# Questions tagged [logic]

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

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### What are the origins of the A,E,I,O notation for the four types of categorical proposition? [duplicate]

The labels A, E, I, and O are traditionally given to the four types of categorical proposition. Each is one of the first two vowels in the Latin words affirmo (I affirm) or nego (I deny), a usage that ...
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### A technical question about the limitation of z of "jointing together" or "zus(x,y)" in Gödel Arithmetization

I am recently reading Professor Carnap's Logical Syntax of Language. In p.61 D18.1., the limitation of z is not greater than: pot [prim (sum[lng(x), lng(y)]), sum(x,y)]. Remarks: z is the series-...
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### Why is Occam’s razor faulted for being a heuristic when almost everything in philosophy is?

I am confused as to why any sort of discussion about Occam’s Razor, without fail, has the addendum mentioning how the tool doesn’t prove anything. But quite literally, unless something is logically ...
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### Logic of reflective equilibrium

Reflective equilibrium is the simple but compelling concept that a person reflects on conflicts between different beliefs that they hold, and revises their beliefs to reduce the conflicts, or to ...
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### Is "may exist" and "may not exist" a negation that isn't a contradiction?

As usually happens, a statement (p) and its negation (~p) contradict each other. So, e.g. God does not exist, the negation of, God exists, together form a contradictory pair. A statement (p) and its ...
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### How does one differentiate between the logically possible and the impossible?

The term “married bachelor” seems to be an obvious contradiction. The very definition of bachelor and unmarried are with respect to each other and so it seems nonsensical to talk about a married ...
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### Is asking to align on definition during a debate a derailling or disingenuous demand?

In a recent discussion with a group of friends, we found ourselves in a situation where we appeared to be using the same word, but it became evident that we held different meanings for it. At that ...
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### Type of false reasoning?

I don't have extensive background in philosophy but I try to outline my question clearly. I am arguing with a person who always uses the same logic. We have an outcome X such a medical disease ...
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### Proof of the existence of God?

Here it is, the long-awaited proof for the existence of God (for your consideration). I have taken the liberty of defining discretely what God is, without which there is no question to be answered (...
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### Can A cause B with B preceding A in time?

I am wondering whether or not A can cause B with A occurring after B. Something about this seems nonsensical. But is it logically contradictory? If it is not logically contradictory, does this mean we ...
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### How to discuss subjects with people who are convinced by emotion, not by reason?

Sometimes I must discuss a subject with someone who has an emotional, not necessarily reasonable, connection to a subject. How can one discuss a subject or convince a person who has an emotional ...
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### In logic, is there a name for a secondary contradiction that arises from operating (unkowingly) under a first contradiction?

Say I assume predicate A and B. Say I show that A AND B is a contradiction. If I then apply the law of excluded middle to say NOT A, this is a fallacy, no? Does it have a particular name?
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### Prerequistes for mathematical logic

I have a working knowledge of calculus and linear algebra. But when I pick up books on mathematical logic (for example the ones listed in the logic study guide by Peter Smith), they often use ...
1 vote
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### How this principle related to Golden Rule and Eye for an Eye is called?

Had long admiration to this example: When criminals were sent to isolated island centuries ago they suddenly realized that it's not fun anymore when everyone is criminal. And switched to one of most ...
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### Does probabilistic justification exist?

Is there such a thing as how likely it is for a hypothesis to be true given evidence as a matter of fact? It is certainly true that we might feel strongly about other minds existing based on what we ...
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### Could a quantum computer simulate any system based on different types of logic?

Quantum computing is based on quantum mechanics (obviously) which has different logical rules than classical/Boolean logic. However, does this mean that a quantum computer could simulate or process ...
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### I have taken my midterm exam 1 hour ago, and I am confused about some question meaning

1 what is the defferenece between "the justification of line 6" and "the application of xx on line 6"? For example, we can find that in the line 6, the application is wrong because ...
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### Is the law of identity the same for negative expressions?

Is the law of identity the same for negative expressions? Does 'if not p then not p' have any specific meaning in philosophy? I am asking because I am trying to work out whether the vagueness of 'p' ...
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### Categorizing with metaphor, analogy, and symmetry

Continuing the discussion Categorizing with metaphor, analogy, generalization, and abstraction my next question is how two concepts metaphor/analogy equivalent to symmetry(change without change) .If ...
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### The Liar Paradox: Simply a sentence of indeterminate truth value?

Some sentences are true. Some are false. However, sentences like "What time is it?" or "Wash your hands" can be said to be of indeterminate truth value. This suggests a trichotomy ...
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### Is there a modal modification of the law of excluded middle that may render constructive?

Intuitionistic logic rejects the law of excluded middle, and paraconsistent logic rejects the law of non-contradiction. I wondered whether the rejected laws can still be incorporated, if they're ...
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### Intro to formal logic

We homeschool our kids, and "The Great Courses" offers a lot of good intro college classes that are suitable for 6-12th grade as well. I'm really not into math or logic so please forgive me ...
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### How Does Alethic Nihlism Address The "Changing Of Subject" Objection?

I recently read this article in my pursuit to understand wtf alethic nihlism is trying to say: https://philarchive.org/archive/ASASIT One of the objections to alethic nihlism is that alethic nihlism ...
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### Trivialism vs Alethic Nihlism

What are the similiarities and differences between the two theories (as well as arguments for and counterarguments against). From what I know, trivialism states that everything is true (and I believe ...
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### Is a naïve logical argument against god rational?

