# Tagged Questions

Logic is the study of formal systems of reasoning, especially of the deductive variety. It is one of the few fundamental philosophical subdisciplines, along with metaphysics, ontology and aesthetics. Logic has taken on considerable importance in recent mathematical developments, and one of the ...

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### It's not possible to deduce whether this statement is true or false

Let's first consider the basic contradictory self-reference: P0 = "Statement P0 is false" P0 can't be either true or false without contradiction. This is similar to NaN (Not a Number) in mathematics,...
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### What happens at the event horizon? [on hold]

When watching something fall into a black hole, would we A) See it falling slower and slower eternally or B) See it falling slower and then stop?
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### Solving a logical analysis puzzle

A high school is made by 25 pupils, of which 13 cycle, 11 swim, and 8 go skiing. There is no one practising all three sports. In yesterday's test the sportsmen (those practising at least one sport) ...
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### Name of fallacy when one says he used to have the same views

I was arguing with a friend (we were at loggerheads with respect to our views) and in the middle of the argument he refuted my claims by saying that even he used to have the same views (as I do now) a ...
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### What are the most untrustworthy antithesis in the History of mankind? [closed]

I tried to find a answer, I search a lot and I failed. Can you help me to find the most untrustworthy antithesis in the History of mankind? I need only 2 or 3 examples and they are to be really ...
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### Definitions and choice

My specific question that I want answered is: Among definitions, how do we choose which one is the best? When it comes to definitions of abstract concepts, it seems like we can define things willy-...
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### Is the statement “Nothing is absolute” a contradiction?

When we say "Nothing is absolute", we actually stated that "Everything is absolutely not absolute", is this a contradiction?
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### Did GOD(i.e who created universe) create math first or universe first? [closed]

Did GOD think about math first , and then fit this nature to math ? OR GOD created nature which has accidentally this patterns , WHICH we human call it Mathematics?
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### Commentary on Tractatus 1.21

In Tractatus 1.21 Wittgenstein writes  Each item can be the case or not the case while everything else remains the same. [1] I'm looking for commentary on this point, since it seems out of place ...
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### What does the truth-value of a material implication represent?

This question comes from my attempts to understand what the truth value for a material implication with a false antecedent represents. I have seen several justifications for this convention, usually ...
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### Someone abandoning his own arguments

Is there a name for a fallacy when someone used an argument against his opponent, but abandoned that argument as "unimportant", "invalid" or "irrelevant" when it was turned against him?
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### Why is “similarity” not a logical relation? (from “Natural Kinds” by Quine)

I have two questions regarding Quine's paper “Natural Kinds”: Why isn't similarity a logical relation? Why is our ability to recognize similarity so fundamental? These two things are explained in ...
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### Is If X, then Y. Not Y. Therefore, not X. correct?

If X, then Y. Not Y. Therefore, not X. I don't have the logical or mathematical sophistication to know if this is a correct conclusion or not.
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### Could you really have a dog that can't predict anything?

A little bit of background: in a 1999 episode of The Simpsons, they show the first few seconds of the Guinness Book of World Records. Among the other teasers, they say "you'll meet a dog that can't ...
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### Is the Holocaust an argument from authority? [closed]

Is the belief that the holocaust happened an argument for authority based on non-physical evidence?
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### Is “all swans are white” equivalent to “if it is not white, then it is not a swan”?

By equivalent I mean, each hypothesis can be deducted from the other.
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### What is the origin of the truth table in logic?

Specifically for the material implication if possible. Who was the first to use a truth table for this and justify its validity?
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### Why does Copi / Cohen call “Othello believes that Desdemona loves Cassio” a compound statement?

Copi's Introduction to Logic states that a compound statement is one which consists of 2 or more statements as components. A component is defined as a part of a compound statement that is itself a ...
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### Is “A and not-A” meaningful (and false) or meaningless?

Is there any phrase of the form "A and not-A" that is meaningful? We can imagine vernacular expressions with that form that carry meaning. I could say, "I do like France and at the same time I don't ...
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### A question about statements and conclusion

Consider the following statements: All actors are dancers No dancer is a singer Some singers are musicians Conclusion - 1.Some actors being musicians is a possibility 2.Some singers being actors ...
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### How is this Announcement NOT an explanation?

Source: With Good Reason, An Introduction to Informal Fallacies (6 ed, 2000) by Prof. S. Morris Engel PhD. [p 14:] *16. [Premise 1:] Because of recent cutbacks in our custodial staff due to ...
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### How are announcements, complaints, compliments, or apologies always NOT arguments?

Source: With Good Reason, An Introduction to Informal Fallacies (6 ed, 2000) by Prof. S. Morris Engel PhD. Here, 'apology' means expression of regret, and not the Ancient Greek meanings [p 10:] As ...
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### Why did Aristotle choose the terms 'Major Term' and 'Minor Term'?

I have not (yet) studied Ancient Greek. This comment introduced me to the pertinence of Aristotle's Prior Analytics, but the translation and commentary below do not answer question entitled above. ...
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### Why did Aristotle describe as Extremes: the Major Term and Minor Term?

