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61 votes

Fallacy by Sherlock Holmes 'Eliminate the impossible, and what remains must be the truth'

There's a fallacy called Holmesian fallacy. A Holmesian fallacy (also Sherlock Holmes fallacy or process of elimination fallacy) is a logical fallacy that occurs when some explanation is believed to ...
Double Knot's user avatar
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51 votes

If math is so deductive, why is it so hard to discover new math?

If the rules of chess are so simple, why is it so hard to beat a grandmaster? The answer is the 'combinatorial explosion'. You have a small and well-defined set of moves you can make at each step. Let'...
Nullius in Verba's user avatar
44 votes

Fallacy by Sherlock Holmes 'Eliminate the impossible, and what remains must be the truth'

Holmes' advice is correct if and only if you assume a complete search was done to list all possibilities before starting the elimination process. Note that Sherlock Holmes is both incredibly observant,...
Flater's user avatar
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13 votes

If math is so deductive, why is it so hard to discover new math?

“Doing mathematics” or “discovering new math” is not the same as “giving new formal mathematical deductions”. Here is an analogy: Why is it hard to write new literature, or new poetry? It’s extremely ...
Peter LeFanu Lumsdaine's user avatar
12 votes
Accepted

Are "if smoke then fire" arguments deductive or inductive?

Such inferences are neither deductive (which assumes application of a valid inference rule) nor inductive (which assumes a generalization from a pattern of cases). This type of inference is called ...
Conifold's user avatar
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12 votes

If math is so deductive, why is it so hard to discover new math?

I think the premise of the question is false. Actually, it's easy to discover new math. Here's one way to find some new math. Take a sheet of paper and write down a bunch of "nonsense" ...
Tanner Swett's user avatar
10 votes
Accepted

Is there a deduction analog to the problem of induction?

When it comes to justification there is indeed a symmetric problem of deduction. But forming general opinions or laws is not part of deduction, it is abductive (or in older terminology inductive), ...
Conifold's user avatar
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10 votes
Accepted

If turtles see everything, and nothing seen can see, does it follow that non-turtles exist?

First, your premises are inconsistent: your second premise implies that turtles do not see other turtles, or themselves, yet, according to the first premise, they see everything. So, taking y=x, we ...
Conifold's user avatar
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10 votes

Fallacy by Sherlock Holmes 'Eliminate the impossible, and what remains must be the truth'

Deep down, mechanically, it's merely a false dilemma: assert that one of these options must be true and disprove all but one. A traditional false dilemma is an attempt to bully and has only 2 options -...
Owen Reynolds's user avatar
10 votes

If math is so deductive, why is it so hard to discover new math?

To elaborate on Nullius in Verba's answer (this started as a comment but became too long!). You can think of each step in a proof as an application of a valid rule of deductive inference to the axioms ...
Avi C's user avatar
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9 votes
Accepted

Why does Gensler's Star Test not work on some syllogisms?

Gensler's star test is a simplified method for determining the validity of a syllogism proposed in 1973. According to the test, one stars (asterisks) the first (capital) letter after "All", ...
Conifold's user avatar
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8 votes
Accepted

Is the logic of this argument valid?

This argument could hardly be rendered into a valid form without all kinds of additional assumptions and clarifications. For example, Assumes we know what God wants and what he/she might or might ...
Bumble's user avatar
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8 votes

Are "if smoke then fire" arguments deductive or inductive?

If the question is raised in an intro to philosophy course (like critical thinking or scientific reasoning), the answer should be that the above inference is an example of inductive logic. There are ...
Nanhee Byrnes PhD's user avatar
7 votes

If math is so deductive, why is it so hard to discover new math?

Math proofs are deductive, but the discovery of math proofs is an abductive process which requires a healthy exercise of expertise and intuition. Mathematical argumentation, like all argumentation, ...
J D's user avatar
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6 votes
Accepted

Implication Introduction formulated as a theorem?

The two different symbols on the page you link to are indeed different. The first is the turnstile symbol Ⱶ which may be read as 'proves', while the arrow → is material implication. These are very ...
Bumble's user avatar
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6 votes

What is a natural deduction proof from ~(A↔B) to ~(A→B)?

