Logical Gal, Pinterest and the Hebrews

6 Dec

Today, let’s talk about conversions of propositions that begin with the quantifier ‘all’: 

Here’s a true or false question about a favorite hang-out place of many women: If it’s true that all classy gals who decorate their homes stylishly spend time on Pinterest….is it ALSO true that all those who spend time on Pinterest will decorate their homes stylishly?

No….this is because you cannot convert A statements

All S is P does NOT equate to All P is S

At best you can say: Some P is S so that in the above example, it would be true that:

Some of those who spend time on Pinterest are classy gals who decorate their homes stylishly

Don’t forget – it only takes ONE to have a SOME as a quantifier!

I read another useful example of the trap of converting A statements in an explanation about the name, “Son of Man”.  This was Jesus’ favorite title for himself.

The title actually comes from the book of Daniel in the Old Testament. Here was the statement that I read:

“(the Son of Man)..could represent Israel but Israel itself cannot be the son of man” (Tabletalk Magazine, devotion dated  5 Nov 2013) 

Apparently Jewish scholars like to plug in the nation of Israel as that which the Prophet Daniel referred to.  But given the limitations of conversion of propositions, one cannot do that.  Putting the above quote in logical form we have this:

All Son of Man is Israel

All Israel is the Son of Man

Just by looking at the 2nd proposition you can see the ‘switcheroo’ doesn’t work. 

Question:

Where have you encountered advertising or an argument whose weight rests shakily on an invalid conversion like these? 

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