Questions tagged [logic]

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

Filter by
Sorted by
Tagged with
0
votes
0answers
22 views

Name for a logical fallacy: quantities that measure different aspects of the same thing are not themselves the same

This question is related to a specific issue that I have encountered related to concepts in my research. I describe a made-up but probably more accessible analogy, and then the actual problem below. ...
5
votes
3answers
378 views

What's the right term in logic for this phenomenon?

The statement "My mother is my parent" is always true, however, the opposite statement "My parent is my mother" is not always true because my father is also my parent. What's the ...
3
votes
3answers
277 views

Can a category of non-difference exist in logic?

Indian philosophy has a logical category of non-difference (related somewhat to abheda) in which something is different from something else but identical to it as well. An example is that of the the ...
-1
votes
2answers
33 views

Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C)

Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C) How do I prove this using statement logic? I know I need to start with a supposition ...
2
votes
1answer
38 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'...
0
votes
0answers
13 views

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 ...
0
votes
0answers
6 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-...
1
vote
2answers
89 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 ...
3
votes
2answers
1k views

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

:= What does the "colon-equal symbol" mean, and how is it used?
3
votes
3answers
84 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 ...
-1
votes
0answers
96 views

Is uniqueness necessary in the case of God — the Creator?

====================================================================== Let us assume God as the Creator. Suppose: By similar/same process; with the same materials, God A, God B, and God C created ...
0
votes
0answers
28 views

What topics/niches are most influenced by Aristotelian logic? [closed]

Obviously Aristotle had a huge influence, but I want to focus specifically on his logic and syllogistic.
0
votes
1answer
65 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 ...
-1
votes
0answers
28 views

How would one derive “Q” if given the premises “PvQ” and “P->(R&~R)”

Im quite new to logic and symbolic logic and i’ve stumbled across this problem and i can’t understand how to solve it using rules of derivation.
0
votes
0answers
38 views

Questions on some proofs in Yablo's “Aboutness Theory” [closed]

I would like to ask some help about Yablo's Aboutness theory as expressend in the hyperlinked appendix of his book: https://www.academia.edu/2604116/Aboutness_Theory X ’s subject matter is the m whose ...
0
votes
0answers
51 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 ...
1
vote
2answers
53 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 ...
2
votes
1answer
54 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 ...
1
vote
2answers
87 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 ...
0
votes
2answers
132 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 ...
-2
votes
1answer
38 views

How do I prove (A | B) & (C | D) & ~(B & C) therefore (A & D) using natural deduction?

My best guess is to start out with DeMorgan's law and prove ~B | ~C but from there I don't know where to go.
0
votes
1answer
54 views

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

Is the premise really enough to prove this?
-1
votes
1answer
56 views

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)...
0
votes
1answer
43 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 ...
13
votes
10answers
3k views

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 ...
0
votes
1answer
62 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 ...
0
votes
0answers
26 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?
0
votes
1answer
30 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 ...
0
votes
1answer
43 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 ...
2
votes
1answer
114 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 ...
-1
votes
0answers
16 views

When evaluating a proposition of predicate logic, do we interpret the main quantifier first i.e. the leftmost quantifier first? [duplicate]

For instance, this proposition (∀x)(Hx ≡ (∃y)(Fy & Rxy)) Should we expand the universal quantifier on the left first i.e. solve the conjunctions of all x variables before considering the ...
2
votes
1answer
230 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? ...
0
votes
1answer
45 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?
0
votes
1answer
80 views

“A is logical/logically possible/proven logically true”

Hello I am debating 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 a dissonance ...
1
vote
2answers
51 views

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?
0
votes
0answers
63 views

Why is Entscheidungsproblem problem undecidable? [duplicate]

I have been trying to wrap my head around Gödel's Completeness Theorem, Incompleteness Theorem(s) and undecidability of Entscheidungsproblem. Turing wrote: It should perhaps be remarked what I shall ...
2
votes
2answers
148 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 ...
0
votes
2answers
83 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, ...
-1
votes
1answer
23 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!
0
votes
1answer
71 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 ...
1
vote
0answers
35 views

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 ...
1
vote
3answers
636 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 ...
1
vote
1answer
64 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 ...
-1
votes
2answers
40 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 ...
1
vote
2answers
91 views

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 &...
1
vote
1answer
46 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 ...
-3
votes
3answers
117 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 ...
0
votes
1answer
44 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
0
votes
0answers
13 views

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 ...
1
vote
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 ...

1
2 3 4 5
59