A Logic Problem from my Philosophy Final

Logic Level 1

When Mark wears white, that means it is going to snow.
It is summer and 100 degrees outside.

Is it true that Mark will not be wearing white?

True False Cannot be determined

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Drex Beckman by Drex Beckman , 23, USA

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4 solutions

Drex Beckman
Jan 27, 2016

The statement is a false premise and therefore fallacious. It can be summed thusly: x->y, does not imply ~y->~x.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Actually, if you do a table of logical value, x->y is equal to ~y->~x. However I still think the statement is fallacious because all the statements are "weak", that means they are not stated precisely. E.g. summer and 100 degree does not imply not snow...

Tran Hieu - 5 years, 4 months ago

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Okay, I see. So maybe instead of x->y, not ~y->~x, could you say x->y, not y->x? Like saying "It's raining therefore the streets are wet" but the opposite is not true: "The street is wet, therefore it is raining". So "White, therefore snow" but not true is "Snow, therefore white." But as you said, x->y, and ~y->~x is valid, so "No snow, therefore no white" is just as fallacious as the inverted premise, correct?

Drex Beckman - 5 years, 4 months ago

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Yes, white --> snow is equally to no snow --> no white. You can prove it simply by " reductio ad absurdum" (sorry for my english), that, if "no white" is false, then it is white, therefore it is snow, contradict with the "no snow" condition, that leads to "no white" must be true.

Tran Hieu - 5 years, 4 months ago

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@Tran Hieu – Cool. I only ask because I used the aforementioned approach, and got it correct, so I knew it was right with some justification but not certainty why. Thanks. ;)

Drex Beckman - 5 years, 4 months ago

@Drex Beckman , i like that word: Fallacious its soooo interesting!!! i like saying it!!

A Former Brilliant Member - 3 years, 7 months ago
Alex Wang
Oct 10, 2017

it is fallasious because 100 degrees could mean kelvin (in which case there is a possibility 4 snow)

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~ Amelia Zhang ~
Mar 8, 2021

The statement does not specify what form of degree the "100 degrees" is, so it could basically mean a range of temperatures, from very cold to very hot.

Even if 100 degrees was Celcius, there is still a possibility, however small that it could snow.

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It can be degrees Celsius that means ,he will not wear white

It can be in degrees kelvin too that means he will wear white

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