Questions tagged [logic]

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

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Does modus tollens capture the essence of “necessary condition”?

Does modus tollens capture the essence of "necessary condition"? (1) P → Q, ¬Q, … so ¬P. (2) So Q is a necessary condition of P. Is (1) the inner structure of (2)? Are any of these true: The ...
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Is the Law of Identity a Logical Absolute? Can it be doubted, violated, or disproven (i.e., proven false)?

**The First Law of Thought: The Law of Identity** Something is what it is [L_1], and it is not what it is not [LI_2]: -| yields the logical conjunction: [LI_1 & LI_2], & = “and”; Therefore, ...
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Are these two propositions equivalent?

Are the propositions "Everything happens for a reason", and "Nothing happens without a reason" logically equivalent?
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Explanation of a quote from Spinoza

Notandum, dari necessario unius cujusque rei existentis certam aliquam CAUSAM, propter quam existit. Et notandum, hanc causam, propter quart aliqua res existit, vel debere contineri in ipsa natura et ...
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What happens when you blame someone [closed]

When you blame someone, are you asserting an opinion or a fact? For example, Let's begin with this: Person A and Person B get in a car accident. Person A was on his phone, while Person B was abiding ...
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What comes before propositional logic? [closed]

Essentially, what tools does a human require to figure out or build propositional logic?
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Can’t we assume that the Boltzmann Brain scenario can be cognitively stable?

In the Boltzmann Brain scenario, we are all brains produced by random fluctuations within a high entropy universe. The argument which I had accepted before was that our very reasoning can not be ...
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56 views

Can statements about the future be facts?

Let's set some context: Person A and Person B have a group project. They are both assigned a slide (Slide A for Person A and Slide B for Person B) Person A has finished his slide, yet Person B hasn't. ...
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What's wrong with this syllogism?

No one held for murder is given bail Smith isn't held for murder Hence Smith is given bail no M is B s is not M s is B What's wrong with the conclusion?
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Name of logical fallacy that compares “our noble hero” to their “ridiculous clown” [closed]

On social media we often see inflammatory partisan image memes, that compare conservative vs liberal, or past generations vs today's. (Or anything really.) For example: The youth from past ...
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Why all the dismissal for Circular Reasoning? [duplicate]

In my studies of Mathematics and (mostly) Theoretical Computer Science I've encountered what is known as Munchhausen's Trilemma which purports to demonstrate nothing can be actually be proved because ...
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How can this shorten ( ~p v r ) $\and$ (~q v r) to ((~p $\and$ ~q) v r)?

I am just confused how this be possible, what rule is been used?
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Validity/Soundness of an argument from R. Carrier

This is about training in argumentation. I use a text from R. Carrier: https://www.richardcarrier.info/archives/468, where he claims that from nothing everything follows. (Don't get shocked, the ...
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Difference between a law of logic and a logical principle

The traditional notion of logic, broadly speaking) is that it is a system of laws and principles governing valid inferential reasoning (i.e. laws of logic logical principles). But what precisely ...
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Explain what is wrong with the logic in the following statements. Then name the fallacy or fallacies involved [closed]

After slicing a Golden Glow orange, Nancy discovers that it is rotten. “I’ll never buy another Golden Glow product,” she declares emphatically. A campaigning politician states that unless the federal ...
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Deductive reasoning & conditionals

What would be a good example of explicit deductive reasoning that doesn't seem to be possibly interpreted correctly as a conditional (If A, then B)?
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How to draw a truth table on Stack Exchange? [migrated]

I need to draw/input tables, such as truth tables in order to ask and answer questions about logic. Can someone please instruct me on how to make a truth table on this site. My goal is to make a truth ...
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244 views

Is it logically permissible to neither believe nor disbelieve a proposition X? Or does this violate the law of excluded middle?

Given a proposition X, one can either believe it or disbelieve it. Is it logical however to neither believe X nor disbelieve X? Is it logical to neither believe proposition X nor its negation ~X? I ...
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60 views

In logic, can we or can we not prove that a formula is invalid?

I'm a novice in this field of logic. While reading about soundness and completeness of a method, I read this line: "a logical system has the soundness property if and only if every formula that ...
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Equivalence Thesis

What is, if any, the canonical justification accepted in mathematical logic for the Equivalence Thesis, asserting (1) that indicative conditionals are truth-functional logical expressions and (2) that ...
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Fallacy and guilt by discussion?

I recently encountered a discussion that went along the lines of: A: Pedophiles are not just old men touching little kids. They're also 23 year olds going out with 16 year olds. B: Pedophilia ...
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How would I start a formal proof for the conclusion (P → Q) ↔ ¬ (P ∧ ¬ Q) with no premises? [closed]

There are no premises, and I'm doing this in fitch
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Is a 'creatio ex nihilo' logically impossible?

Please look if my following argument is correct, otherwise point to my mistakes! I distinguish two cases: We have nothing but logic, i.e. we have an empty set of premises. And here the answer seems ...
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75 views

How to prove A<—>not A

So basically there are no premises, but the file I have received to start this problem has a contradiction symbol as step one. I’m not sure if this was a mistake or purposeful, and if it was ...
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Truth-value injection in quasi-empirical theoriess

While reading about quasi-empiricism I have encountered the following statement: "Thus the logical channels of theories are not downward transmission of truth but for upward re-transmission of ...
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When is a wish not a proposition?

