# Questions tagged [logic]

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

2,369 questions
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### How do quantifiers work in predicate logic?

Predicate logic is somewhat like propositional logic, except that where propositional logic only works on the level of whole sentences (e.g. A = "Socrates is mortal", B = "All ...
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### How to use “some” and “not all” in logic?

As asked here about the difference between "some" and "not all". I'm looking for a practical example in real world where these two can be applied. Do we have a situation where we can use either of ...
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### A (possible) puzzle regarding John Lane Bell's “Abstract Sets”

John Lane Bell, is his paper "Abstract and Variable Sets in Category Theory" (go to Bell's Homepage to download it), defines an abstract set as follows: "An abstract set is then an image of pure ...
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### What do “universal” and “existential” mean in logic?

What's the difference between "universal" and "existential" when used in the context of wff (well-formed formulas)? We have a universal quantifier, which can be written as (x), and an existential ...
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### How to check if this proof is valid?

I'm having some doubt if this proof is valid or invalid, especially regarding the line 4 derived from line 2. Do I need to change the letter in there? 1. (z)~Fz ∴ ~(z)Fz Using Indirect proof ...
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### Inference rules for quantifiers in logic

I have come across an inference rule that if I had statements like: Not all are birds which translates to ~(x)Bx, is equivalent to, Some are not birds which translates to (∃x)~Bx. According to this ...
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### Question about “Some A is B” in logic

In logic we say, "All A are B" to mean (x)(Ax ⊃ Bx) "Some A is B" to mean (∃x)(Ax . Bx) I can see how (x)(Ax ⊃ Bx) makes sense, By looking the table if we had A = 1, B = 0 then this statement wouldn'...
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### What's the difference between “not all” and “some” in logic?

We have, not all represented by ~(x) and some represented (∃x) For example if I say, Not all are animals. Some are animals. Because we aren't considering all the animal nor we are disregarding all ...
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### Is it possible to determine the truth values of propositional proof?

I have been trying to solve some propositional proofs, E.g. (A ⊃ B) (~A ⊃ B) Therefore, B And I know that this is valid argument. Can we ever know the real values of A and B from the truth table or ...
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### Can death be given meaning through the theory of evolution?

Disclaimer: I haven't seen any other posts about this anywhere and one night, I was just thinking and scribbled this down, so I don't know where this could be found otherwise. What if, there is no ...
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### How can we reason about “if P then Q” or “P only if Q” statements in propositional logic?

When you have a propositional sentence of the form P ⊃ Q  — which we might read as "if P, then Q" — how can you tell when it is true, or false, based on the truth-values of P and ...
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### If-then meaning in logic [duplicate]

Possible Duplicate: How can we reason about “if P then Q” or “P only if Q” statements in propositional logic? In a logic exercise, suppose this argument is given: P1: If there's a God, then ...
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### Proving a propositional argument [duplicate]

Possible Duplicate: How can we reason about “if P then Q” or “P only if Q” statements in propositional logic? Are both forms of arguments correct? If not then why? To me both seem correct because ...
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### What does “the case” mean?

Reading some philosophy articles, I keep coming across the phrases "it is the case that X" and "it is not the case that Y". I get the impression that this phrase has a somewhat different nuance than "...
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### Conditional statements truth table [duplicate]

Possible Duplicate: How can we reason about “if P then Q” or “P only if Q” statements in propositional logic? I have read in quite a few books that the proposition 'p->q' can be read as either '...
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### Does Cogito ergo sum need to be more specific?

Something about my translation has bothered me since I originally posted my question (which follows below). It concerns what Bertrand Russell wrote in "On Denoting". Ryno indicated a circularity with ...
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### Statements in sybolic logic

I have 3 statements I want to convert into symbolic logic (P, Q, etc.) All men are people. Some men are clever. Therefore, all people are clever. First of all, I know this is illogical, but I'm ...
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### Denying a conjuct in propositional logic

According to Conjunctive syllogism, We accept one part of the statement as true and reject the other part as false. Truth table for AND _____________ | P Q | (P.Q)| | 1 0 | 0 | | 0 1 | 0 | ...
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### If-then in propositional logic [duplicate]

Possible Duplicate: How can we reason about “if P then Q” or “P only if Q” statements in propositional logic? Here's the table for If-then _____ ___________ | A B | (A ⊃ B) | | 0 0 | 1 ...
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### Does quantificational logic replaces syllogistic?

If so, does it mean we should always use quantificational logic since it combines both syllogistic and proportional logic? Also, Is there any other logic which further builds on quantificational logic?...
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### Are all non self-referential statements true or false?

It is well known that there exists self-referential statements which are neither true or false, such as "I am lying". Is it possible to have statements neither true or false which are not self-...
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### Argument “a is b” but “b is not a” valid?

Is it true that in logic "a is b" but "b is not a"? Does it work one way or both ways? For example: a is b Therefore, b is not a If this is valid, How can you prove?
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### What does “classical logic” mean?

I'm a junior researcher in Computer Science field and I've had some difficulties with some scientific terms like the one on the title "classical logic" which is used to represent and identify some ...
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### Can knowledge about argumentation be sufficient for philosophical logic without too symbolic or mathematical concepts?

The most important element for expression of truth is trough an argument, with premises and conclusion. Argumentation requires to avoid fallacies and adhere to the truth. However logic if treated as a ...
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### What form of logic is necessary for practical philosophy?

