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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What is wrong with the following case against determinism?

I am thinking of determinism in the following way: if we knew all the laws of nature and the complete state of the universe at a given time, we could predict everything that would happen in the future....
user52932's user avatar
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Relativistic formal ethics

I was contemplating the ethics of abortion. It seems like people expect that we have to make a definitive decision about at what age it becomes unethical to abort a fetus / young person. And yet, it ...
D J Sims's user avatar
16 votes
5 answers
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Is there a name for the argumentative tactic where you play dumb and ask for extreme simplification?

My day job is research in economics. In economics seminar culture, a common way to demolish the speaker is to play dumb and say "I don't understand what you are saying", implying that the ...
kmf's user avatar
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2 answers
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How is it possible that state change exists? [closed]

We observe the passage of time, change in location of particles, reality is changing its state. Initially the thought arises that if state change ability were derived, created or began to exist, that ...
Wowser's user avatar
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4 answers
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How to motivate ‘unless’ = ‘if not’, with etymology?

My high school students still reckon Lande’s two motivations for ‘unless’ = ‘if not’ (below) too abstract, formalistic! Thus I need a third, but simpler, motivation with merely etymology. But how do I ...
H7 De's user avatar
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1 answer
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Demonstrate that a term cannot be well-typed?

This problem is coming from Exercise 3.3 in Bacon's A Philosophical Introduction to Higher-order Logics. I am trying to do my due-diligence here and not skip problems, but this one stuck out to me. ...
C D's user avatar
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What is the difference between temporal logic and Dialectical Logic (Hegel)?

I have been reading Hegel's Science of Logic where he critiques its generation understanding of logic known as Formal Logic. As I have come to understand one of the main differences between Hegel's ...
GONZALO ROCHA DE LA CRUZ's user avatar
2 votes
4 answers
134 views

Can God violate the laws of mathematics and logic? [duplicate]

Can an omnipotent being like God violate the laws of mathematics and logic? Personally, I don't even believe in God, but I am just asking purely hypothetically if such a being could violate the laws ...
user107952's user avatar
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Logical statement, is the deduction correct?

I found a theorem that is like this: If A and B are true, then C is true if and only if D is true. In other words: Can we deduce, If D and ( not (A) or not (B) ) then not (C)? Of course "and"...
Mathisfreedom's user avatar
3 votes
3 answers
144 views

Factual and linguistic propositions

This is from "Language, truth and logic": A good example of linguistically necessary proposition which appears to be a record of empirical fact is the proposition, ‘Relations are not ...
Егор Галыкин's user avatar
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Symbols and Signs by A.J. Ayer

This is from Ayer's "Language, truth and logic": A factor which complicates the structure of a language such as English is the prevalence of ambiguous symbols. A symbol is said to be ...
Егор Галыкин's user avatar
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1 answer
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Signs and symbols in "Language, truth and logic"

"A factor which complicates the structure of a language such as English is the prevalence of ambiguous symbols. A symbol is said to be ambiguous when it is constituted by signs which are ...
Егор Галыкин's user avatar
2 votes
4 answers
206 views

Interesting non-mathematical tautologies

Are there any interesting examples of tautologies that are not mathematical? Something non-trivial like It is raining or it is not raining. I can't come up with one nor have I found any on the ...
Александр's user avatar
2 votes
1 answer
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What is the nature of the difference between a contradiction and a paradox (as apparent contradiction)?

Given the recent PhilSE question What framework or tool solves the Barber Paradox? it emerged from a number of answers including Bumble's and Mauro's that there is a technical distinction between ...
J D's user avatar
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9 answers
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What framework or tool solves the Barber Paradox?

The Barber Paradox is usually phrased as follows: I know a barber whose policy is to shave everyone who doesn't shave himself. If a person shaves himself, the barber does not shave that person. If ...
pygosceles's user avatar
1 vote
1 answer
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Facts and the denial of "Iff it is true that A, then it is true that it is true that A"

The SEP article on axiomatic theories of truth goes over a theory in which "the truth iteration axiom ∀A(T[TA] ↔ TA) is inconsistent." Apparently (and this sentence is an edit), it's ...
Kristian Berry's user avatar
1 vote
0 answers
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Is there a difference between the purpose of logic and metamathematics?

