# Questions tagged [logic]

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

2,264 questions
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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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### 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 are the most popular introductory logic textbooks, and what sets them apart from each other?

I plan to choose one and read it.
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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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### Hume: excavating the is/ ought gap

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 ...
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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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### 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
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### What is an example of a predictive conditional?

Can someone explain to me with an example what a predictive conditional is? Does this type of conditional have necessary and sufficient conditions?
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### How do I operate with philosophers if I reject deductive reasoning?

Deductive reasoning is the one that takes premises for granted. I never do it. Therefore I never do deductive reasoning. Well, enough jokes. It is safe to assume that deductive reasoning never should ...
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### How is “~A. Therefore A -> B” a valid argument?

I’m teaching myself logic from ‘Logic: The Laws of Logic’. In this book it states that 1) any sequence of propositions counts as an argument. 2) valid is when true premises of an argument cannot ...
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### Do Alexius Meinong's impossible worlds describe all impossible worlds/things? [duplicate]

Does his impossible worlds category include (and can describe) literally all impossible things/worlds? Inconsistencies, paradoxes, impossible solutions to problems (and impossible problems); really ...
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You play a game with a fortune teller. There are two cards with the face down on the table; he wins if you raises the card's suit he foresees, you win if his prediction turns out to be wrong. Suppose ...
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### Basic Logic: Arguments with Unnecessary Premise

Should an argument be considered invalid if there is an unnecessary premise? P1: A dog is a mammal. P2: All mammals have hair. P3: A dog is an omnivore. C: A dog has hair.
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### Describing differences between “computational” and “non-computational” proofs

Is there a term that distinguishes proofs that can be performed by a straightforward computation related to the meaning of the proposition from proofs that build a tree of intermediate expressions ...
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### How is the argument “I love all logic, but I don’t love deductive reasoning. Therefore, the moon is made of green cheese.” valid?

This example came up in class: I love all logic, but I don’t love deductive reasoning. Therefore, the moon is made of green cheese. I understand the premise is contradictory and the conclusion ...
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### Derive |- [(P>Q)>P]>P using only primitive rules

I've been having issues trying to derive |- [(P>Q)>P]>P in natural deduction using only primitive rules. Wondering if anyone would have a solution to it. Thanks
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### Why cannot the following theory be refuted by logic but is rejected because of lack of empirical support?

The following statements are taken from a book: The man in the street, and also the philosopher K. Marbe, believe that after a run of seventeen heads tail becomes more probable. This argument has ...
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### Logic Either..Or

In the book: "Elementary Logic" authored by Brian Garrett, he has a few examples, one with solution and one without that conclude the following: 1) Either many people will attend the concert, or it ...
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### Is Tarski's schema T trivial?

Tarski's schema T asserts that: (T) x is true if and only if p where x is the name of any sentence of the language in question and p is the expression which forms the translation of this sentence ...
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### Is there a truth value for a predictive conditional?

Does a predictive conditional have a truth table value? I have this question because we can't check if the antecedent or consequent is true or false.
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### Syntactic and semantic eliminability/conservativeness

Let L be a ground language, and L+ the extension of L with additional signature terms and axioms. We say L+ is syntactically conservative over L if every sentence in L that is provable in L+ is ...
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The pace of reading, clearly, depends entirely upon the reader. He may read as slowly or as rapidly as he can or wishes to read. If he does not understand something, he may stop and reread it, or ...
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### Basic Logic: Presuming Truth

Given my belief that X is false, is it still possible for me to agree that if X were true, then Y?
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### Are the following statements necessarily true, necessarily false, empirically true, or empirically false?

All cats are animals. TV's did not exist before the 20th century. All bachelors who are married are both married and unmarried. What I think is the classification of each statement: Necessarily true....
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### Is it possible to know the truth value of a statement without knowing any information about that statement?

Is it possible to know the truth value of a statement without knowing any information about that statement? If no, then to me that would imply that truth values are not absolute and depend on how we ...
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### ~(P&Q) derive to ~Pv~Q

I would be grateful if someone could derive, by showing the proofs that: ~(P&Q) derives to ~Pv~Q. The same derivation would be appreciated for |- [(P>Q)>P]>P
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### What's the meaning of the meaning of life? [closed]

Let's say that the meaning of life is X (avoiding evil, fulfilling our desires, obeying God, fleeing the pain of the fear of the death, collecting turtles – anything). What is the meaning of X? Even ...
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### Hypothetical syllogism

So hypothetical syllogism is: if a then b if b then c so, if a then c . According to wikipedia, "In short, it states that if one thing happens, another will as well. If that second thing happens, ...
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### Can any logic system provide the impossible solution to Russell's paradox in naive set theory?

In naive set theory in classical logic, we cannot describe or find a solution to Russell's set paradox (it is impossible). But is it there any logic system or any method that can provide this ...
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### Understanding hypothetical reasoning and material implication

I am a little bit frustrated in how we use hypothetical reasoning in everyday life. Many times we make "if-then" statements. For example, if i get ill ,then i cant go to work and if i cant go to work ,...