Logic is broad and concerns different fields, so to be more specific with the purpose of logic what is the most important form of which required for practical philosophy?
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### What is the logical contradiction that occurs in certain self-referential multiple choice questions?

Consider the following multiple choice question: If you randomly chose and answer to this question, what is the probability that you are right? a) 17% b) 0% Note that when I heard ...
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### What philosophical tradition/ school advocates the use of informal logic as a better tool than formal logic?

There are some notable persons who criticized formal logic in favor of informal logic for various reasons, like Schiller. So what is the school of thought or tradition that incorporates or adheres to ...
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### To what form of logic shall political and moral philosophy best conform with: formal or informal logic? [duplicate]

Possible Duplicate: Is it informal logic which is the only necessary shade of logic for political philosophy? I greatly require intellectual concurrence to this; Political and moral philosophy is ...
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### Is it formal logic which is the “most essential element” to philsophical logic?

Logic sprouted of different branches and now there is for computers, but as it grows the symbols tend to deal with problems not in accordance with what central philosophy tackles. It should therefore ...
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### Is “Don't blame me; I voted for ___” a bad argument?

Is there a fallacy in the argument, "Don't blame me; I voted for ..."? Or is a voter's entire responsibility for their contribution to whatever current state of political affairs they experience ...
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### Can I introduce myself as a self taught philosopher? [closed]

I did not ask such for pretentiousness, but for the reason that I may be characterized along with my arguments distinct of other scholars for nobody will know of my endeavor unless I tell them. I ...
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### Proof Universe Came From Nothing?

Consider the following proof: (1) Let the Universe be defined as the set of all things. (2) It is impossible for a thing to come from itself. (You can't be your own parent) (3) 2 implies a set of ...
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### Do the laws of logic exist independently of human or animal consciousness?

Are the laws of mathematics and logic, such as if a=b, and b=c, then a=c just constructs of the human mind, or does the universe hold an innate logical structure to it, which the physical part of the ...
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### What is a good table format for diagramming logical conclusions?

I am looking for a visual organization format that can help group logical conclusions. Basically, If people are given 3 options, and I am looking to interpret their vote, what is a clean manner of ...
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### What logical fallacy is this?

You tell a person to try something. On the 1st & 2nd attempts, they succeed. On the 3rd attempt, they fail. They give up, saying "I failed, so I will always fail." From only 1 data point (of 3) ...
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### What logical fallacy is made in this statement?

Consider this text: Researchers conducted two different types of test on a large group of people. After that, the researchers subjected the people to situations like Z and noted their response R. ...
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### On consistency as a univerally recognized value, and arguments using this principle

Consider this dialogue: John: If I bet you a dollar this quarter would land heads, would you accept? Jane: Yes. John: If I bet you a dollar this nickel would land heads, would you accept? ...
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### Is it possible for something PERFECT to be created by humans?

Once in high school, a philosophy professor asked us the following question, as homework: Is it possible for something perfect to be created by humans? We were to discuss this question in the next ...
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### If the universe is infinite, shouldn't I already have been contacted by a time and space travelling doppelgänger?

If the universe is infinite, by virtue of chance it means that every possible configuration of matter must exist somewhere (according to this documentary). Therefore, if the universe is infinite and ...
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### Are there any resources for teaching young children philosophy and logic?

My oldest child is nearly six years old and will be starting his first level of formal schooling in a few weeks. I don't believe he will be taught philosophy and logic in the classroom, so I would ...
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### Does a Background in Mathematics Make One a Better Philosopher?

I was a Philosophy major as an undergrad and became obsessed with the beauty of rigorous argumentation. There I didn't take a single class listed under the Mathematics department and was almost ...
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### Can Tao Te Ching be translated using paraconsistent logic?

Lao Tsu's Tao Te Ching is full of paradoxes. Is paraconsistent logic sufficient to translate Tao Te Ching to formal logic? To be specific, how can I get started with the following passage from J....
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### Is Dunn/Belnap's 4-valued system a product system (as a many valued logic)?

The description of Product systems in the SEP entry on Many-Valued Logic uses Dunn/Belnap's 4-valued system as an example of a product system: In this way, the truth degrees of Dunn/Belnap's 4-...
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### Is this paragraph in The Age of Reason by Thomas Paine an example of a rhetorical argument?

I found the following passage in The Age of Reason by Thomas Paine When Samson ran off with the gate-posts of Gaza, if he ever did so, (and whether he did or not is nothing to us,) or when he ...
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### Is there an unambiguous way to state the biconditional in everyday language?

I am having a hard time understanding this section in Wikipedia's article on Logical biconditionals: Colloquial usage One unambiguous way of stating a biconditional in plain English is of the form "...
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### Is First Order Logic (FOL) the only fundamental logic?

I'm far from being an expert in the field of mathematical logic, but I've been reading about the academic work invested in the foundations of mathematics, both in a historical and objetive sense; and ...
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### Are multi-valued logics a figment of a mathematicians imagination?

Once logic has been formalised, it's an easy move to ask whether certain axioms can be altered. One of these is that logic is two-valued. This has been done and we have formal multi-valued logic. ...
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### Wittgenstein on algorithm decidability and Incompleteness Theorem [closed]

I found Internet resources a bit confusing, so I ask this question: What are Wittgenstein's arguments on algorithm decidability and Godel's Incompleteness Theorem?