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In the usual modal logics, are there tautologies of the form ◊¬X or ¬☐X?

And not when, "Possibly not X," or, "Not necessarily X," are implied by, "Impossibly X," already. But so is it possible to have a tautology be a statement of mere ...
Kristian Berry's user avatar
2 votes
4 answers
214 views

Interesting non-mathematical tautologies

Are there any interesting examples of tautologies that are not mathematical? Something non-trivial like It is raining or it is not raining. I can't come up with one nor have I found any on the ...
Alex's user avatar
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3 answers
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Are these statements tautologies?

On p22 in The Big Questions by Solomon: A tautology is a trivially true statement. Some examples: A man is free if he is free. You can't know anything unless you know something. I wouldn't be here ...
Tim's user avatar
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1 answer
129 views

What is the difference between a tautological corresponding conditional and (P v ~P)?

The Wikipedia article on the corresponding conditional contains the following sentence: An argument is valid if and only if its corresponding conditional is a logical truth. Some sources use "...
user51462's user avatar
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3 answers
845 views

What is the relation between a priori and tautologies?

I have just started learning Epistemology. I am not sure about the relation between a priori and tautologies. My textbook has given definitions for a priori and tautology. A priori: knowledge which is ...
Heidi Zhang's user avatar
23 votes
13 answers
9k views

Why is it wrong to answer a question with a tautology? Isn't "2+2" correct when answering 'What is "2+2"'?

Many times in class, we are asked to answer, "What is 2+2?" or "What is the derivative of the function x?". It would not be the intended answer to write "2+2" or "...
user107952's user avatar
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-1 votes
2 answers
119 views

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

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 ...
Muskaan Mehta's user avatar
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0 answers
144 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-...
Pri's user avatar
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0 votes
1 answer
517 views

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 ...
user avatar
-1 votes
1 answer
239 views

Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days (NOT duplicated)

First of all, please don't close this question cause I don't get the explanation given in: Use the Fitch system to prove the tautology (p ∨ ¬p) I have been trying to solve this exercise for days ...
Luen's user avatar
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Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days [duplicate]

I'm having trouble solving this one. I've been stuck in step 9 for days now. Any help is very much appreciated.
Luen's user avatar
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0 votes
2 answers
173 views

Is every reason reducible to a sequence of tautological statements? [closed]

I think of tautological statements as those statements which when explained should repeat themselves, and should intuitively explain the reason. For example, A = A because 'A is equal to A'; Dog is ...
Ajax's user avatar
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0 answers
164 views

If logical propositions aren't tautologies (a la Wittgenstein), then what could they be?

This is a historical question about philosophical views. I believe I understand the claim made by Wittgenstein and others that logical propositions are tautologies. I'd like to know what other views ...
Max Wallace's user avatar
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1 answer
2k views

Making 'sense' of Wittgenstein's senselessness / nonsense distinction in the Tractatus

For this question I'm just considering Wittgenstein's theory at the time of the Tractatus. As far as I know, for Wittgenstein: Meaning - The object denoted by a word (i.e. referent). Sense - The ...
M. Guillaume's user avatar
2 votes
1 answer
126 views

The Law of Identity and Emptiness

If all rational, logical, philosophical, scientific, and mathematical reasoning starts with the initial axiom that 'X=X' - that is a 0 information tautology - can it be said that all ensuing rational, ...
Ilya Grushevskiy's user avatar
3 votes
6 answers
7k views

What is the difference between a logical truth and a tautology?

Some papers I read seem to be referring to a distinction between logical truths and tautologies. At first I thought something was wrong since I thought they are the same by definition. I checked the ...
peticrust's user avatar
2 votes
0 answers
256 views

Counterexamples to Occam's Razor and tautology

I read here and here that, strictly speaking, there are no counterexamples to Occam's rozar, because the latter implies no need for pluralism when unecessary, which is to be understood as "for the ...
luchonacho's user avatar
11 votes
5 answers
17k views

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 (language), it mentioned that circular reasoning and tautology are different....
shivams's user avatar
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2 votes
2 answers
1k views

Valid arguments as tautologies

I don't quite understand this : "As it turns out, all valid arguments can be restated as tautologies - that is, hypothetical statements in which the antecedent is the conjunction of the ...
Hiroki Hirayama's user avatar
4 votes
7 answers
4k views

How do you prove that this is a tautology?

((p->q) and (r->s) and (p or r)) -> (q or s) How would you prove that this is a tautology? Using natural deduction? My attempt on this question is the following. Since a tautology means W entails ...
Tom chan's user avatar
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3 votes
4 answers
2k views

How can a tautology not be necessarily true?

My logic/philosophy exercises include the following statement: "Every tautology is knowable a priori but not every tautology is necessarily true." I'm bamboozled. How can a tautology not be ...
Brendan Hill's user avatar
2 votes
1 answer
3k views

What distinguishes logical necessity, logical consequence, logical truth, and tautology from one another?

The text I'm reading distinguishes logical necessity, logical consequence, logical truth, and tautology from one another; however it doesn't make their distinctions especially perspicuous. As far as ...
Hal's user avatar
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2 votes
3 answers
1k views

Is "Unreasonable Effectiveness of Mathematics in the Natural Sciences" a tautology?

According to Gelfand, "Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more ...
Michael's user avatar
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5 votes
3 answers
582 views

Why does logic emphasize tautologies rather than contradictions?

Why does logic emphasize tautologies rather than contradictions? I think the answer is something like the following: We can't cover all cases by contradictions. For example: if I have to prove that ...
TLE's user avatar
  • 291
8 votes
4 answers
1k views

Does the phrase "vacuous tautology" have specific meaning?

I just came across a use of the phrase "vacuous tautology" used in a piece of writing. Now, based on my understanding, by definition a tautology has no content and is therefore always vacuous. This ...
yamad's user avatar
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