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Questions tagged [logic]

Use this tag for general questions about logic that are not categorizable under some more specific tag, like "mathematical logic", "informal logic", "classical logic", etc.

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Do philosophers do research in mathematical logic at the same level as mathematicians? [closed]

I am neither a philosopher nor a mathematician but I am assuming that philosophers don't know a lot of math. So, does that keep them from doing similar research in mathematical logic as mathematicians ...
user56417's user avatar
1 vote
4 answers
274 views

Why is "the present king of France is bald" considered false?

Why is "the present king of France is bald" considered false? Because "present" means "existing" so it's paradocixal. Because the concept of "the present king of ...
user avatar
2 votes
4 answers
717 views

"something white doesn't exist" -> "at least one of things that doesn't exist is white" [closed]

If something white doesn't exist, at least one of things that doesn't exist is white? Is it logically correct?
user avatar
0 votes
1 answer
109 views

Existence as a Predicate

In Predicate logic if I wanna say, Atoms exist, I don't/*can't (?) use Ex = x exists (make existence a predicate) and state Ea, where a = Atoms. The correct way to express Atoms exist is Ex(Ax), Ax = ...
Hudjefa's user avatar
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5 votes
3 answers
265 views

Questions about categorial propositions

I have some doubts regarding categorial propositions used in syllogism. Does "No A is B" implies "Some A is not B" and "Some B is not A"? Is there any counterexamples to ...
Ray Siplao's user avatar
1 vote
1 answer
94 views

Is Arithmetic more Extensional than Probability?

One of the views of probability is that it should be viewed as a multi-valued logic where p(A) represents the probability that a proposition A is true. In a discussion of this, I once read that ...
David Gudeman's user avatar
2 votes
2 answers
91 views

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 ...
KarmaPeasant's user avatar
2 votes
0 answers
33 views

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), ...
Kristian Berry's user avatar
2 votes
1 answer
53 views

The relationship between logical systems and natural language semantics

Every student of philosophy knows that there are systems of logic and that those systems are analyzed in terms of logical properties like soundness, consistency, decidability, completeness, etc. These ...
Julius Hamilton's user avatar
2 votes
2 answers
64 views

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 ...
Vendetta's user avatar
1 vote
1 answer
40 views

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 ...
Toothpick Anemone's user avatar
2 votes
1 answer
46 views

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 ...
Damon Fernandez's user avatar
2 votes
0 answers
44 views

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 ...
user51462's user avatar
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1 answer
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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 ...
Gion's user avatar
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1 answer
202 views

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=...
Display name's user avatar
2 votes
4 answers
946 views

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 ...
Vihan 's user avatar
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5 votes
3 answers
2k views

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?
John Smith's user avatar
-1 votes
1 answer
102 views

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 ...
dyy's user avatar
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3 votes
2 answers
74 views

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 ...
Damon Fernandez's user avatar
8 votes
7 answers
1k views

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 ...
Meanach's user avatar
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1 vote
4 answers
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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 &...
Kalcifer's user avatar
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1 answer
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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 ...
Damon Fernandez's user avatar
2 votes
4 answers
102 views

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, ...
Danyel 80be's user avatar
1 vote
3 answers
78 views

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. ...
Hudjefa's user avatar
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0 votes
2 answers
126 views

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 ...
Jérôme Verstrynge's user avatar
1 vote
1 answer
123 views

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 ...
user avatar
5 votes
2 answers
827 views

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 ...
user51462's user avatar
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1 vote
1 answer
197 views

Gödel's Asymmetry

First of all, The Liar sentence, off of which Gödel constructed his argument. L = This sentence is false. As the story goes, L implies contradiction AND ~L implies contradiction. So far so bad. Then ...
Hudjefa's user avatar
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-2 votes
2 answers
167 views

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 ...
Display name's user avatar
6 votes
3 answers
604 views

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 ...
user51462's user avatar
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5 votes
1 answer
346 views

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 ...
Iain's user avatar
  • 153
-2 votes
2 answers
131 views

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&...
Cerise's user avatar
  • 99
1 vote
2 answers
152 views

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-...
Ioannis Paizis's user avatar
2 votes
2 answers
93 views

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 ...
Zachiel's user avatar
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0 votes
4 answers
198 views

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 ...
Display name's user avatar
5 votes
4 answers
326 views

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 ...
user107952's user avatar
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1 vote
2 answers
206 views

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 ...
Jimmy Yang's user avatar
0 votes
2 answers
180 views

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 ...
8Mad0Manc8's user avatar
0 votes
1 answer
76 views

Is there any logic where P->P is not a wff [closed]

Basically the title. Are non reflexive logics one such logical system?
Vihan 's user avatar
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1 vote
1 answer
182 views

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 ...
Kristian Berry's user avatar
3 votes
6 answers
359 views

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 ...
More Anonymous's user avatar
3 votes
5 answers
146 views

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 ...
causative's user avatar
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6 votes
4 answers
666 views

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 ...
David Gudeman's user avatar
2 votes
1 answer
70 views

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.
Joselin Jocklingson's user avatar
1 vote
0 answers
52 views

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 ...
J D's user avatar
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0 votes
3 answers
174 views

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 ...
Display name's user avatar
-2 votes
1 answer
100 views

Please evaluate my argument about incompleteness theorem and first cause

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 ...
Display name's user avatar
2 votes
2 answers
59 views

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.
Danyel 80be's user avatar
3 votes
2 answers
117 views

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 ...
user51462's user avatar
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-1 votes
1 answer
119 views

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 ...
Display name's user avatar

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