For Jim Stone: Proof that Unicorns Exist

[Ridseard]

1. If unicorns exist, then they have one horn. (In a conditional statement, if the consequent is true, then the statement is true.)
2. If unicorns do not exist, then [if unicorns exist, then they do not have one horn]. (This, believe it or not, is a tautology. Check the truth table.)

By 1, the consequent of 2 is false, therefore by modus ponens, the antecedent of 2 is false. I..e., it is not the case that unicorns do not exist. Therefore...

3. Unicorns exist.

[Walden]

A one-horned goat?

[TXwhistle]

Why are they called unicorns instead of unihorns? I don't say, "My billy goat has two corns." (Unless he's holding two ears of corn, but even then I'm grammatically incorrect and implying my goat has hands.)

[spittin_in_the_wind]

[Ridseard]

"Cornu" means "horn" in Latin. "Corno" means "horn" in Italian. Similarly for other Romance languages. The cornet is a type of horn. In older musical scores, "corno" often designates "French horn." How about the cornucopia (horn of plenty)?

However, it's usually not corny to be horny.

[TXwhistle]

Should have paid more attention in English.

[AaronMalcomb]

Ah, syllogisms... syllogisms aren't allways true though.

Cheers,
Aaron

[jim stone]

1. If unicorns exist, then they have one horn. (In a conditional statement, if the consequent is true, then the statement is true.)
2. If unicorns do not exist, then [if unicorns exist, then they do not have one horn]. (This, believe it or not, is a tautology. Check the truth table.)

By 1, the consequent of 2 is false, therefore by modus ponens, the antecedent of 2 is false. I..e., it is not the case that unicorns do not exist. Therefore...

3. Unicorns exist.

Ok, so there are unicorns. Anybody have a problem with that?

Thanks, Ridseard. I take your point. The fallacy in the above
argument, given the truth table account of conditionals,
is that 1 doesn't deny the consequent of 2. They are both
true if unicorns don't exist. So the argument is invalid.

And I reckon the idea is that this applies to the version
of Anselm's proof I gave. 'If God exists, then he exists
necessarily' doesn't deny the consequent of
'If we can think of God and he doesn't exist, then
if he did exist, he would not exist necessarily.

Two responses (forgive me, I'm taking you seriously):

1. The truth table account that you deploy in the argument
about unicorns is pretty plainly defective.
On this account, any conditional (if-then) statement
with a false antecedent or a true consequent is true.
So 'If Gore is president then Gore is not president'
is true--well that's strongly counter-intuitive.
'If unicorns exist, then unicorns don't exist' is true.
Kookie. Anselm won't touch this with a ten foot pole.

On the face of things, an adequate account of conditionals
will preserve the intuition that 'If God exists, then he
exists necessarily' and 'If God exists, then he does NOT
exist necessarily' can't both be true.

And it will preserve the intuition that 'If unicorns exist,
they have one horn' and 'If unicorns exist, they do
NOT have one horn' can't both be true.
This is a constraint on an adequate account
of conditionals. (Of course
we don't have an adequate account of conditionals,
but, hey, it's only been 2500 years of trying.)

Why then doesn't the ingenious argument you gave
above prove unicorns exist? After all, the inference
to the conclusion is valid, on an adequate account of conditionals.
The answer is that the second premiss is false.That is, the claim that if there are no unicorns, then
if there are unicorns, they don't have one horn, is
false. The truth is that if there are no unicorns, then,
if there are unicorns, they do have one horn.

Now let's think intuitively.

1 If God did exist, then God would exist necessarily.

That's true.

2. If we can think of something that, in fact, doesn't exist,
then, if it did exist, it wouldn't exist necessarily.

That's true, too. Unicorns, for example. We can think of then,
they don't exist, and if they did, they wouldn't exist
necessarily.

