4 ms·

The "proof" you're most likely talking about doesn't show why this is true. Merely shows that it is true. Exhaustion doesn't qualify as a real argument, in my

The "proof" you're most likely talking about doesn't show why this is true. Merely shows that it is true. Exhaustion doesn't qualify as a real argument, in my opinion.

wetmore 12y ago
People often talk about the proof as if they just enumerated every possible planar graph and checked. Which is true in a sense, but disregards the work that went into making it possible to enumerate the cases in the first place. There are infinitely-many possible planar graphs, so you of course need to find some invariants that allow you to bring the necessary number of graphs to check to be finite. Beyond that, the techniques in the 4CT which make it actually possible to reduce the number of cases to a feasibly enumerable number are very clever and require some insight.
jordigh 12y ago
Proof by exhaustion is considered a real argument as long as there are not too many cases to exhaust. One of the most dramatic examples is the proof of that result that goes... if RH is true, then the result is true. If RH is false, then the result is true. Therefore, the result is true! So, why make the cut-off point of when exhaustiong is an explanation at some finite number of cases?
deleted 12y ago
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GFK_of_xmaspast 12y ago
Personally, I think it's totally valid. (PhD mathematician here).
- evanb 12y ago
  It's certainly a valid argument, but it's not... enlightening in the same way other kinds of arguments are.
- JadeNB 12y ago
  > Personally, I think it's totally valid. To be fair, though it's a bit ambiguous, I read sebastialonso's post https://news.ycombinator.com/item?id=8799362 https://news.ycombinator.com/item?id=8799362 as indicating that he or she believes that the result is true—i.e., does not necessarily reject the validity of proof by exhaustion as a style of argumentation—but does not feel that the proof by exhaustion is an explanation.

The "proof" you're most likely talking about doesn't show why this is true. Merely shows that it is true. Exhaustion doesn't qualify as a real argument, in my opinion.

wetmore 12y ago

People often talk about the proof as if they just enumerated every possible planar graph and checked. Which is true in a sense, but disregards the work that went into making it possible to enumerate the cases in the first place. There are infinitely-many possible planar graphs, so you of course need to find some invariants that allow you to bring the necessary number of graphs to check to be finite. Beyond that, the techniques in the 4CT which make it actually possible to reduce the number of cases to a feasibly enumerable number are very clever and require some insight.

jordigh 12y ago

Proof by exhaustion is considered a real argument as long as there are not too many cases to exhaust. One of the most dramatic examples is the proof of that result that goes... if RH is true, then the result is true. If RH is false, then the result is true. Therefore, the result is true! So, why make the cut-off point of when exhaustiong is an explanation at some finite number of cases?

deleted 12y ago

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GFK_of_xmaspast 12y ago

Personally, I think it's totally valid. (PhD mathematician here).

evanb 12y ago
It's certainly a valid argument, but it's not... enlightening in the same way other kinds of arguments are.
JadeNB 12y ago
> Personally, I think it's totally valid. To be fair, though it's a bit ambiguous, I read sebastialonso's post https://news.ycombinator.com/item?id=8799362 https://news.ycombinator.com/item?id=8799362 as indicating that he or she believes that the result is true—i.e., does not necessarily reject the validity of proof by exhaustion as a style of argumentation—but does not feel that the proof by exhaustion is an explanation.