45

Do you have a proof that we don't hold ourselves to higher standards? There's actually a rather interesting little corner of mathematics called "proof theory." It deals with the question of what a proof is and how can we use them. It starts to look like philosophy from time to time. I think the real difference is that mathematics typically starts with a ...


36

Reductio ad absurdum is not a fallacy. Rather, RAA is correct reasoning that exposes a fallacy. From the Logically Fallacious page for it: [RAA is a] mode of argumentation or a form of argument in which a proposition is disproven by following its implications logically to an absurd conclusion.... The fallacy is in the argument that could be reduced ...


35

Your example is not a valid case of Reductio ad Absurdum. It's just an example of an absurd argument. A real example would be: Miles: "Copying a DVD is stealing" Frank: "Why?" Miles: "If someone created a piece of art, they have full rights to allow or prohibit its reproduction" Frank: "Oh, so when I take a selfie in the city, I need to ...


21

Frank’s argument is not a reductio. It is an argument from analogy, which is not deductive reasoning and needs to be evaluated differently (Mark’s answer adequately covers the fact that reductio is a valid form of reasoning.)


19

If I'm understanding your question correctly, then you're basically asking "why doesn't philosophy have the same level of rigor as mathematical proof?" I think there's two parts involved in answering this. First, one aspect of philosophy for many philosophers (arguably all) is that philosophy is actually a form of history, meaning we are studying ...


15

The error is to leap from "everything happens for a cause/reason" to "everything happens for a good (or desirable) cause/reason". Example: I was careless and broke a priceless Ming vase. There is a cause/reason for why the vase was broken (viz. I was careless). This cause/reason was "good" (or desirable). The error is in Step 3. This error could arise ...


14

Philosophical theories are more like scientific theories than mathematical theories, in that they have empirical content. As such, there aren't any (universally agreed upon) "first principles" that must be respected. Any potential first principles might get discarded if the reasons for doing so are compelling enough. And even if there are some such ...


10

A proof is only as strong as the axioms it is built upon. Mathematics works over a very limited number of strong axioms to work with, which gives it a limited number* of things that can be proven, but the proofs are very strong thanks to the axioms they work with (and prior proofs relying on the same axioms). Philosophy works with much broader field of ...


9

Because it would then cease to be philosophy. Philosophy sees itself as the progenitor of all the sciences, as its questions lead to the paradigm shifts upon which branches of science are founded. To limit itself to a predetermined set of rules would be to strip itself of the flexibility needed to come up with the next new thing. In other words, it is ...


9

Non sequitur I'll go off of the example in the comments, namely “One dollar” = “money” : “Nickel” = “money.” Therefore, “one dollar” = “nickel.” This is non sequitur - there's no logical reason to assume that Therefore. Or, alternatively, this could be ambiguity fallacy as this seems to be caused by (intentional?) misapplication of the symbol "=" with ...


8

What fallacy is it when someone says "this is true/it happened, therefore there are good reasons for it"? There is no fallacy described here. The argument uses the Principle of Sufficient Reason. The Principle of Sufficient Reason is simply stated: “For every fact F, there must be an explanation why F is the case” (Melamed and Lin 2016, §1). The ...


7

Reductio ad adsurbum requires that there be a valid chain of reasoning that leads from the initial premise to an impossible or unacceptable conclusion. Your example is not RAA because Frank's response does not describe an actual consequence of the Miles's statement. There may be some similarity between the two situations in Frank's mind, but Miles argues ...


6

This is a question in philosophy that deals with the metaphysics of identity. A classic problem in philosophy is the Ship of Theseus and goes back to the pre-Socratics, particularly Heraclitus and his proposition that one cannot stand in the same river twice. In logic, one often draws a distinction between a name (symbol) and the thing it represents (...


6

To approach this from a slightly different angle, this concept is important in computer programming. In a lot of languages, the programmer can decide what attributes make an object "equal to" another object. For example, if you have two "People" objects represented by "first name", "last name" and "address"; you could choose to say that if the first and ...