It follows as a substitution instance of 2 that

3. If we can think of God and, in fact, he doesn't exist,
then (if he did exist, he would not exist necessarily).

But now, very intuitively and reasonably, 1 denies
the consequent of 3. Note, please, the subjunctive
nature of 1 and the consequent of 3. Nobody thinks
the truth table method captures subjunctive
conditionals. I say 'If I were an accountant, I would
be earning a lot more money.' Somebody says:
'True. And it's just as true that if you were an accountant,
you would NOT be making a lot more money. After all,
you're not an accountant!''

No it isn't just as true, it's false. The truth-table
account of conditionals doesn't capture subjunctive
conditionals, so it doesn't apply to Anselm's argument.
If you rephrase the conditional in your unicorn argument
subjunctively ('would', 'did'), 2 would be false.
That says that if unicorns don't exist, then, if they did
exist, they would not have one horn.

Well, if that doesn't satisfy, I'll just prove that
God exists another way--but later.

Thanks so much for the ingenious objection.

[Ridseard]

Thanks, Jim. Yes, I deliberately avoided subjunctive phrasing in order to make it appear as though the sentences were not subjunctive conditionals.

I still think something's wrong with Anselm's argument.

[jim stone]

It;s hard to believe it works,
but it's also hard to find a
fallacy. After a thousand
years of dealing with these
arguments, the people who think they're fallacious disagree about what's the matter with them. I remember in grad school a prof put one of these on the board and challenged all of us hotshots to refute it. After two hours of failure I was sweating and my hair was standing on end. Fear of God!
If there is a knockdown, drag out
PROOF that God exists, Anselm
gave it. Thanks again

[TelegramSam]

I've seen Anslem's argument. It's not airtight. I've also seen arguments that are pretty convincing that God can't exist until you really look at them and pick out the one or two fallicies.

Frankly, I think it's all kind of silly to debate the existance of God, or unicorns for that matter.

"Unicorns don't care if you believe in them anymore than you care if they believe in you."

[PhilO]

Okay, I can neither whistle nor work out today, because I awoke with a killer sinus headache and congestion (a changing season tradition this time of year); then I saw this thread and now my head really hurts. Thanks guys. Problem is at some point, I could almost swear I was understanding...

Anyway, I hope both God and unicorns exist. I've always felt that anything we can imagine can somewhere, sometime actually be. I feel that God exists. Moreover, how could just some chaotic accident account for the oneness of things that we feel and the resultant universal laws evidenced every moment?

My clogged two cents..

Regards,

PhilO

[jim stone]

Here's the grand-daddy of all arguments for God's existence,
Anselm's Proof, so-called.

Anselm uses 'God' to mean 'a being greater than which none other is possible--the greatest being possible.'

For Anselm, 'greater' means 'more worthy of acclaim,' 'of greater stature than,' 'superior to,' 'more wonderful than,' 'more worthy of worship than.'

1. God is possible.

(That is, God isn't something the existence of
which involves a logical contradicition, like a married bachelor
or a five-sided triangle. Even if God doesn't exist,
he's no worse off than unicorns or Santa. He isn't an
impossible being, something that couldn't have been.)

2. If God is possible, then there is a possible being that is God.

(Anselm thinks a possible being is a being that can exist.
Anything the existence of which doesn't involve
a logical contradiction is a possible being.

There are two
kinds of possible beings:

A: possible beings that don't exist
(aren't actual), like Godzilla, Sherlock Holmes, all the
kids who might have been conceived but weren't, The
Fountain of Youth. These are things that might have
been actual but aren't, and

B. possible beings that do exist,
like you, me, the USA, the planet--things that exist
CAN exist, of course, so they're possible beings.
So the second premiss asserts that
if God's existence wouldn't involve a logical contradiction,
he's in A or B)

1, 2, therefore

3. There is a possible being that is God.

(3 is asserting that God is in A or B--he's a possible being
that doesn't exist or a possible being that does exist..)

4. If God exists, God is greater than if God is a possible being that does not exist--a mere possibility.

(Existence is a great-making property for God; he's more wonderful, more worthy of acclaim, more worthy of worship, of greater stature,
if he exists than
if he's a mere possibility, something that might have been
actual but wasn't.)

The question now is this: God is in A or B. Which is it?