I have seen a short clip recently, in which someone used a proof by contradiction that a being cannot be omniscient (including past, present and future) and have free will at the same time. There are ...
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### What is the philosophy that deals with concepts being correctly fitted to reality or "carving reality at the joints"?

In philosophy of science thinkers sometimes speak of certain theoretical concepts "carving nature at its joints" (I think this might have been used prominently by Hilary Putnam but I can't ...
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### What's so special about Tarski's T-Schema?

It seems fairly obvious. Even a five year old could probably come up with it. Its obvious that if something is the case, it is true (literally synonyms). So, am I missing something? Is there a gulf ...
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I found myself thinking about the liar's paradox of the form "This sentence is false" and how it relates to one's conception of "Truth" and "Falsity". After deliberating ...
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### abductive reasoning in many fields of study

In continuation of the discussion What is the relation between abductive reasoning and fallacy? my question is that if medical science judiciary history all uses abductive reasoning (almost all the ...
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### Can a quantifier bind a name in FOL formulas

For example, if I have ∀a(∀x∃z(P(m) & Q(x,z,a)) || R(a,b)) (|| means OR), can I say it is a well formed formula in FOL. If I remove the ∀a at the beginning, can I now claim it is a well formed ...
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### Question about disjunction elimination in Fitch

I was recently using https://proofs.openlogicproject.org/ and realized that their version disjunction elimination is fairly restrictive. I had a proof set up something like this: p∨q (Premise) p∨r (...
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### FOL Equivalence and Theorems

So, this is sort of a 2-in-1 question. There is no sentence W of FOL such that: ∀yB(y)⟛¬W True or False? Now, my interpretation is: There is no sentence W in FOL where for all y in the extension of B, ...
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### Is backtesting inductive reasoning?

WE do backtesting in finance, that is we guess hypotheses/premises and then use previous data to verify it. https://en.wikipedia.org/wiki/Backtesting. https://www.investopedia.com/terms/b/backtesting....
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### Am I misinterpreting formulas from which to derive a conclusion in FOL?

The two premises and the conclusion are below, together with my interpretations: P1) ∀s∃t(¬R(s,t) ∧ ¬(s=t)) - For every element s in the domain, there is a t which R doesn't relate to s and that is ...
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### What is an explanation really?

Let's consider a hypothetical 'Church of the Moon' on a distant planet with a huge moon. The members of this church base all their beliefs about the moon and their religious practices on their holy ...
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### Internal vs External Statement in Homotopy Type Theory

I would like to clarify the precise difference between the phrases "statement inside/ internal the theory" and "statement about the theory" in context of Homotopy Type Theory. A ...
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### Does THIS fallacy have a name? [duplicate]

Three examples of what I mean: I argue against trying to increase social equality in your country, because there will always be much poorer countries. I argue against exercising, because you will ...
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### How do you symbolize "the x" when x has a condition

Let me explain. Suppose I have a question that asks me to symbolize "the smallest car has no air conditioning" from the domain of vehicles. I am thinking like this: "1.If x is a car AND ...
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### Alternate way to symbolize there is exactly one

So we all know the common way of denoting there is exactly one in First Order Logic: ∃x[(A(x) ∧ ∀y(A( y) → y = x)) ∧ B(x)] But, I was thinking and I wonder if there is another way to do it. Like let's ...
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### How do you symbolize Only A's are B's with an every in it

So I have this FOL question with the following key: A-forall E-there exist |-or &-and B(x):x is a basketballer F(x):x is a footballer S(x): x is a swimmer H(x,y):x is more lazy than y Now, we were ...
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### Question about equivalence and equality [closed]

What is it that equality and equivalence have in common, and how are they distinct. Please give detailed answer
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### What is Alethic Nihilism?

I recently came across this reddit post: https://www.reddit.com/r/askphilosophy/comments/15chen5/comment/jtwnkkw/ I think it has something to do with denying the truth predicate without denying the ...
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### Is there a Formal discipline of tying Logic Puzzles to Mathematical Equations?

I am attempting to find the answer to a long standing question in mathematics, known as the Collatz Conjecture. In this attempt, I’ve figured for myself, in a way that I haven’t seen produced anywhere ...
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### Provenance of 'malicious joke' "He has not interpreted my words as I intended. For I intended that there be no counterexamples."

I doubt this could be where I originally came across this quip/joke, but a google search found it in footnote #2 of [1]. The footnote reads: 2 Compare the malicious joke: 'Mr. Z claims to have found ...
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### Epistemic circularity and skepticism about reason

Disclaimer: I'm not a philosopher and I'm not a native speaker, so apologies if my question is somehow flawed as a result. I'm happy to clarify anything that is unclear. So here it is: Reason's own ...
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### Fitch derivations for equivalence relation properties

Primarily, this a request to check Fitch-style derivations in the file, https://drive.google.com/file/d/1du-EIZG3CSdrcfDbldlzwgRftDzeVc8K/view?usp=drivesdk This is not trivial. The reflexiveness ...
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### How did Aristotle discover his logic?

Supposedly Euclid employed analysis (conclusions→principles) and not synthesis (principles→conclusions) when he devised his definitions/postulates/axioms in his Elements. How did Aristotle discover ...
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### What are some ways of understanding plural predication (and what are some academic resources on the matter)?

The particular case I'm thinking about has to do with existence. Peter Van Inwagen writes: 'When I say that affirmation of existence is denial of the number zero, I mean only that to say that Fs exist ...