6

The problem is that you've created your logical statements in the form of a causal relationship when no causal relationship exists. Normally we would expect the statement: If I stay, I will eat fish to mean that 'eating fish' is a logical consequence of 'staying', which carries the implication that if you have not eaten fish, you must not have stayed. But ...


5

Another thing I would add is that proofs are built on strong axioms, but also on precise definitions. It's hard to find a precise and universally accepted definition for any complex concept in philosophy. What is life? Soul? What is a cause, an action? What is truth? Those are a much harder to define than a point, a circle or a function (not that they're ...


5

What is stopping the philosophical community from holding themselves to the same standard? The impression that the philosophers' "standards" are not sufficiently high, I think, is due to (1) the apparent lack of progress in solving philosophical puzzles in conjunction with (2) the deceiving simplicity of these puzzles. In fact, nothing stops the ...


5

You said in a comment that you were referring to the material conditional, not other notions of if/then like the antecedent being a cause of the consequent, or the antecedent logically implying the consequent. So let's get rid of the if/then structure and write them explicitly as material conditionals: A) "I stay" -> "I eat fish" B) "I didn't stay" -> "I ...


4

Cookies are not matter. Cookies are made up of matter. They are a structured form of matter. The logic you provided does not prohibit the existence of matter that existed before the epoch where these three statements hold true. The initial creation of all matter at the beginning of the universe is a complex thing. It is not clear whether "Matter cannot ...


4

I do believe you've missed the point of 'duplicate' here. 'Sameness' in this context is a fairly loose and utilitarian construct. Consider: if the temple priestess says she needs a statue of Zeus for entryway, and everyone in the village steps up to sculpt a statue of Zeus, well... the priestess still only needs (and will only use) one of those statues. The ...


4

Some texts call the fallacy of an appeal to a Nazi comparison to be "Reductio ad Hitlerum" or 'argumentum ad Hitlerum' (in this case 'Hitler' and 'Nazi' are synonymous or interchangeable). The nice thing about informal logic is that an argument made in a natural language often require us to paraphrase it so that it can be presented as an actual argument. ...


4

This would be a straight-forward case of "absence of evidence is not evidence of absence" or what is called argument from ignorance. As the article states: This represents a type of false dichotomy in that it excludes the possibility that there may have been an insufficient investigation to prove that the proposition is either true or false. Hence it is ...


4

The use of modus tollens is valid only when used with propositions containing valid logical predicates. And here it is not. A logical predicate is commonly understood as a boolean function P: X → {true, false} (source). In other words, "predicate" any kind of a mechanism that, when given an object X, provides you with a yes/no answer to the question "Is ...


4

There is no problem here. Assuming material conditionals, if it is the case that If A then B, and if not-A then B, then B is simply a tautology, as it is true in every possible case. You are right the the above conditionals entail If not-B then A, and if not-B then not-A, but this shows that not-B cannot be true. Given that B is a tautology, this is ...


4

I'm not sure how closely the concepts I'm familiar with might match what you're aiming for, but I do have some familiarity with the development of Proof Theory, and your search for terms seems to line up with some ideas we've explored in that field. In proof theory, particularly in discussions around Natural Deduction, we sometimes talk about a proof or ...


4

See this post about the spectrum of formality of a mathematical argument. What you described as "every step and premises are explicitly stated" would be classified as "absolutely formal" (and "formal proof" without any qualification often means this). Most mathematical arguments are not expressed as absolutely formal proofs, but rather fall under "reasonably ...


4

Thank you Conifold for mentioning this in the comments. Appeal to self-authority (self-expertise) https://rationalwiki.org/wiki/Ipse_dixit Self-superiority bias https://en.wikipedia.org/wiki/Illusory_superiority Here's the backstory. Occasionally, I've heard people try to appeal to a great many books they've read on the matter at an argument. For ...


4

tl;dr– Sounds like the basic premise behind conservativism (as opposed to liberalism). In general, both conservatives and liberals favor intelligent consideration when able; but, when it's unclear if a tradition has due motivation, more conservative positions weight the tradition's possible wisdom more heavily while more liberal positions weight the ...


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