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Is there any logical operator that indicates tautology (in the form of truth table)? And, if so what could be it's possible significance?

is there such a logical connector and so if there is what is its significance In the context of classical propositional logic and the truth table method: all the 2^4, i.e. 16, possible binary ...
Julio Di Egidio's user avatar
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Is there any logical operator that indicates tautology (in the form of truth table)? And, if so what could be it's possible significance?

A Boolean formula F is a tautology if and only if its negation “non-F” is not satisfiable, i.e. if non-F is false independently of the truth value of each variable of F, see tautology. There exists ...
Jo Wehler's user avatar
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The implication if we discovered that natural abiogenesis is statistically nearly impossible

As long as our sample size is 1, it doesn't matter what we think the probability of us happening randomly is, as long as we also believe in an infinitely large universe. Even if it was extremely ...
kutschkem's user avatar
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3 votes

Is there any logical operator that indicates tautology (in the form of truth table)? And, if so what could be it's possible significance?

The symbol: ⊨φ (called double turnstile), means that formula φ is a valid formula, that in case of propositional logic menas that it is a tautology. The symbol ⊥ (called False) is a propositional ...
Mauro ALLEGRANZA's user avatar
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The implication if we discovered that natural abiogenesis is statistically nearly impossible

I won the main prize the very first time I bought an Art Union lottery ticket. I was about twenty at the time. After that, the chances of me being a lottery winner went to 100% and stayed there. ...
Peter Wone's user avatar
1 vote

Arguments Against Quantifier Neutralism?

Azzouni's thesis is that accepting the truth of a quantified expression does not automatically commit oneself to the existence of the things quantified over. Yet, I could only really believe that all ...
Speakpigeon's user avatar
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1 vote

Arguments Against Quantifier Neutralism?

Azzouni's position is that quantifiers in natural language are not fundamentally ambiguous, hence neutral. It stands in distinction to the position that quantifiers differ between a domain reading and ...
Bumble's user avatar
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1 vote

The implication if we discovered that natural abiogenesis is statistically nearly impossible

I would say that even if we were able to calculate this probability with absolute certainty (let's assume we can), than it wouldn't necessarily imply creation. Assuming that the probability of ...
AccidentalTaylorExpansion's user avatar
2 votes

To what extent are reasoning and arguments essential to bridge the gap from sense perception to the belief in an external world?

To what extent are reasoning and arguments essential to bridge the gap from sense perception to the belief in an external world? Strictly speaking, reasoning and arguments are totally redundant. Any ...
Speakpigeon's user avatar
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1 vote

To what extent are reasoning and arguments essential to bridge the gap from sense perception to the belief in an external world?

Firstly, you need to be clear what you mean by reasoning and argument. If you mean deliberate conscious reasoning, then the answer is 'not very much'. Most of our interactions with the world are ...
Marco Ocram's user avatar
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2 votes

To what extent are reasoning and arguments essential to bridge the gap from sense perception to the belief in an external world?

Let A denote the set of sense perceptions of a conscious being, and let B represent that conscious being's belief in the existence of an external world. With this understanding in mind, are reason ...
SystemTheory's user avatar
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To what extent are reasoning and arguments essential to bridge the gap from sense perception to the belief in an external world?

To hypothesize an external world provides the simplest explanation for our varying but regular sense perceptions. Closing one's eyes and ears etc. changes the content of our mental conscious processes ...
Jo Wehler's user avatar
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2 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

If we were to discover somehow that (sentient) life was so unlikely that it were almost impossible that it forms even once in the whole universe... That doesn't seem like something that could ...
gerrit's user avatar
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0 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

It would change nothing whatsoever for me. "Nearly impossible" is an empty phrase. Either something is possible, or it is not possible. We know that it is possible (we have a positive test ...
AnoE's user avatar
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12 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

If, and it's a big if, it could be proved that the probability of the emergence of life through natural causes was exceedingly close to zero, then you could still assume life emerged by chance. Before ...
Marco Ocram's user avatar
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2 votes

How do I solve logic derivations with disjunctions?

