Closure Argument

By Michael Gakuran | | Philosophy | 1 Comment |

closureOkay! Back into Philosophy again. The focus over the next few days will be Epistemology (the theory of knowledge). I wrote a little about the origins of modern Epistemology some time ago. Remember Descartes and his Evil Demons? Go and read it for a light introduction to some of the worries we have with regard to knowing things about the world. It is really the case that we can know nothing? Are we just dreaming? Being tricked by an evil demon or actually a brain in a vat having electronic signals sent to us by a supercomputer? Let’s see if we really are knowing nothing…

    The Closure Argument

Sounds tricky, but bear with me and I’ll attempt to give a summary of what this is about. Ever heard the expression ‘knowledge is closed under entailment’? Unless you’ve dabbled in philosophy, my guess is probably not.

This is just a technical way of stating the common sense view that many of us probably intuitively hold. Basically the idea that we can enlarge our knowledge by accepting those things that we can correctly deduce from (are entailed by) what we know. Take a look at this statement:

If subject (S) knows that p, and p entails q, then S knows that p.

What now? Entails? The notion of entailment can be understand as something like this: The truth of one statement (A) necessarily implies the truth of the other statement (B). For example:

(A) The crow is black. entails (B) The crow is coloured.

If the crow doesn’t have a colour, it cannot be black! How about another:

(A) Charlie was murdered. entails (B) Charlie is dead.

If Charlie wasn’t dead he couldn’t have been murdered, right!? So in our Closure Argument, if we say p entails q and if for some reason q turns out to be false, p is false too.

So back to our Closure Argument. Take this example of it:

I know that my philosophy exam will take place at 9.30am in The Great Hall. That my exam takes place in The Great Hall entails that ‘The Great Hall’ is not just an imaginary place. Therefore I also know there is a place called ‘The Great Hall’.

This seems to be very intuitive, but we need to be careful with our wording here. One might fail to agree that ‘p entails q’. Or perhaps I come to know q (there is a place called ‘The Great Hall’) by some epistemically unjustified source. E.g. I found it existed because a fortune teller told me so.

Or perhaps I just fail to believe q altogether. (Most people agree that if you fail to believe in something, you cannot know it either). In the above example, pretend that The Great Hall is also a website on which I am supposed to take the exam. I take the exam by logging onto ‘The Great Hall’ website while I am sitting in the real, concrete Great Hall. As such, even if I am told that the exam takes place in ‘The Great Hall’, I might not believe it is a real, concrete place that exists at first.

To avoid niggling little counterexamples like this, we need to clear up our terminology:

If subject (S) knows that p, and believes q by correctly deducing it from her belief that p, then S knows that q.

In this revised version of the Closure Argument, I think the phrase ‘correctly deducing’ would avoid the problems above.

Note: An explanation of ‘closure’. Why talk of knowledge being ‘closed’? When we speak of ‘closure’, we are referring to a particular set of things (for example, the set of things known by me) that bear a special relation (such as being ‘correctly deducible’/entailed by) only to other members in that set. Basically then, in this case, if we accept the principle of entailment (knowing things by correctly deducing them from others), then everything we ‘know’ is limited by this principle. I.e. This is the way we have knowledge of the world, so if the Closure Argument fails, then we have to look for a different way of explaining how we know things.

Some philosophers have argued exactly this. Closure fails. Let’s take a closer look at the problems.

    An argument *for* skepticism?

Here’s how the skeptic, our arch nemesis, can argue against our knowing things using the same argument. It’s the old ‘how do I know I’m not just a brain in a vat being sent signals by a supercomputer?’ argument:

(P1) I do not know that I am not a brain in a vat (BIV).
(P2) I know that ‘I have hands’ entails I am not a BIV.
(P3) If I know something p, and I believe q by correctly deducing it from my belief that p, then I know that q. (Closure Argument)
(C) Thus, I do not know that I have hands, because I do not know that I am not a BIV.

So, if we wish to go on accepting the Closure Argument, then we have to accept that we do not know if we have hands. (We cannot both be sure we have hands and not know if we are a brain in a vat. If I am a brain in a vat, then I cannot hands hands!)

Interestingly enough however, this argument can be turned on its head, as was done by the philosopher G.E. Moore:

(P1) I know that I have hands (I can wave my hands around in front of my face to prove it).
(P2) I know that ‘I have hands’ entails I am not a BIV.
(P3) If I know something p, and I believe q by correctly deducing it from my belief that p, then I know that q. (Closure Argument)
(C) Thus, I know that I have hands.

As you might think, Moore’s argument is circular because it has to presuppose that ‘I am not a brain in a vat’. Since this is the very thing we are trying to prove, we can’t tacitly presuppose the conclusion in the first premise (P1).

Moore would reply by saying that, of the two arguments, ‘I know I have hands’ and ‘I don’t know that I’m not a brain in a vat’, the former is much more obvious and plausible, so we should accept it over skepticism. Moore argues that we have much less reason to accept these ‘philosophical intuitions’ that cause us worry than our common sense by which we can clearly see such things as having hands.

But if I were a brain in a vat, then waving my hands in front of my face to demonstrate my point would still convince me that I have hands. But in actuality it would just be a figment of my imagination! So Moore’s argument doesn’t do much for our worries does it? Perhaps finding a better argument other than Closure is the way forward. Let’s charge on…

Other reasons to doubt Closure include:

Relevant Alternatives
Nozick’s truth-tracking


Sources: Lecture handouts written by my lecturer Daniel Elstein, The Internet Encyclopedia of Philosophy and The Stanford Encyclopedia of Philosophy

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