I have not (yet) studied Ancient Greek. This comment introduced me to the pertinence of Aristotle's Prior Analytics, but a translation below does not resolve my question entitled above. Source: ...
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### Do premises in modus tollendo tollens arguments require greater certainty than others?

In a standard syllogism, the two premises of the argument are independent of each other, so all extrinsic warrant being equal, the argument will prove the conclusion to be probable if and only if... ...
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### Only valid syllogisms are syllogisms?

If I have an invalid syllogism, it can still be considered a syllogism, right? Example: All A is B All B is C All C is A It is invalid. But it's still syllogism? (I know that may seem obvious, ...
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### Is there a name for this type of situation in the most abstract sense?

This is hard to describe so please bear with me. Is there a name for the condition of a 'meta property' that arises from some sorts of artifacts, becoming a governing, self-sustaining situation, but ...
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### What is the explicit reasoning behind proof by contradiction?

From my understanding, proof by contradiction consists of the following steps. 1. Show that p -> q, where "->" is the conditional. 2. Show that q is false. 3. Deduce from a truth table that p must be ...
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### Is this argument a deduction or induction?

I'm reading the book A Concise Introduction to Logic (12th edition), and they say that this is a deduction: Gabriel is a wolf. Gabriel has a tail. Therefore, Gabriel’s tail is the tail of a wolf. ...
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### What are factual propositions?

I've been reading up on epistemology, after having studied a bit of logic. Given that, I am in a good (or at least better) position to understand a proposition, and it's properties. One such property ...
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### Truth Value of Sentences Containing Logical Contradictions

Do propositions containing logical contradictions have truth values, or are they meaningless? For example: A) Some married bachelors exist. B) 95% of married bachelors live in Maryland. C) ...
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### Self-referring propositions

This proposition is false As you can see in the proposition above, there is a problem. This sentence can't be true, but it can't be false either. I believe that this issue comes from the fact that ...
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### To Check or not to Check? [closed]

Samuel and Paul make a wager. They want to know if a certain professor held class the day prior when they were absent. The professor is unreachable, though, so they have to ask students from class. If ...
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### How to prove that what we will know isn't true isn't true?

My apologies for the convoluted question. I'm still (kinda) arguing with someone that if we have knowledge then there are facts. One way I've argued for this, is by saying that what we will know isn'...
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### A and ~A in logical proof

In my logic class last semester, we went over proofs with the rules of induction and replacement. In a couple of the exercises, I noticed something. In each of the exercises in question, all of the ...
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### A Critcism of the Ontological Argument for God

Allow me to present the argument: (1) By definition God is that being which possesses every perfection. (2) Existence is a perfection. (3) Therefore, God exists. Whether you agree is not important,...
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### What do you call the output of a truth table?

I know that the value of said output can be either True of False, but what is the actual output called? Another way of phrasing the question is, is what do you call the resolution of a complex ...
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### Thieves are they who do theft [closed]

Thieves are they who do theft. Theft is when A takes from B what belongs to B without B's consent. Gov't takes from B what belongs to B without B's consent. What is Gov't then?
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### Can one be a Modal Realist without also having to incorporate the existence of impossible worlds?

I know Modal Realism well enough itself, and have read many of the objections (and subsequent responses) that David Lewis himself took up in relation to the philosophical position. My question is, do ...
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### Difference between Tautology and Circular Reasoning

Often it is considered that a tautology is the same as a circular reasoning. However, in the Wikipedia entry of Tautology, it is mentioned that circular reasoning and tautology are different. Can ...
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### Omnipotence Paradox Defense and Meinongianism/Neo-Meinongianism

I was considering a solution to the omnipotence paradox in which excluding logical impossibilities from the definition of omnipotence is justified as follows. Consider the proposition, "God could ...
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### What are some active areas of research in proof theory?

Is there any research activity going on in the field of proof theory today? If so, what are some of the most active areas, what types of questions do they deal with, and where can I go to find out ...
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### Can all mathematical reasoning be translated into traditional logic?

Can all mathematical reasoning be translated into traditional (Aristotelian, syllogistic) logic? It would seem not ∵ one cannot syllogistically establish the validity of the reasoning in the ...
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### Probability and logic

Is probability theory (using Kolmogorov's axioms) an extension of the propositional calculus, or an extension of first order logic?
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### What does the term “mathematical logic” mean?

What is "mathematical logic"? Is it the logic of mathematical reasoning, or is it the claim that mathematics and logic are identical? Also, is "quantificational logic" a particular type of "...
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### Within philosophy, is “reason” a broader concept than “logic”?

Within philosophy, is "reason" a broader concept than "logic"? In a comment under this question Jon Ericson suggested a case could be made for "reason" to include "logic" but not vice-versa. I had ...
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### Is a social construction a social construction?

I've been thinking a bit about the core argument of social constructionism. Whenever I see the argument being employed, it seems that it means that if something is a social construction, then this ...
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### Why does what I've written fail to define truth?

(Also posted in mathstackexchange prior to this). I stumbled across a set of axioms for first order logic a bit ago. Intrigued, I decided to try to write it all down and organise what I read. After I ...