## Friday, 3 May 2013

### Plantinga and his BS5

In my on-going adventures in Craig-Land, I have been challenged recently by a chap with the handle “cpdavy24”.  What follows is my response to him, after he suggested that Plantinga’s version of the Ontological Argument using his own corruption of S5 is not controversial.

I'm using the blog as a vehicle for the response because it's just too awkward to present the data on the forum (and some other people might get a giggle from it).

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It’s nice to see Plantinga’s argument formalised.  It’s so rarely seen.

So let’s look at it closely:

This appears to mean (note that I’ve added the word “where” for the sake of clarity):

Assertion:
it is possible that it is necessary that (there exists a being x) [where] x is a Maximally Excellent being

Premise:
(IF) it is possible that it is necessary that (there exists a being x) [where] x is a Maximally Excellent being
(THEN) it is necessary that (there exists a being x) [where] x is a Maximally Excellent being

Conclusion:
Therefore
it is necessary that (there exists a being x) [where] x is a Maximally Excellent being

We can try to simplify things a little by generalising.  Let’s use precisely the same structure where (\$x)Ex is replaced with A, being shorthand for proposition A is true and A can, if you want, mean “there exists x which is a Maximally Excellent being”. Therefore:

And so:

Assertion:
it is possible that it is necessary that proposition A is true

Premise:
(IF) it is possible that it is necessary that proposition A is true
(THEN) it is necessary that proposition A is true

Conclusion:
Therefore
it is necessary that proposition A is true

This doesn’t read right, does it?  Of course not, because this is where Plantinga does his little switcheroo.  He implies the use of modal logic in the assertion but then applies Kripke semantics in the middle step.  He wants the terms to mean:

= in some possible world it is true that

and

= in every possible world it is true that

So Plantinga’s (simplified) premise is now:

(IF) in some possible world it is true that in every possible world it is true that proposition A is true
(THEN) in every possible world it is true that proposition A is true

This premise might be valid in “multiple worlds” semantics, but it is not uniformly valid.  Generally the system of modal logic know as “S5” (of which this is a variant) is expressed as:

or

(IF) it is possible that A
(THEN) it is necessary that it is possible that A

This is valid.  So is the “multiple worlds” semantics variant:

(IF) in some possible world it is true that A
(THEN) in every possible world it is true that in some possible world it is true that A

However, as already mentioned, Plantinga’s preferred wording of S5 isn’t universally valid.  Let’s look at a generalised expression in the “multiple worlds” semantics version (version A of S5):

AS5
(IF) in some possible world it is true that in every possible world it is true that A
(THEN) in every possible world it is true that A

and then in the classic modal logic version (version B of S5):

BS5
(IF) it is possible that it is necessary that A
(THEN) it is necessary that A

Let’s use these statements in a real example.  Say A is the proposition that “my car runs on diesel”.  I know that there are cars that run on diesel, cars that run on petrol (gasoline), cars that can run on ethanol, cars that run on LPG, cars that are battery powered, hybrids that run on both fuel and batteries, solar powered cars, prototype cars that run on rapeseed oil and then there are dragsters that run on a mix that is heavy on nitromethane.  It’s not certain, therefore, that my car runs on diesel.  I can be pretty sure that you don’t know for sure what fuel my car uses.

So as to not be confused by the “possible worlds” scenario, let’s replace “world” with “country”.

Therefore we can apply AS5:

(IF) in some possible country it is true that in every possible country it is true that it is true that my car runs on diesel
(THEN) in every possible country it is true that it is true that my car runs on diesel

This is a valid statement.  I’ll make it more specific for those who may be confused:

If in Thailand (which is a possible country) it is a universal fact (meaning that it is a fact that is true in all countries) that my car is a diesel, then it is a universal fact that my car is a diesel.  If we picked a different possible country, say Poland, it would make no difference as to the truth about my car’s fuel arrangements.

However, if we use BS5 we get:

(IF) it is possible that it is necessary that it is true that my car runs on diesel
(THEN) it is necessary that it is true that my car runs on diesel

We can see that this simply isn’t true.  It is possible that there is a universal fact that my car is a diesel and, if it was a diesel, it would certainly be a universal fact that it was diesel – but only if my car was a diesel.  You’d have to know more than the fact that it is possible that my car is a diesel (and it’s possible that anyone’s car is a diesel) before you came to the conclusion that it must be a diesel.

When it comes to filling my car, it really helps me to know what fuel it needs.  So, I am likely to use evidence based methodology to determine the fuel required rather than using Plantinga’s bizarre corruption of logic.

It seems, however, that when it comes to answering one of the “Big Questions” – namely “Is there a god?” – some people are more than willing to risk filling their brains with the wrong answer, so long as it’s the answer they prefer.

(Murder mysteries must be much less interesting for Plantinga than for the rest of us.  Usually a viewer is presented with a range of suspects all of whom are possible murderers, and the pleasurable challenge is derived from the guesswork required to identify which one is the actual murderer.  Plantinga, however merely applies his BS5 and can confidently state since each individual is possibly the murderer then, therefore, each individual must be the murderer.  I don’t want to give away any plots here, but I have visions of joining Plantinga on an exotic train trip with a bunch of my fellow non-theists.  In these pleasant daydreams, you may rest assured, Plantinga is not cast as the gentleman detective.  He is, after all, no Hercules Poirot.)