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I'm struggling to explain why this statement is false.

My understanding is: - for an argument to be valid, there must be no interpretation under which the premises are true and the conclusion is false. - It is the form of the argument which determines whether it's valid or not - For example, in the argument: premiss 1 = Donald Trump has black hair premiss 2 = All people with black hair live in California conclusion = Donald Trump does not live in California

This argument is not logically valid because the conclusion does not follow from the premisses, NOT because the premisses are false (ie it is false that Donald has black hair, and it's not true that all poeple with black air live in California). We could keep the premisses as they are (ie false), but if we gave them the conclusion 'Donald Trump lives in California', the argument would be valid on the basis of its form alone.

Is my reasoning correct?

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  • $\begingroup$ I'm not sure if this is the right community for this question, but idk $\endgroup$ – John Lou Jan 19 '18 at 16:22
  • $\begingroup$ What if "argument" is replaced by "proof" and "premises" is replaced by "axioms"? $\endgroup$ – imranfat Jan 19 '18 at 16:23
  • $\begingroup$ See Valid argument: " an argument is valid if and only if it takes a form that makes it impossible for the premise to be true and the conclusion nevertheless to be false" $\endgroup$ – Mauro ALLEGRANZA Jan 19 '18 at 16:53
  • $\begingroup$ Thus, the argument: "All philosophers are male. Therefore: All males are philosophers." is not valid. $\endgroup$ – Mauro ALLEGRANZA Jan 19 '18 at 16:57
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Yes, you are correct.

I think your confusion is that it is frequently stated "a false hyphothesis implies anything" which on the face of it seems to contradict this. It seems to be saying 1)If Donald Trump has black hair Therefore Conclusion: the San Francisco Bay Bridge is made of marshmallow, is a valid argument.

But the argument is not valid (in fact there is no argument). What "a false hypothesis implies anything" means is... well, what it means is that as a logical sentence "If Donald Trump has black hair then the bay bridge is made of marshmallow" has the logical value true. Logic values do not have implication or inference; they merely are factual. "If p then q" does not mean "q follows from p" but that "not p AND q" is impossible.

Some take it further that: If we assume that universe has logical and consistant and completer rules of inference, then if we assume a false premise we can reach by implication any result. That's kind of true.

Donald Trump has Orange Hair. So "Donald Trump has Orange Hair OR the bay bridge is made of marshmallow" is true. If Donald Trump has Black Hair than he doesn't have orange hair. He has black hair. So he doesn't have orange hair. "Donald Trump has Orange Hair OR the bay bridge is made of marshmallow" is true but he doesn't have orange hair. THerefore the bay bridge is made of marshmallow.

But to do this we need to dig into all known premises and results-- not merely the ones we were given. (This includes the True premise that contradicts the false premise.

A less "cheaty" argument would be: Black falls within a spectral range and we measure the spectral range of his hair and subtract to get that a significant positive number is $0$. Thus all values are $0$ and equal to each other. The distance of every inch of the bay bridge from the marshmallow peep in my pocket is $0$ and as two different objects can't occupy the same space and time, every inch of the bay bridge is my marshallow peep. So not only is the bay bridge made of marshmallow. I have the bay bridge in my pocket right now. (Do you want to buy it?)

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Yes, your reasoning is all correct!

Here is an even simpler one:

Snow is purple. Therefore, bananas are pink.

Clearly false premise, and clearly an invalid argument.

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