# Questions tagged [logic]

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

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### I would like to learn about theory of supposition. Can you recommend any good books/video/etc about it?

I encountered following syllogism as an example of false equitation: Man is a species Socrates is a man Therefore, Socrates is a species The text ("An Introduction to Traditional Logic" by ...
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### Is there a detailed doxastic logic with a doubt operator?

I was "experimenting" with a doxastic logic with a doubt operator D besides the belief operator B, trying to come up with intuitive equivalences of interleavings (e.g. DBA = BDA, perhaps), ...
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### Deductive systems which deduce the structure of logics

“Logics” are frequently defined as having both a “syntax” and a “semantics”. For example, first-order logic is a deductive system or formal language with an alphabet (collection of symbols) and ...
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### Applying “properties” of logical systems to natural language semantics

Is there a logically definable complete set of logical properties? Like soundness, consistency, decidability, completeness, etc? Has anyone tried to apply them to natural language semantics? In other ...
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### How do you know two premises are combined to support an argument?

forgive me if I'm asking a simple question, but I'm trying to learn Introduction to Logic by Irving M Copi. I'm trying to learn how to analyse arguments. One of these arguments he uses as an example ...
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### Using the Universal Quantifier, Existential Quantifier, and logical connectives, write a description of a time when somthing bad for you was not bad

The following is an exercise in ethics, logic, the use of the universal quantifier and the the use of the existential quantifier. In the following context, the syntax for the universal quantifier is ...
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### Inductive Reasoning: Enumerative Induction question

In enumerative inductions like the following, would the target group be "most Canadians" or would it just be all Canadians? "Most Canadians agree that allowing the slaughter of dogs for ...
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### What's the name of a fallacy when a debater selectively picks facts and ignores others?

In many debates in various fields of political science, it happens that historical events are called upon to make a case or support an argument. However, it also happens quite often that a debater, in ...
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### Where do presuppositions fit into Grice's theory of meaning?

To clarify, by "Grice's theory of meaning" I am referring to the view that the informational content or meaning of an utterance is made up of three components: what is said - the actual ...
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### formalization: definite description (narrow reading)

I am not sure which formalization is right [1] or [2]: 'The teacher of Plato does not exist.' [1] ∃x(Tx,p ∧ ∀y[Ty,p → y=x] ∧ ¬∃y[y = x]) [2] ∃x(Tx,p ∧ ∀y[Ty,p → y=x] ∧ ¬∃z[z = x]) Is it possible to ...
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### Questions about the meaning of Vacuous Truth [closed]

If the proposition “It rains today” is false, then the situation “It rains today” does not exist. If a proposition is false, the situation it represents does not exist If (p=false and a=true and q=...
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### Is Fermat's last theorem a logical necessity or a different kind of necessary truth?

Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The question was, is this a logically necessary ...
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### What's the difference between "iff" and "=df"?

Just a quick question I stumbled upon from my readings. When some philosophers write A ↔ B and others write A =df B, is there supposed to be a difference?
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### Proof verification of god existence theorem

NB: My question was closed on math stack exchange. They advised me to post it here, but due to the lack of LaTeX formatting, I had to upload it as images. Apologies for that. I am a first year student ...
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### Categorical Syllogism Question: What would be the categorical syllogism conversion for this passage?

Passage "Some electric vehicles are “clean” vehicles, since all clean vehicles ultimately get their energy from renewable resources, and some electric vehicles do not ultimately get their energy ...
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### Can reason be precisely defined?

Reason, or rationality, is classically defined as deriving a conclusion from observations. Again, classically this is achieved by the application of logic. Aristotle explained it in this way. There ...
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### Is affirmation of the consequent always invalid?

Examples that I've seen usually go something like "If the lamp is off, then the room is dark. The room is dark, therefore the lamp must be off." However, what about the following example &...
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### Propositional Logic: Truth table for a certain argument form

I'm confused about evaluating a certain argument form with the truth table approach. I think below argument matches the corresponding truth table I made, but if my truth table is right it means the ...
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### Is symbolic logic just a non scientific way when it comes to interpret human natural language?

Let me ask you a thing it is about implication: when I say, if I go to London, I will talk to Paul, I mean an implication, or S=>P. Well, implication means it is necessary that S belongs to P, ...
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### On Modus Ponens/Tollens Fallacies

Modus Ponens IF p THEN q p Ergo, q Valid! Modus Tollens IF p THEN q ~q Ergo, ~p Valid! Converse Fallacy IF p THEN q q Ergo, p Invalid! Inverse Fallacy IF p THEN q ~p Ergo, ~q Invalid. ...
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### Is Gödel's incompleteness theorem based on premisses bearing a contradiction? [closed]

In a 7-page article, Chaim Perelman provides an argument supporting the idea that Gödel's premises for the incompleteness theorem bear a contradiction. Has this ever been refuted? If yes, how? Does ...
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### How is Hegel's dialectic a logic?

There are several features of this account that Hegel thinks raise his dialectical method above the arbitrariness of Plato’s dialectics to the level of a genuine science. First, because the ...
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### Why is the identity predicate needed?

