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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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Question regarding diagonalization

Suppose we construct a choice function that separates R/{0} in the interval (0,1) (viewed in base 2) into two sets A and B each consisting of an arbitrary element chosen from every pair of complements....
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How does one go about proving (A&B)⊃C |- A⊃(B⊃C)?

I am relatively new to logic and deductive reasoning, so this problem has been giving me some trouble. I want to start with an assumption of (A&B) and try to isolate a subproof where I can then ...
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How do you prove B v A |- A v B?

I am having trouble with how to use the assumption, which I feel that I will need for this proof. If any one can demonstrate or give hints for this proof, I would greatly appreciate it.
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Why nations of Earth have forbidden the cloning on humans?

Suppose, there’s WW3 and a country is out of soldiers, and the only thing a country can do to have more soldiers is by cloning a person. I heard that it is illegal to clone humans, but only animals ...
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Does rejecting the law of the excluded middle mean rejecting it for all propositions or only for those one cannot derive?

Wikipedia describes the law of the excluded middle as such: In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is ...
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Why do we answer questions based off philosophers from the past (i.e. Aristotle, Socrates, Plato, etc.)?

I've noticed on the Philosophy Exchange that all questions are answered with references to secure a more logical and strengthened argument (which is sensible), but why do we assume that these ...
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Logic related to Cantor's argument [on hold]

Suppose we construct a choice function that separates R/{0} in the interval (0,1) (viewed in base 2) into two sets A and B each consisting of an arbitrary element chosen from every pair of complements....
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How to translate classical logic to basic Kripkean logic?

I'm trying to semantically prove the following argument (sorry about the formatting - I'm new to stackexchange): if P ⊨c Q then ⊨k 򪪪(P → Q) However, I don't know how to translate or relate the ...
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McGee's Counterexample to Modus Ponens

I'd like to start off by saying that I have read the other posts in the Math StackExchange and here about this paper, but I think my question is a bit different from those although it does stem from ...
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if only one thing exists, nothing exists?

If one thing does not differ from any other, it has no identity (it has no properties, features, limits...). If something has no identity, it's not a thing. So only one thing can't exist. i.e.: I ...
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Are analogies logical arguments?

I have heard several analogies that attempt to give people a better understanding of the Christian trinity. Some compare it to H2O and how water can be solid, liquid, or gas. However, this is a form ...
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How to derive (∃x)(y)(Ax ⊃ By) from (x)Ax ⊃ (y)By?

Upon multiple attempts, I keep arriving at the same conclusion, but I believe this is not right. How shall one proceed with this one? I've exhausted the resources I have at my reach.
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Can we ask an infinite amount of questions or is there a limit to how many questions we can ask? [on hold]

I've been thinking about the nature of questions and answers to questions. Can I ask people opinions on whether they think it is possible to ask an infinite amount of questions or do we as human ...
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Is there any worth—other than historical—to reading Aristotle's works on logic?

What I mean is that presumably a topic such as logic would have, at this point, been so advanced that the ancestral works are unnecessary. I would read it for pleasure, but have they been ultimately ...
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What's a Good Introduction/Summary to Probabilistic Logic?

I hadn't even heard of Probabilistic Logic before today. My world view was already leaning in this direction as I never really put much stock in either the law of the excluded middle or the principal ...
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What does predicative mean?

I'm reading this page https://plato.stanford.edu/entries/type-theory/ where the words predicative and impredicative are used in this context: Notice that for defining the predicate R, we have ...
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How to denote physical (not logical) impossibility in modal logic?

Say I want to note that in this world, it's physically impossible to jump over the Eiffel Tower. I can just write ¬◇x, but this seems to say that in all possible worlds x is impossible, and I want to ...
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Can a reason cost 5 dollars?

Imagine a school where no one can wear a red hat. John goes to school with a red hat costing 5 dollars. Someone says John's red hat "is" the reason why he can't get into the school. What is the ...
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‘The claim that I had an affair with Miss A and that I didn’t father her child is false’

The prosecutor asks, ‘Did you father the child of the murdered victim Miss A?’. Mr. N replies, ‘The claim that I had an affair with Miss A and that I didn’t father her child is false’. In response ...
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Is there a rigorous definition of ‘everything’?

Is there a rigorous definition for this concept? ‘The collection of every individual thing’? If an ‘individual thing’ is something that is different from something else, ‘everything’ could be the ...
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Why do we think objects and beings are real? [closed]

How can we tell if we are real and not a simulation that we perceive to be real. Given we know not what the universe is except what we perceive it to be. What if galaxies are just but other ...
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Disproving the Gambler's Paradox [closed]

A certain slot machine for Philosophers is rigged to pay out, on average, once every 10 games. It costs 1 dollar to play, and the machine pays out 12 dollars if you win. On average, then, you will be ...
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Why do humans make infants? [closed]

Considering that humans are the most intelligent species on earth, why do humans make infants? I cannot understand the reason why humans make infants, when humans can't predict whether the ...
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Is first order logic with fixed domain of discourse decidable?

Whether an arbitrary statement in first order logic has a valid model is undecidable. But what if we constrain the domain of discourse to say, integers, or real numbers. I'm thinking of its ...
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How to prove ~ (~P & ~Q) : P ∨ Q by natural deduction

Here's another of Tomassi's exercises I can't solve (Logic, page 106): ~ (~P & ~Q) : P ∨ Q I have to use natural deduction and the only rules I know are: assumptions, modus ponendo ponens, ...
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How could we get a world where only impossible things happen? [closed]

Imagine a universe where 1+1=3. This contradiction would trigger the effects of the principle of explosion, and thus, literally everything (possible and impossible things) could happen. If we lived in ...
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What is the difference between the “is” of predication and the “is” of identity?

