Questions tagged [logic]

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

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117 views

Tarski's convention-T and inductive definition

I am studying the famous tarskian theory of truth ad there is a thing not clear to me. 1)Why does the T-schema "'S' is true if an only if S" specifies the truth-condition for the sentence 'S'...
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TFL - Natural Deduction Problem Solving

I am using a website called Carnap.io for submitting my proofs for natural deduction for TFL. It keeps telling me the proof for the following premise is wrong: ⊤ ⊢ (A ↔ ¬B) → (¬A → B) but I'm not sure ...
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15 views

Natural Deduction for TFL

Is the proof below correct for the following premise?: ⊤ ⊢ (B → ¬B) → ¬B 1 B → ~B :AS 2 B :AS 3 ~B : → E1,2 4 ⊥ 5 ~B :~I1-4 6 -- 7 (B->~B)-> ~B :->I1-...
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124 views

What is the difference between these two types of proofs?

While employing induction method for proving, is deriving the string(formula) "Fn → Fn+1 " any different from showing that if Fn holds true, then so does Fn+1 ? By showing I mean that we use ...
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1k views

What does the symbol “:=” mean in formal logic?

:= What does the "colon-equal symbol" mean, and how is it used?
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97 views

What is an author? [closed]

If you make a program to write a book, are you considered the author? I’m sorry if this is off topic, but I couldn’t tell if that was included in the ‘on-topic’ list of acceptable questions, and I ...
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1answer
71 views

Functional Abbreviation for Inst Expression in Turing's Paper [closed]

In Turing's 1936 paper On Computable Numbers Page 30-31, and its Correction Page 1-2 For a Turing Machine M, Inst(i,j,k,LEFT,l) means that if M scans symbol j under m-configuration i, then the symbol ...
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61 views

Prove that p → □p is not derivable in system K?

The only way I could think of doing this is to show that p → □p with the K axioms would imply a contradiction, but I don't think that's true. Not sure how to get started on this. Do I just have to ...
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2answers
56 views

Knowing versus understanding the composition of the universe

The mass-energy content of the Universe is approximately this: 5% normal matter, 20% dark matter, and 75% dark energy. Because we don't know much about dark matter and dark energy, apart from the fact ...
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67 views

Are inferences in everyday life often combinations of inductive, deductive and other possible methods of inference?

Logicians have distilled methods of inference into some fundamental kinds like deduction and induction. In everyday conversation, though, we are constantly making inferences both inductively and ...
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108 views

Is it necessary for something to be observed for it to exist?

Say something was to happen in the universe, so minuscule that no one notices it, and it has no effect on history whatsoever. Is it correct to say that it never happened, because when we say something ...
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143 views

Is truth status of statement “1/0=666” false or unknown?

Suppose we have following logical statement: if and only if x=666 is a true equality, then x is the devil's number (we assume that there is only one devil's number in existence). Now let's use 1/0 as ...
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63 views

How does one prove (A->B)vC from the premise ~A? [closed]

Is the premise really enough to prove this?
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How to prove the following arguments [closed]

I'm trying to do a bunch of proofs to get better at them but it seems like I need some help with negation. Can anyone who has time prove the following arguments? I would really appreciate it! ¬(P ∧ ¬Q)...
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90 views

A thought experiment: will the following observations lead you to question Aristotle's syllogism?

Many philosophers think that logic are "inherently right" and cannot be refuted by empirical observations. Below is a thought experiment that questions this view. Let's take Aristotle's ...
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How can we overcome the challenge of the anti statistical philosopher?

Conventional statistical inference has been strongly challenged by the anti statistical philosopher who uses the following example: Imagine a man. Imagine that every time a man opens his front door ...
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1answer
69 views

How can we prove this argument is invalid?

Let's say below is the argument, Premise 1: All men are mortal Premise 2: Socrates is a man ------------------------------------------ Conclusion: Therefore, Socrates can think Now, to prove an ...
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31 views

What are the differences between a Statement and a Premise?