In Logic: The Laws of Truth the identity predicate is introduced as an extension of general predicate logic (GPL). The following propositions are given as motivating examples: (1) "Mark Twain is ...
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### Gödel's Asymmetry

First of all, The Liar sentence, off of which Gödel spun his yarn. L = This sentence is false. As the story goes, L implies contradiction AND ~L implies contradiction. So far so bad. Then G = The ...
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### Prove that there is a first cause [closed]

If p->q, then p is the cause of q P is a proper subset of Q A proper subset of a proper subset of a proper subset... In other words, the cause of the cause of the cause of the cause... For this to ...
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### What does "unqualified notion of truth" mean in this passage?

From pages 252-253 of The Laws of Truth by Nicholas Smith: If we consider bare, uninterpreted closed wffs, we can say that they are true in some models and false in others, but we cannot say that ...
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### Origins of the syntactic form for rules of inference in modern presentations

I have been wondering where the form originates from. The turnstile ⊢ famously comes from Frege, but I haven't been able to find where the vertical notation was introduced. In the field of ...
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### Must all sentences be true or false?

Suppose there is a entity with which you can write down a self-contradictory sentence.Does the entity still exist?For example you know Russell's paradox?There is someone who says:"I always lie&...
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### Applicability of Mathematics

Suppose that an alien civilization exists, in a planet somehow similar to our own (oxygen-based, plants, animals), in an evolutionary stage similar to ours (large cities, advanced communications, near-...
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### Can fatalism be disproved by fate-changing magic?

In a world where magic exists, fate-spinners are people with supernatural powers that influence the chances of events happening. Their power has been proven by countless experiments where they compare ...
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### Does the empty set exist? [closed]

Does the empty set exist? I don't think it exists because If there are no constituent elements of an object, it can be said that the object does not exist. Can't this be the reason why the empty set ...
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### Must physics obey logic?

Must all physical theories conform to the laws of logic, such as being self-consistent? I am asking this because I once had an argument with a friend regarding the physics of time travel. I argued ...
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### Is modus ponens inherently circular?

Consider this simple argument for why Socrates is mortal: All men are mortal. Socrates is a man. Thus, Socrates is mortal. This argument can be roughly formalized as follows: IF P THEN Q R R≡P Q ...
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### Do you gain further truth from syllogisms

If you have a valid syllogism thats conclusion is true, have you gained any further truth? I'll explain my reasoning. The syllogism: All men are mortal. Socrates is a man Conclusion: Socrates is a ...
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### Is there any logic where P->P is not a wff [closed]

Basically the title. Are non reflexive logics one such logical system?
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### Should proofs of God involve the infinitary language ℒ(∞,∞)?

If God is an infinite being (per Scotus, say), and if no finite number of steps in an argument is adequate to the scope of the divine majesty, then the strictures of monadic theism aside (God as a ...
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### Freewill independent of determinism? [duplicate]

So I'm confused on how this is possible. If determinism is true freewill does not exist: If determinism is true, then every event has a cause, and every cause has a unique effect. If every event has ...
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### Does philosophy involve long inferential chains?

An inferential chain is a series of inferences where each depends on the previous in sequence. "From A we conclude B, from B we conclude C, and from C we conclude D." That would be a chain ...
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### General sentence operators

There are lots of operators that act on sentences. Here are a few examples: P and Q not P forall x.P necessarily P eventually P x believes that that P it is obligatory that P etc. The first two ...
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### Examples of situations where explaining the situation destabilizes the mind [closed]

Could someone please provide, using logic, or some other reasoning or portrayal, an example of a situation where explaining the situation destabilizes the mind? Thank you.
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### Missing two syntactical expressions of rules of inference in sentential logic

I have a table of the rules of inference in propositional logic. Among the entries are an Associative and a Commutative. The Associative rule is expressed with disjunction, but the commutative is ...
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### What happens when you deny an axiom? [closed]

There is no proof that the axiom is true. There is no proof by “Proof by contradiction”. That means that even if you deny the axiom, there will be no contradiction. And if a contradiction is created ...
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Here is my argument: One of the incompleteness theorems is “If a system is noncontradiction, it is incomplete” Incomplete means that there are propositions that are true but cannot be proven. The ...
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### Can you help me with the inference: if ¬( P & ¬Q ) and Q, then P

I'm taking my classes of symbolic logic, so my question is a bit naïve, but: If this expression is correct: ¬( P & ¬Q), P then Q. Why not the following is not: ¬( P & ¬Q), Q then P. Thank you.
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### Implicature justification for translating "P unless Q" as (¬Q → P)

In The Laws of Truth, Smith translates utterances of the form "P unless Q" as (¬Q → P) and takes the further suggestion that (Q → ¬P) to be an implicature of the utterance. The justification ...
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### truth set of the axiom [closed]

Edited to add content If p->q P is a subset of Q In other words, the truth set of the cause is a subset of the truth set of the effect. There is no proof that the axiom is true no reason to be ...
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### What do the meanings of ponens and tollens have to do with Modus Ponens and Modus Tollens? [closed]

There are two inference rules in propositional logic called Modus Ponens and Modus Tollens. I was wondering how the meanings of ponens and tollens have to do with the rules? That is, how does the ...
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### Is the concept of (Total) Nothingness self-refuting?

I've been reading the SEP about Nothingness and it gives a good summary of the philosophy around "Why is there something rather than nothing?". One of the confusions it notes is that "...
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### What defines if an inference is correct or not, (regarding different logics)?

For me, it makes sense to say for example: From a follows b. Not b. Therefore not a. I can't explain it, but it's "logical". Now I've read that there are different kind's of logic out ...
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