## Thursday, July 30, 2015

### An argument that there must be infinitely many horses

1. For any finite number n, if there can be n horses, there can be fewer than n horses.
2. There cannot be fewer than zero horses.
3. Thus there must be an infinite number of horses.

The inference proceeds as follows. Imagine that there can be some finite number, say 10, of horses. Then by applying (1) ten times, we will conclude that there can be fewer than zero horses.

:-)

SMatthewStolte said...

The problem has never been of horse scarcity but of distribution.

Heath White said...

The problem is in the second premise. You just have to count negative horses. You may think such things do not exist. But as Meinong showed, they can subsist, and therefore we can count them.

Alexander R Pruss said...

Would be interesting to have a negative horse and a positive horse together. You could ride a horse even though there are zero horses.

Dagmara Lizlovs said...

Infinite horses = lots and lots of manure. :-)

Dagmara Lizlovs said...

Alex:

Yes, you can ride a horse even though there are zero horses as this video of an "equestrian" completion, the SIHS Human Horse High Jump Competition, shows us:

http://www.bing.com/videos/search?q=people+jumping+horse+jumps&qpvt=people+jumping+horse+jumps&FORM=VDRE#view=detail&mid=02E20939FF77350A7BCA02E20939FF77350A7BCA

Maybe this should be posted under your post "Value of species membership". Are the participants highly athletically endowed humans or deficient horses? :-)

Anonymous said...

"For any finite number n, if there can be n horses, there can be fewer than n horses."

Zero is a natural number, so, premise one asserts that there can be fewer than zero horses.

"There cannot be fewer than zero horses."

Premise two directly contradicts premise one.

Alexander R Pruss said...

The argument is certainly faulty, but there is no contradiction. Premise one does not assert there can be fewer than zero horses. It asserts that IF there can be zero horses, there can be fewer than zero.

In case anybody hasn't noticed, this was meant to be a parody of the so-called Subtraction Arguments (which are meant to establish the possibility of there being nothing).

Anonymous said...

So, from premises one and two, we can infer that there cannot be zero horses. From this conclusion and premise one, we can infer that there cannot be one horse. But if there is any natural number of horses and that number is greater than one, then there is one horse. Accordingly there cannot be any natural number greater than one of horses, neither can there be one horse, but that is equivalent to there being zero horses. As we have concluded both that there are zero horses and that there cannot be zero horses, we have a contradiction.

Alexander R Pruss said...

"But if there is any natural number of horses and that number is greater than one, then there is one horse."

By "there are n horses", I meant "there are *exactly* n horses". Sorry for the ambiguity.

But one can still conclude:
"Accordingly there cannot be any natural number greater than one of horses, neither can there be one horse, but that is equivalent to there being zero horses."

So there cannot be any natural number of horses. But that's not a contradiction: that just implies that there is an infinite number of horses. :-)

Anonymous said...

You'll need to deny the principle that given n horses, we can remove n-1 of them. In fact, you'll need to deny that for any m less than n, given n horses we can remove n-m of them. How will you reconcile that with premise one?