# Talk:Reductio ad absurdum

Isn't a reductio ad absurdum the going about proving the validity of argument X based on the fact that if the conclusion of argument X were not true then a contradiction would arise, therefore the conclusion of argument X must be true. An appeal to ridicule explains aptly what this article summarises, but nowhere is my aforementioned definition of reductio described on this site?

## Example in "In Mathematics"[edit]

Shouldn't the hypothesis say "Two *distinct* straight lines that intersect do so in one and only one point." since two lines intersect in all their points if they are identical? --91.56.252.207 (talk) 19:43, 4 January 2014 (UTC)

- This is correct. I've made the change. - GrantC (talk) 20:32, 4 January 2014 (UTC)
- You could conceivably argue that "to intersect" already presumes two distinct lines, since intersection between lines is usually taken to mean "lying across", but in rigorous mathematics the language is such that "intersection" means the same elements contained in both sets. There's some merit to using the specific language of mathematics in a mathematics example, I suppose. Nullahnung (talk) 20:43, 4 January 2014 (UTC)
- Indeed; the addition of a single extra word isn't likely to cause an uproar, I figure. Besides, one could argue (on the side of the language of mathematics) that the use of the word "straight" is entirely unnecessary, as in mathematics, the word "line" implies that it is straight. Otherwise, we would use the word "curve" instead. But that would be a bit
*too*mathematical, I think. ;) - GrantC (talk) 20:56, 4 January 2014 (UTC)- As long as we're reconsidering the mathematical rigor of this example, it might be worth pointing out that since the example relies on one of Euclid's axioms, it is not applicable to non-Euclidean geometry that doesn't use that axiom. For example, it's quite possible for two "straight" lines on the surface of the Earth to cross each other twice. Any thoughts on whether this would be too detailed? 192․168․1․42 (talk) 03:33, 5 January 2014 (UTC)
- Heh, well my comment about the necessity of the word "straight" was in jest. I don't think there's much value in adding more mathematical detail to this example, despite the truth of what you're saying. Let's pretend we can take Euclidean geometry as a given for this one. :) - GrantC (talk) 05:08, 5 January 2014 (UTC)
- I think most people capable of grasping the example will assume Euclidean geometry. But what about "gay" lines? Is the example not somewhat homophobic?
^{d hominem}23:08, 8 January 2014 (UTC)- This is a social injustice that cannot be left to stand! ... Or something. - GrantC (talk) 23:12, 8 January 2014 (UTC)
- Are we talking about great circles, or fabulous ones? Seriously, there is no need for assumptions, warranted or otherwise, since the example plainly says "found in euclidean geometry" right up front. Sprocket J Cogswell (talk) 23:40, 8 January 2014 (UTC)

- This is a social injustice that cannot be left to stand! ... Or something. - GrantC (talk) 23:12, 8 January 2014 (UTC)

- I think most people capable of grasping the example will assume Euclidean geometry. But what about "gay" lines? Is the example not somewhat homophobic?

- Heh, well my comment about the necessity of the word "straight" was in jest. I don't think there's much value in adding more mathematical detail to this example, despite the truth of what you're saying. Let's pretend we can take Euclidean geometry as a given for this one. :) - GrantC (talk) 05:08, 5 January 2014 (UTC)

- As long as we're reconsidering the mathematical rigor of this example, it might be worth pointing out that since the example relies on one of Euclid's axioms, it is not applicable to non-Euclidean geometry that doesn't use that axiom. For example, it's quite possible for two "straight" lines on the surface of the Earth to cross each other twice. Any thoughts on whether this would be too detailed? 192․168․1․42 (talk) 03:33, 5 January 2014 (UTC)

- Indeed; the addition of a single extra word isn't likely to cause an uproar, I figure. Besides, one could argue (on the side of the language of mathematics) that the use of the word "straight" is entirely unnecessary, as in mathematics, the word "line" implies that it is straight. Otherwise, we would use the word "curve" instead. But that would be a bit

- You could conceivably argue that "to intersect" already presumes two distinct lines, since intersection between lines is usually taken to mean "lying across", but in rigorous mathematics the language is such that "intersection" means the same elements contained in both sets. There's some merit to using the specific language of mathematics in a mathematics example, I suppose. Nullahnung (talk) 20:43, 4 January 2014 (UTC)

## Philosophy[edit]

In philosophy (although it is really the same form as in mathematics), a reductio ad absurdum is an argument formed from a valid argument (i.e there is no case where the premise is true and the conclusion false) in which the conclusion is false. The negation of this argument's premise is the conclusion of the reductio and the rest of the premises are the premises of the reductio. It is *always* a valid argument. Here is an example:

(1) If I am a human being, I can run up a building.

(2) I am a human being.

(3) Therefore, I can run up a building.

It is not true that I can run up a building. (3)

Therefore, reductio:

(1) I am a human being

(2) It is false that if I am a human being, I can run up a building

## This thing needs a rewrite[edit]

The reductio method is very poorly explained in the current article. It's not made clear that it stems from the law of identity^{} and the law of noncontradiction^{}. Leibniz^{}' role is not made clear, either. The *essential* reliance of the reductio on the law of the excluded middle^{} is not explained either. Furthermore, the application of the reductio is far, far more intuitive than the examples currently give it credit for — for example, any situation in court where testimony or evidence ends up fatally contradicting the story of the accused (irrespective of if the court case ends in aquittal or a sentencing) is an example where the reductio method was applied to reach said verdict (aquittal or no). Reverend Black Percy (talk) 21:59, 6 November 2016 (UTC)