You may have to move things around first in order to apply the syllogisms that you have, but this is the idea: (P ∨ R) → S :: 1 Premise (¬ P ∧ ¬ R) ∨ S :: 2 Logical Equivalence + De Morgans (S ∨ ¬ ...
Michael Carey's user avatar
1 vote

The implication if we discovered that natural abiogenesis is statistically nearly impossible

No it doesn’t imply creation for the simple fact that no matter how improbable life is “statistically”, it would not be deemed impossible through natural means. And even if it was deemed impossible ...
Baby_philosopher's user avatar
-2 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

I would call your attention to the following two resources. The first is to a public lecture by Professor David Kipping: "Why we might be alone". https://www.youtube.com/watch?v=zcInt58juL4 ...
user284898's user avatar
1 vote

The implication if we discovered that natural abiogenesis is statistically nearly impossible

You noted that the existence of sentient life is a necessary condition for anyone to observe life, and that this might imply that no explanation is needed for such a vastly improbable event. This ...
Some mathematician's user avatar
1 vote

The implication if we discovered that natural abiogenesis is statistically nearly impossible

It all depends on your theory of probability. If you are using probability as a frequentist, then you would appeal to the set of all known universes with life. In this case, there is exactly 1 known ...
J D's user avatar
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0 votes

Is dialetheism falsifiable?

No. It doesn't really make sense to "falsify a system of logic". There are two manners in which a theory can be read: on the correspondent reading, a theory is about corresponding to a state ...
J D's user avatar
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9 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

It's perfect valid to say that something being near-impossible doesn't say much about other possibilities, unless you have some independent insight into how likely those possibilities are. Of course, ...
NotThatGuy's user avatar
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5 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

It is generally a bad idea to invoke an infinity of other universes to explain away an otherwise reasonable inference about OUR universe. It is far simpler, and much more testable/refutable, if one ...
Dcleve's user avatar
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4 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

Short answer According to Eugene Koonin, it would serve as an argument for believing in an infinite (or at least hugely vast) multiverse. Longer answer About Eugene Koonin Eugene Koonin, Ph.D. NIH ...
Mark's user avatar
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12 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

[This is a complete rewrite of my answer.] If I understand you're question, you're presuming that we somehow determine that the chance of all the conditions necessary to result in intelligent life is ...
Barmar's user avatar
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0 votes

Hume's Guillotine

From what I find, the nicer description is about a distinction between IS and OUGHT and how you can't really deduce an OUGHT-statement (moral judgement, prescriptive statements) from an IS-statement (...
haxor789's user avatar
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0 votes

Differentiating an argument from authority from expert testimony

If so, how come there is no contradiction in the same argument being fallacious/valid based on context? This comes because in your second case ("Mr. X said it's true") this is not an appeal ...
AnoE's user avatar
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-1 votes

Hume's Guillotine

I think I understand your question — and I think you are right, Hume's Guillotine makes no more sense than the example from Philosopher’s Toolkit. Or, strictly speaking, Hume's Guillotine makes no ...
Yuri Zavorotny's user avatar
3 votes

The implication if we discovered that natural abiogenesis is statistically nearly impossible

I agree with you that there are two different questions about an event: Question 1 (Yes-No?): Did the event happen or not? Question 2 (How?): If the event happened, how did it happen? Solving the ...
Jo Wehler's user avatar
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2 votes
Accepted

Is there any self-contradiction in this statement that "everything is beautiful"?

You reach an absurd conclusion because your argument assumes both a premise and its denial. There is nothing self-contradictory in the statement everything is beautiful- it is simply a matter of ...
Marco Ocram's user avatar
  • 18.6k
0 votes

Differentiating an argument from authority from expert testimony

The difference is that one is a fallacy and the other need not be. If your expert gives a statement, the statement itself ought not to contain anything fallacious. Where a fallacy arises is if you ...
Marco Ocram's user avatar
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3 votes

Differentiating an argument from authority from expert testimony

I see a lot of good responses here, but the informal fallacy of the Appeal to Authority is often misunderstood. It is only the case that an appeal to the expertise is a fallacy IF the inference fails ...
J D's user avatar
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2 votes

Differentiating an argument from authority from expert testimony

A "fallacious argument from authority" is fallacious because it is not certain. The authority can be incorrect or lying. What you have done is transformed the reliability of statement X ...
Yakk's user avatar
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1 vote

Computable syntax

To me it sounds like you are asking some ill-formed questions that could be clarified if you were familiar with some basic concepts. You say the following: how do I make sure my theory is "...
BurnsBA's user avatar
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1 vote

Computable syntax

You ask: So what makes one system of syntax capable of being reasonably (usefully) computable? I'm not sure that I can find a source for what makes a good formal system, however, here are some ...
J D's user avatar
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1 vote
Accepted

Is it consistent with beginning/ending principles for an interval-based temporal logic to cover a time that is exactly ω+ω intervals long?