Considering a definition by Heidegger stating that logic is the study of the properties of discourses and considering that metamathematics is defined as the study of the foundation of mathematics from ...
Jérôme Verstrynge's user avatar
3 votes
6 answers
170 views

Do contingent propositions about the world rely on the consistency of mathematics?

Assume that a contradiction in mathematics is discovered, say '0=1'. Then, by the principle of explosion from classical logic (by the rules of which, arguably, the world adheres as well) we can derive ...
Александр's user avatar
8 votes
5 answers
2k views

Are opinions considered sentences in logic?

I am beginning to read the book titled forallx An Introduction to Formal Logic by P.D. Magnus. This is an open source book. On page 4 Magnus states: In this open source book found here: https://math....
Dr. J's user avatar
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Can the universe have had a beginning and have not had a beginning?

I don't know if this question belongs on the physics SE or here. It's a very simple question however it may have a complex answer, if at all. The apparent proposition in the question appears ...
8Mad0Manc8's user avatar
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1 answer
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Can several logic systems coexist physically in the same world?

In mathematics, each logic system is associated with an abstract model. In physics, similarly, each logic system is associated with a physical model that models a part of the universe, but I don't ...
Sayaman's user avatar
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Turing machines, thinking and category mistakes

According to my recollection, some philosophers have argued that it is a category mistake to ascribe intelligence to Turing machines, because Turing machines are abstract mathematical objects. What ...
Frode Alfson Bjørdal's user avatar
1 vote
2 answers
80 views

A priori argument fallacy

Considering the "A priori argument logical fallacy" (see https://utminers.utep.edu/omwilliamson/engl1311/fallacies.htm) Is there a way to formalize it (technical expression) using the ...
Vincent ISOZ's user avatar
2 votes
2 answers
164 views

Can a "paradox of understandability" be devised following Fitch's paradox of knowability?

Fitch's paradox of knowability is a testament against at least naive/moderate anti-realism as based on the principle that all truths are knowable. The derivation is split into two major sections, the ...
Kristian Berry's user avatar
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2 answers
72 views

Colored areas in categorical proposition Venn diagrams

This recent question prompted me to read about the square of opposition and I am confused about the purpose of red and white regions in Venn diagrams from this diagram. I think these Venn diagrams are ...
John Davies's user avatar
1 vote
1 answer
39 views

What is a "sphere model"?

I'm reading the SEP entry on multi-modal logic and there's this passage: Is this related to what the SEP entry on infinity says about probability, here?: Kolmogorov notes that if the original ...
Kristian Berry's user avatar
-2 votes
2 answers
129 views

What is a philosophical proposition?

There seems to be confusion on this exchange as to what constitutes a proposition in philosophy. This seems to extend to the burden of proof. The classical burden of proof is "onus probandi ...
Meanach's user avatar
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5 votes
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Existential import in "No A is B"

I have doubts about the existential import in categorial propositions of the form "No A is B" under Aristotelian interpretation. In "No A is B", it is assumed that both A and B are ...
Ray Siplao's user avatar
1 vote
2 answers
107 views

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
230 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
715 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?
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1 answer
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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 = ...
Agent Smith's user avatar
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5 votes
3 answers
262 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
83 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
0 votes
1 answer
56 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
32 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
0 votes
1 answer
58 views

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 ...
D J Sims's user avatar
2 votes
1 answer
47 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 ...
D J Sims's user avatar
2 votes
2 answers
60 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
37 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
44 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
43 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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0 votes
1 answer
48 views

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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0 votes
1 answer
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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=...
Display name's user avatar
2 votes
4 answers
933 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
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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?
John Smith's user avatar
-1 votes
1 answer
90 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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0 votes
1 answer
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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 ...
Damon Fernandez's user avatar
8 votes
7 answers
996 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 answer
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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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