What is the difference between these, the "is" of predication and the "is" of identity? For example, when I say, "my pet is a cat", am I using "is" as an identity or as a predicate?
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Can this computer model simulate/program completely inconsistent/logically impossible/illogical theories?

(https://groups.google.com/forum/#!msg/everything-list/Ba1ggVKSpg4/CkA-u1DutmsJ) In this thread it is discussed that a computer model could simulate/program inconsistent theories (logically imossible/...
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Does relationism resolve the Sorites paradox?

The ancient Sorites paradox, 1 grain of wheat does not make a heap. If 1 grain doesn’t make a heap, then 2 grains don’t. If 2 grains don’t make a heap, then 3 grains don’t. … If 999,999 grains ...
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Are there degrees of rationality/plausibility to assumptions?

There are many kinds of premises, in every possible field. I'll limit this question to metaphysics, although it can definitely be applied to each and every scientific/philosophical study. For example,...
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In logic, do propositions default to true or false when objects in them do not exist?

In this hypothetical: Firefighters always tell the truth, while politicians always tell lies. Suppose three people, who are either a mix of firefighters and politicians, all politicians, or all ...
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Is “(1) All humans are mortal. (2) Socrates is mortal. Conclusion: Socrates is human.” unsound argument?

I am new to a philosophy course and recently learned about validity and soundness of an argument. In this exercise: Premise 1: All humans are mortal. Premise 2: Socrates is mortal. ...
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Łukasiewicz & statements about the past

I think this is a fair presentation of Łukasiewicz's view on past, present, and future statements in an answer by Johannes https://philosophy.stackexchange.com/a/31995/29944: "His view is that ...
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What is an example of a monadic predicate calculus argument that cannot be represented by the 19 classical Aristotelian syllogisms alone?

While reading Wikipedia's description of the monadic predicate calculus, I read the following: Inferences in term logic can all be represented in the monadic predicate calculus. and Conversely, ...
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Is there such a thing as unary logic?

Is there such a thing as unary (as opposed to binary, ternary, …, n-ary) logic? cf. Is there any reason for the heavy focus on binary relations in formal logic?
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Can randomness be random?

In mathematics, a true random number generator it's impossible, because any formula defines a process that, however complex, is not random. A random event must be unrelated to any cause or condition, ...
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Books on the logic of science

I was recently skimming through Nagels "The Structure of Science", and I wonder if there are other books that go through the philosophy of science through a logical point of view; That is, I am ...
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Proof from tree to steps

I'm able to get the proof in a tree form (it's invalid). Is there a method where I can transform it to steps method indicating the rules of inference and replacement?
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meaning of (r .⊃. s ⊃ r) [the syntax meaning]

I'm trying to to determine whether the following is a tautology, contingency, or contradictory: (p ⊃ q) ∨ (q ⊃ p) .⊃. (r .⊃. s ⊃ r) This is school work. I'm getting that it's a tautology, but only ...
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Why does Hume believe that ought brings a new relation?

If means-end reasoning, where we can say that one is ought to do X in order to get Y, does not bring a new relation, then in order to tell that ought brings a new relation, we ought to assert that ...
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What is the difference between ampliative, abductive and inductive arguments?

I know all these arguments are kind of the same but what is the border dividing them?
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You disagree with me, therefore you are X. What is the name of this fallacy (manipulative trick)?

Across my life I have encountered this numerous times. One recent example: If you don't think those are a crime, you are not adult enough or logical enough to have a conversation with me. While ...
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Is arguing that one's opponent has “no evidence” an example of some identified logical fallacy?

I sometimes hear someone claim that the person they are arguing with has "no evidence" for whatever they are arguing for. Although I usually dismiss such claims thinking that what "no evidence" means ...
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Is circular reasoning always a fallacy?

Suppose the following dialogue: ... "I accept only one notion of land property. Namely, 'I am doing my stuff here, therefore I am here". "But this means," he responded, "you can break ...
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Can an argument be formally valid with sound premises and still be informally fallacious?

Consider the following two assumptions: Validity Assumption: Assume an argument is valid. It follows all the formal logical rules of inference. The inference contains no formal logical fallacy. ...
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Does Hume reject the possibility of is-ought syllogisms?

Suppose the following syllogism: It is impossible for anyone to get X without him/her doing Y. It is possible to get X (by doing Y). I want to get X. Therefore I ought to do Y. There is, very likely,...
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IF, THEN and exceptions

I'm trying to figure out if (2) necessarily follows from (1). Or can (1) and (2) be true together? 1) whoever does X, except for the reason of Y, commits Z 2) whoever does X, for the reason of Y, ...
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What exactly were Alexius Meinong's impossible worlds? [duplicate]

I've been told that Alexius Meinong talked about impossible worlds, but I have not found anything like a specific theory from this author that talks about impossible worlds/objects. So, is there a ...
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Prove transitivity in Fitch

How to prove transitivity in Fitch. Is it Ok? | 1. a = b | 2. b = c | 3. c = c =Intro | 4. a = c =Elim: 3, 2 | 5. b = c =Elim: 4, 1