trying to prove the following argument (∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx) Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try ...
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Difference between “neither true nor false” and “either true or false.”

What is the difference between "neither true nor false" and "either true or false."? I was reading about definitions And I read a line saying "Lexical definitions are either true or false". After ...
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2answers
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Clarification on what is and isn't a logical statement

After reading the article from Wikipedia I feel more confused on what the scope of the definition of a 'logical statement' or proposition is. First, is the statement "It is raining" considered to be ...
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1answer
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What is the difference between a function and a relation in first-order logic?

Consider this definition of first-order (or Herbrand) logic syntax. Here is the vocabulary: Definition (Vocabulary): A vocabulary V consists of: A set of relation constants {r1, ...,...
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The perfect definition of impossible [closed]

When i think about the true impossible, for me is a very dark area, that causes depression, because when we think about this simple question that begins whit, an example, "God creates the Human ...
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What's the difference between a second-order relation and a relation between objects?

I was reading an article in philosophy and found this: Some philosophers have denied that there is such a relation as identity. Thus Ludwig Wittgenstein writes (Tractatus 5.5301): "That ...
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How should one symbolize “and then” in logic?

Graham Priest observed that not all uses of "and" in English commute: (page 15) ...according to the truth table for &, 'a and b' always has the same value as 'b and a', namely, they are both ...
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What's the difference between “All A are B” and “A is B”?

I'm having trouble catching the difference between these two forms. I tried to draw some Venn diagrams but it's not helping. "All A are B" means A is contained in B. Does "A is B" mean A is also ...
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logical fallacy (or pseudo-logical, or rhetoric) corresponding to unduly extending my argument to make it false

This is probably similar to my preceding question: What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true? but I'm not sure ...