What are the differences between a Statement and a Premise? I wonder if they are same or not? Any counterexample where a statement is not a premise?
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1answer
32 views

Is it a valid argument?

I wonder if the below argument is a valid or invalid? Premise 1: All the humans can fly Premise 2: I am a human --------------------------------- Conclusion: Therefore, I can fly I also wonder, if ...
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1answer
58 views

Does the existence of a thing necessarily imply its logical necessity?

In formal logic, does the existence of a thing necessarily imply its logical necessity, i.e., is it possible for something to exist without being logically necessary? Can a logically unnecessary thing ...
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1answer
480 views

How can we differentiate between change and progress in the area of math and ethics?

I'm studying epistemology, and I want to use reason and language as tools for carrying an investigation. How do I discuss the subjectivity inherent in change and progress, and also whether change and ...
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1answer
237 views

Which logic quantifier takes precedence when we are trying to evaluate a forumlaic interpretation?

Given: ∀y∃x Ryx ∃x∀y Ryx How do we know if these formulas are true? Are they true as long as some instances are true or must all be true? In other words, how can we identify the main quantifier? ...
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1answer
47 views

Quine said that even logic could be revised on empirical grounds. Did he later reverse that position? Where?

Quine said that even logic could be revised on empirical grounds. Did he later reverse that position? If so, in which of his writings?
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“A is logical/logically possible/proven logically true”

I am debating with my friend and want to quote some statements I disagreed with him about. Please try to give an unbiased answer because I feel like there is a lot of misunderstanding or dissonance ...
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Could you give me a list of the most authoritative and prestigious manuals for introduction to classic logic?

Could you give me a list of the most authoritative and prestigious manuals or textbooks for introduction to classic logic currently used in higher education?
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173 views

Santa Claus does not exist. Therefore, something does not exist. Valid?

My professor defines logical validity (in the English language) like so: 'An argument is logically valid if and only if there is no (uniform) interpretation (of subject-specific expressions) under ...
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89 views

When can I discharge an assumption? or better put, When can I not discharge an assumption?

It's homework, so I won't give the example, but when is it legal for me to discharge an assumption? Basically, I'm introducing a conditional to prove a theorem that does not rest on any assumptions, ...
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27 views

Modal Logic Proof in System T

I need to provide an axiomatic proof of the following formula in System T of modal logic: ◇(A→□B)→(□A→◇B). Any advice on how to start would be great!
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75 views

Do you think that the 'descent class' is paradoxical?

It is well known that something goes wrong with Russell's class of all classes which are not members of themselves. If this class is a member of itself then it is not a member of itself, and if this ...
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Philosophical meaning of the Curry Howard Correspondence

At a technical level, I understand the Curry-Howard correspondence in various settings, and its usefulness as a technical tool. What I'm looking for is a fairly rigorous discussion of genuinely ...
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3answers
639 views

Is this mathematical answer to randomness question philosophically satisfying?

The question was asked on this page Is there anything that is totally random? but I was not allowed to answer due to lack of reputation. Yet I wonder if my mathematical answer that follows is ...
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1answer
67 views

What is “Can't make X? Don't criticize it.” fallacy called?

What is the name of the fallacy that attempts to invalidate a criticism of an instance of doing an activity because one providing the criticism is not very proficient in said activity (or not doing it ...
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43 views

how do you prove ¬E ∧ A, A → (B ∧ C), B → D∴ C ∧ (D ∧ ¬E)

I have to give a formal proof of this argument. I put my premises, and got to here: ~E /\ A :PR A->(B/\C) :PR B->D :PR And we want the conclusion to be C/(D/~E) ~E :/\E1 A :/\E1 But stumped on ...
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Is the use of this conditional proposition correct, or does it violate the rules of logic?

