Tag: Hans Kamp

As it stands, Fitch’s argument is water-tight, air-tight. But as it stands, it relies on a very shallow representation of being known.

To say that something is known is to say that someone knows it.

First point: such words as “someone”, “everyone”, “anyone” are used with some range implicitly in mind. For example, if I say “Everyone is vulnerable to the Covid 19 virus”, you aren’t going to object by mentioning Napoleon and Julius Caesar. You will have understood that I meant everyone alive now. In any interpretation of a text, along the lines of our familiar ‘truth-and-reference’ semantic analysis, the quantifiers range over a specific set, the domain of discourse.

So let us look at Fitch’s argument with the relevant range made explicit. Instead of “It is known” let us write “It is known in Seattle”. Let us take it that A is true, but it is not known in Seattle. My friend David lives in Seattle, and so I can deduce at once that David does not know that A, and certainly does not know that (A and it is not known in Seattle that A).

But is it the case that David could not know that? In actual fact David lives in Seattle, but there is nothing impossible about his living in Tacoma instead. And if he were living in Tacoma, there would nothing impossible about him knowing that A is both true and unknown in Seattle.

So the equivocation that tends to give us a sense of unease with Fitch’s argument is this. It is impossible that someone knows that (A and no-one knows that A). But for each person X we can also hold, without running into contradiction It is possible for X to know that (A and no-one knows that A).

The reason is that, what ever is the range associated with the use of “someone” in this context, it is possible for X to be outside of that range.

First objection: surely there is a sense of the words “some”, “every”, in which there is nothing relevant is outside the range? For example, “everyone” could in this case be all humans.

That does not include the gods on Mount Olympus. They are not real, but they could be. If it could be the case that they know that truth (which refers to the ignorance of all humans) then that truth is knowable. There are other possibilities to consider. My friend David is human, but it would be possible for him (in purely logical possibility!) to be transformed by a witch’s spell into a frog, while retaining all his cognitive powers and resources. If he were a frog then he could know that A and that no humans know A.

Second objection: surely there is an absolute sense of the words “some”, “every”, in which there is nothing outside their range, period? Bring up any thing at all that could know something, or any thing at all for that matter, and it is covered.

That is daring. It means that in our language we can quantify over all the denizens of all possible worlds. We have to take it seriously, because David Lewis once said that this was the case for his language:

“I can. Some say they can’t. They say their understanding is limited to what can be expressed by modalities and world-restricted quantifiers. I have no help to offer these unfortunates, since it is known that the expressive power of a language that quantifies across worlds outruns that of the sort of language they understand.” (Lewis 1979, footnote on page 517) 

Second point: as Lewis himself made very clear in his article “Anselm and Actuality” (1970) we need to take seriously the logic of the word “actual” as an indexical. In unadorned simple sentences, the word “actual” is logically negligible: I actually have ten dollars if and only if I have ten dollars. But embedded in modal contexts, it takes on a dramatic role:

I wish I had more money than I actually have!

Here you cannot drop the “actually”, for it is certainly not the case that I wish for the impossible situation in which (BvF has more money than he has).

So, it is possible for my friend David to know that A is true and that actually no one knows that A. That is,

(*) there is a possible world β in which David knows that in world α it is the case that A and that no one knows that A.

That means equivalently that the following is true in our world:

(**) It is possible that David knows that Actually( it is the case that A and no one knows that A).

Very odd though! If you take possible worlds seriously, in a metaphysical sort of way, you may insist that the denizens of one world cannot know about those in another world.

(Well, maybe you will not insist; in the Appendix I’ll mention an example.)

But as a point of logic, it should count — metaphysical scruples aside. Think of this similar case (which is how Hans Kamp began): the word “now”. It may be true in 2075 that there were men on Mars years earlier, but it certainly won’t be true in 2075 that it is now the case that there were men on Mars years earlier. And there is no difficulty, of course, in someone knowing in 2075 that a certain proposition was already true in 1900 but that no one knew that even now.

So, if we had discussed this with David Lewis, what should we have said? To those of us who are a-metaphysical, the possible world machinery is just for modeling, to capture inference patterns in language. So we have no difficulties with the weirdness of (*) or (**). We can live with it.

Some say they can’t. They say their understanding is constrained by a reasonable metaphysics about the reality of other worlds. We have no help to offer these unfortunates …

So, to summarize, the impact of Fitch’s paradox is, on my diagnosis, due to an equivocation. When we say that it is possible for someone to know that something is true which no one knows, what do we mean? Is the word “actual” there implicitly or not, does the possible knowledge refer to us actual knowers, or does it refer to all possible knowers? In the first case we have a real possibility related to our world:

there are truths which are actually unknown, and they are knowable

In the second case, there are no unknown truths, but that is something that is not a fact about actual knowledge. And surely it is the actual knowledge, rather than any other sort of knowledge, that we, inhabitants of this actual world, like best.

Does this feel like a satisfying response to the Knowability Paradox?

SOURCES

David K. Lewis, “Anselm and Actuality”, Nous 4 (2) (May 1970): 175-188; “Attitudes de dicto and de se, The Philosophical Review 88 (4) (1979): 513-543.

Hans Kamp, Tense Logic and the Theory of Linear Order. Dissertation, Ucla (1968); “Formal properties of ‘now'”, Theoria 37(3) (Dec 1971): 227-273.

APPENDIX

Would someone who takes other worlds seriously, in a metaphysical way, ever allow that a denizen in one world could know things about denizens in some other world?

Yes. Quite a long time ago I came across a periodical called The Fortean Times, in which I found some disturbing news. One article broached the question: why are psychics’ predictions so often false? The answer offered was: actually their predictions are typically true! But often, what they are true about, is what is to happen in other worlds than our own.