The following truth table shows that ~(A↔B) → ~(A→B) is not a tautology: If A is False and B is True then the antecedent is True but the consequent is False making the conditional False. Because ...
Frank Hubeny's user avatar
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6 votes

Deductive reasoning & conditionals

It would be worthwhile distinguishing between a conditional sentence in the object language and a conditional in the metalanguage. Some deductive arguments have a conditional in the object language, e....
Bumble's user avatar
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5 votes

Is the logic of this argument valid?

The argument is not logically valid. You need a sixth step, along the line of A method of knowing God without interpretation exists. As to the point about the circularity; It's incorrect to reduce ...
Taemyr's user avatar
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5 votes

Is there a deduction analog to the problem of induction?

I typically present 'The Problem of Deduction' as a the following analogy to the better known 'Problem of Induction': One of the workhorses of deduction surely is Modus Ponens ... but why do we trust ...
Bram28's user avatar
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5 votes

Does an implied premise mean a formal fallacy if used in deduction?

See Enthymeme : An enthymeme is a logical fallacy in which a categorical syllogism omits a premise that is necessary for the conclusion to be true or omits the conclusion itself. The missing ...
Mauro ALLEGRANZA's user avatar
5 votes

Is there a single definition of truth?

welcome to PSE. The concept of truth is one of the head-spinners of philosophy. Some philosophers believe that truth is a property possessed by all and only true propositions, statements, sentences, ...
Geoffrey Thomas's user avatar
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5 votes

What is a natural deduction proof from ~(A↔B) to ~(A→B)?

You can't derive ~(A→B) from ~(A↔B). Consider: A = I'm in Paris. B = I'm in France. ~(A↔B) is true, because being in Paris is not equivalent to being in France (I could be in France but not in ...
E...'s user avatar
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5 votes

Why is this deductive reasoning incorrect?

It's incorrect because its logical form is incorrect. If we use notation similar to what's used in Tarski's world (a good program to learn the basics of first-order logic, see the lecture notes on it ...
Hypnosifl's user avatar
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5 votes

Fallacy by Sherlock Holmes 'Eliminate the impossible, and what remains must be the truth'

I think another point worth mentioning is that even if Holmes has correctly enumerated all possibilities, he is invoking the Law of the Excluded Middle[1]: Either a proposition is true, or its ...
usul's user avatar
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4 votes

If "All S is P" is true, does it contradict "No non-S is non-P"?

You are right from the "traditional" point of view. The issue is with the existential import of categorical propositions: If a statement includes a term such that the statement is false if the ...
Mauro ALLEGRANZA's user avatar
4 votes

Proof for the Rule of Absorption in Natural Deduction?

The rule of absorption can be proved via truth table (which is neither a "conditional proof" nor an "indirect proof") like so: P Q | P ⊃ Q | (P ∙ Q) | P ⊃ (P ∙ Q) | (P ⊃ Q) ≡ [P ⊃ (P ∙ Q)] -----------...
Jayson Virissimo's user avatar
4 votes
Accepted

Quick logic deduction question

1) ¬∀xFx --- premise 2) ¬∃x¬Fx --- assumed [a] 3) ¬Fy --- assumed [b] 4) ∃x¬Fx --- from 3) 5) ⊥ --- contradiction: from 2) and 3) 6) Fy --- from 3) and 5) by Double Negation, discharging [b] 7) ∀...
Mauro ALLEGRANZA's user avatar
4 votes
Accepted

Why can't uniformity of nature (in principle) be proven deductively?

The quoted passage is part of an exposition of Hume's original argument. One of the previous paragraphs explains what "deductively" meant to Hume: "The deductive system that Hume had at hand was ...
Conifold's user avatar
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4 votes

How do I operate with philosophers if I reject deductive reasoning?

It seems you don't understand the terms. The essence of deductive reasoning: If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion ...
Dan Christensen's user avatar
4 votes
Accepted

Can all inductive arguments be written as deductive arguments?

...it seems that any inductive reasoning can be done with deductive reasoning by adding in some assumption that a particular pattern continues to hold. You got it exactly right. The assumption is ...
Mark Andrews's user avatar
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