Is the reasoning answering this logic puzzle correct? One of the answers was by Hexomino on question 1: I think that the lawyer's statement does not help the client. Consider the following statement &...
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47 views

Is there a name for this kind of (bad) argumentation?

I get into / come across exchanges like the following all the time. Sally: Murder and cutting in line are similar in that they're both immoral. John: Are you SERIOUSLY comparing CUTTING IN LINE with ...
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131 views

Can the statement, “Suicide is Murder” be written as S = M? If so, could it then also be written as “Murder is Suicide” or M = S? Are either logical?

Webster defines murder as the "killing of another person" and suicide as the "killing of oneself." It seems, therefore, that these are mutually exclusive ideas. They simply are not ...
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45 views

Logic assigment: prove (A->C) v (A->D) therefore A->CvD

just started logic, and I cannot seem to know know to solve this assigment. I've tried this: I suspect I cannot break the disjunction on P, only with A hypotesis. How should I split it? Thank you
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Tautology of p implies q and not p or q [duplicate]

I'm learning about tautologies right now. I see that a tautology is when two propositional statements have the same truth values. But I'm struggle with the truth table my professor provided about the ...
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1answer
104 views

Are there philosophical problems for which there's only a trivial solution?

I can't really think of a philosophical example, but in mathematics, it would be something like 'find the x where f(x) = 0 given that f(x) = x', and the solution would be 'x = 0', which is trivial. Is ...
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If you used intuitionistic logic in real life, would you not sound absurd?

Intuitionistic logic does not include the law of the excluded middle and double-negation elimination. I imagine a real-life conversation with an intuitionist might go like this: Amy said you didn't ...
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29 views

Instantiation and Generalisation and Formal Logic

I was wondering what generalisation and instantiation were exactly because my notes claim it to be: Generalisation: "from elementary to complex propositions" Instantiation: "from ...
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60 views

Is there a semantic version of the deductive theorem for an arbitrary logic system?

As far as I know, any logic system always defines its own semantics $\models$, but doesn't necessarily have a proof system or $\vdash$ which is complete and sound with respect to $\models$. In an ...
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Why did the mid-19th century and earlier thinkers fixate on one-place predicates?

A book I'm reading mentions the following: A major barrier to the development of first-order logic had been the concentration on one-place predicates to the exclusion of many-place relational ...
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1answer
42 views

Relationship between Principle of sufficient reason and Law of identity [closed]

I have an intuition that one can derive the principle of sufficient reason from the law of identity or non-contradiction but i don't know how. If someone knows I'd like some help.
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320 views

Is it possible to define Truth?

I hope this is the right place to ask a question like this. I'm a student, I haven't studied philosophy and I'm not familiar with all of the famous philosophers, so this question probably already have ...
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1answer
72 views

How does Consequentialism handle uncertainty?

E.g. Suppose you are a Consequentialist faced with a variation of the trolley car problem. Your options are to save five people with a 20% likelihood or one person with a 100% likelihood. Which option,...
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63 views

How would you translate “Anything a knave claims is false” into Predicate Logic?

I am having trouble translating this sentence into Predicate Logic: "Anything a knave claims is false" (or "If x is a knave and x claims y, y is untrue.") I have pasted two ...
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218 views

How to reconcile the fact that mathematical proofs are logical implications with the lack of a formal calculus equivalent to the logical implication? [closed]

Theorems follow from axioms. That is, theorems are the logical consequence of axioms. Thus, mathematical proofs are essentially deductive. Proofs are all essentially logical implications. There is ...
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What is the name of this fallacy: Is 101 binary or decimal?

A similar example would be of binary and decimal number where we are not sure about the number system or the person who proposed a number is not remotely available to disclose about number system. e....
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215 views

What are the advantages of Aristotle's term logic over predicate logic?

I have read Wikipedia's term logic entry, and the quote by Gareth Evans in the Revival section that's supposed to argue for term logic's advantages over predicate logic: "I come to semantic ...

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