Consider these sentences: S1. Would that Los Angeles were not that far away. S2. I really wish Los Angeles were nearer to New York. S3. I wish that Los Angeles were not that far away. S4. It is going ...
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Do philosophers generally reject that philosophical reasoning relies on axioms?

The way I've always thought that philosophy worked is that philosophers have a certain set of tools (deduction, laws of thought, basic sources of knowledge) which they use to come to reasoned answers ...
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Do actual and potential infinity collapse into each other?

https://plato.stanford.edu/entries/set-theory/ states outright that set theory "can be defined as the mathematical theory of the actual—as opposed to potential—infinite," and the article on ...
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Is the sentence “all apples are red” an atomic sentence?

In An Introduction to Logic by Patrick Suppes, an atomic sentence is defined as a sentence that contains no sentential connective. However, in a later chapter, a sentence is defined as a formula which ...
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disjointness in logics with higher order plurals

The SEP article on plural quantification has a section on higher-order plurals. First a word on notation, I use ∈ to denote member of an individual in a plural individual, and ⊕ to denote XOR. When ...
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fitch proof chapter 13 (ex. 13.29) [closed]

how to proof exercise 13.29 without using taut con
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Logic – Deduction in Tarski's World (Fitch/LPL 13.22) [closed]

I am trying to use existential elimination to derive Brillig(a) & Tove(a). how would I do this? I have tried to do separate sub proofs to prove both Brillig(a) & Tove(a) but that doesn't work ...
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Did Aristotle make a mistake in the Prior Analytics, Part 5?

Did Aristotle make a mistake in Part 5 of the prior analytics? “If the middle term is related universally to one of the extremes, a particular negative syllogism must result whenever the middle term ...
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If-then statement and time between antecedent and consequent

Suppose the following statement. "If I kick the ball then the ball will hit the wall." Can this sentence have a truth value? I mean the time that I kick the ball, it hasn't reached the wall so the ...
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How to show that a rule of inference is sound or complete? [closed]

I've been reading patrick suppes’ an introduction to logic, and the rules of inference mentioned in it, like universal specification, conditional proof, etc. haven't been proven to be sound or ...
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First order logic - Problem with symbolizing a sentence

I have a sentence like this: Good people should be treated the way they treat other good people. What is the best way to symbolize this? I have a particular problem with should, it seems to be about ...
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Is a fallacy involved in perceiving the solution to a long-standing problem as simple and straightforward?

In university (or, school) we're often presented with a problem, and directly afterwards, the solution is presented. Quite often, the solutions presented for a given problem seem painfully obvious, ...
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“v = 1 m/s”: predicate or relation? Any literature?

This question is partially related to How does "is" work? and What is the difference between the "is" of predication and the "is" of identity?, but more specifically it ...
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Does an English translation of “Logica ‘ingredientibus’” by Peter Abelard exist?

Pretty much the title, first time I'm having trouble finding anything.
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What fallacy is this? “This happened, therefore there must be good reasons for it”

What fallacy is it when someone says "this is true/it happened, therefore there are good reasons for it"? For example: We drive on the left (or right, depending on country) side of the road, ...
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What is the difference between an elimination rule vs an inference rule?

What is the difference between an elimination rule vs an inference rule? They seem like they are the same thing.
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Could someone be lying when using the future for an assertation?

Let's say someone states that if party A wins the elections, they will start killing opponents. Of course, let's say there is absolutely no evidence that support that claim and in a debate I state ...
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Is consistency tautological?

I assumed an idea is consistent with itself if it does not contradict itself, and that this is "tautological" because it can be inferred from itself and nothing else. Is that a misunderstanding of the ...
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Are opinions considered statements?

‘Aristotle was great’. Is this a statement? I consider a statement to be something either true or false (but not both). For an individual, this may be considered a statement (because either you ...
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What's the logical fallacy here?

Where is the logic fallacy here, and which is it? A. Whatever is not normal is abnormal. B. Sleeping is normal. Conclusion: Being awake is abnormal. Better example: A. Whatever is not ...
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What is mathematical logic, really? [duplicate]

Is it math for studying logic or logic for studying math? I'm confused on what it really is.
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49 views

What logic system do you use for day-to-day thinking and why? [closed]

I'm studying various logic systems and I'm wondering what logic systems that you folks use on a day-to-day basis? That is, in your daily lives, what logic system do you use?
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In a deductive reasoning system, what happens if we have unfounded axioms? [closed]

What if our axioms are false? What happens then?
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Life as a formal system

I am curious if there is some existing work on viewing life as a formal system. In formal system we have: axioms and rules of logic (like in math AND, OR) then we derive and prove theorems I see ...
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Why isn't there a unified logic?

It seems that there are numerous systems of logic. Why didn't we just combine them all into one and get the best of all worlds? Like we could combine axiomatic reasoning and analogical reasoning into ...

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