No, any limit ordinal lacks an endpoint. In fact, the ordinals in which the two axioms hold are exactly the successor ordinals (e.g. ω+ω+1 is fine). Or maybe something like ω+ω*, where the * denotes ...
Arno's user avatar
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1 vote

Differentiating an argument from authority from expert testimony

It's an invalid deduction and hence a fallacy in either context. From the fact that someone is an expert does not follow that what they say is the truth. There are countless of examples of experts ...
haxor789's user avatar
  • 5,466
3 votes
Accepted

Computable syntax

You seem to refer to Formal Systems. A formal system is essentially a set of concepts (precise definition of objects) and axioms (atomic principles, which in the context of the current system cannot ...
RodolfoAP's user avatar
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2 votes

Computable syntax

Define your new symbols in terms of your old symbols. Pay attention to grammatical class; your new symbols should have the same class as the productions which they represent. Then, you only have to ...
Corbin's user avatar
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12 votes

Differentiating an argument from authority from expert testimony

"Appeal to authority" (or appeal to expertise) might be one of the most misunderstood and misapplied forms of argument (and that's in terms of both people inappropriately appealing to ...
NotThatGuy's user avatar
  • 7,625
3 votes

Differentiating an argument from authority from expert testimony

ABA - Experts and Opinions (4 pages): https://www.americanbar.org/content/dam/aba/publications/pass_it_on/experts_opinions_witness_testimony_PIO_F14.pdf Rule 702 can give you some guidance. It states:...
SystemTheory's user avatar
  • 1,402
2 votes

Differentiating an argument from authority from expert testimony

The difference is that when mathematician Q is considering mathematician P's statement about theorem T, mathematician Q may be qualified to understand T and the proof of T himself. If so, then Q ought ...
causative's user avatar
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1 vote

Computable syntax

You can start by considering examples of reasoning within the reasoning domain you're targeting. Examples of the form, "from X and Y, Z would follow." Generate a lot of these examples. Be ...
causative's user avatar
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1 vote

Computable syntax

So what makes one system of syntax capable of being reasonably (usefully) computable? Any logical language whose logic you understand and whose vocabulary means real things. So you need to understand ...
Speakpigeon's user avatar
  • 6,937
21 votes

Differentiating an argument from authority from expert testimony

If you try to analyze the argument from authority fallacy in formal terms, it reduces to non sequitur: (1) X says that P. (2) P. (1) doesn't follow from (2), so this is a simple non sequitur (a ...
David Gudeman's user avatar
3 votes

Differentiating an argument from authority from expert testimony

Fallacy: Doctor P says T. Therefore T. Straightforward appeal to authority. Valid but useless: Doctor P says T. T is in category {X}, of which Doctor P has said many things other than T. When ...
g s's user avatar
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1 vote

Translating a sentence with a time element into first order logic

You are trying to do something out of scope. Words such as 'yellow', 'easily', 'Wednesday', etc don't have special representations in logic, and as far as I know, 'sometimes' is no different. You can ...
Marco Ocram's user avatar
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4 votes

Translating a sentence with a time element into first order logic

The issue here is more to do with understanding what you are trying to express, rather than with turning it into formal logic. The word 'some' is vague, but it is usually treated in formal logic as ...
Bumble's user avatar
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5 votes

Translating a sentence with a time element into first order logic

You would need a predicate L(x, t) that says that x lies at time t. Then you could write something like Ex Et P(x) ^ T(t) ^ L(x, t) which say that there is a person which at some point lied.
Johan's user avatar
  • 370
4 votes
Accepted

Logical Meaning of Apostrophe in Formal Notation?

This is a "prime" not an apostrophe, and is read as "P prime": https://en.wikipedia.org/wiki/Prime_(symbol) In general it denotes a variation, but the exact meaning has to be ...
Chris Sunami's user avatar
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