Here we begin a reductio ad absurdum. This is an argument which
supposes a proposition for argument's sake to prove that it's
false by showing that it logically entails an absurdity.

5. Suppose God is a mere possibility.

4, 5 therefore

6. God could be greater.

(If God is a mere possibility, then he could have actually existed,
in which case, according to 4, he would have been greater. So
if he's a mere possibility, he could have been greater.)

Def, 6 therefore

7. The greatest being possible is not the greatest being possible. Koo-Koo!
A logical contradiction.

4 therefore

8. God is not a mere possibility.

(What the reductio has shown is that if existence makes God greater,
he cannot be a mere possibility. 4 entails that God is not something that
might have been but isn't. Either God is impossible or he exists.)

3, 8 therefore

9. God exists.

[TelegramSam]

Ah, the old ontological argument. I remember that thing. I'm tempted to copy my old Philosophy 1000 notes that showed all the little glitches in that thing, but I'm too lazy.

[elendil]

i think the problem with the ontological argument arises from the nature of human knowledge in general.

humans 'deal with' what exists by means of sensation and intellection, in the unity of a human person. concepts or ideas are general but are used to help us 'deal with' existing stuff, which is singular in each instance. the problem arises when humans start dealing with concepts/ideas as if they were existing things. why is that a problem? because existing is not a thing--it's analogous to an action. just as we can form an idea of an action, so too we can come up with an idea we call 'existing,' but that idea does not correspond to a 'thing:' like other ideas it's just a tool for wrapping our minds around a problem. therefore logic, which is a tool for dealing with ideas rather than with 'existing' per se, is not necessarily an appropriate tool for dealing with 'existing,' since existing is at least logically prior to any idea: no existing, no idea.

humans are 'set up' to 'deal with' things-that-exist, and rational knowledge (the application of ideas to things-that-exist, categorizing, comparing, the linking and manipulation of ideas, etc.) is a highly efficient way of doing so--just look at modern technology, which is largely based on rigidly conceptualized approach to science (via mathematics). that's because there really is a 'whatness' component to things-that-exist, in addition to their sheer 'is-ing.' however, humans are not 'set up' to deal very efficiently with questions like, 'how is it that things-that-exist actually exist? are actually is-ing?' that's because existing is logically prior to thought, which means that thinking never make it so, which means cogito ergo sum is backwards, which means that anselm too is wrong--no matter how conceptually appealing his argument.

man's attempt to deal with things-that-are is perfectly appropriate for mundane life. it only becomes problematic when dealing with the ultimate question: is! (as parmenides is supposed to have said.) mythic thinking, as mircea eliade explains it, is precisely the attempt to reify ideas and so to find a conveniet way to 'deal with' ultimate issues. this, in turn, as eliade also notes, led to the greek fascination with formal logic, which they misconceived as the true law of what-is, rather than the means by which humans deal with what-is. this has continued throughout virtually all western thought (and i'm not bashing western thought, per se). the truly honorable exception to all this was thomas of aquino (moses ben maimon is also close). thomas (and moses to a great degree) drew on the doctrine of creation ex nihilo to explain the logical priority of is-ing to thinking, as well as the analogical nature of all attempts to conceptualize is-ing (thomas did not neglect, in this regard, to point out that analogy is a form of equivocation).

ridseard and stoner, i know my attempt, as all such attempts to explain these matters, is utterly inadequate--quite possibly more inadequate than most. however, i would highly recommend the work of etienne gilson: 'the unity of philosophical experience,' 'thomist realism and the critique of knowledge' (translated by yours truly), and 'being and some philosophers.' these are not easy books to wrap your mind around, but the alternatives are more technical, with one exception: a marvellous little book by josef pieper called 'the silence of st. thomas.' there is also a combination of two of pieper's books available as 'living the truth.' this contains his early and outstanding book 'the truth of things' (the original was something like 'die wahrheit der dinge,' but my german is hopelessly rusty). he's using 'things' in the manner i was trying to do: things-that-are. all these works explain what i tried to do, but far better.[/i]