Monday, September 8, 2008

Knowledge and Necessary Truth

by Hanno

Most people grant that the following claim is true: If I know P, then P must be true, or alternatively, then necessarily P. What is the meaning of the consequent? There are at least three. The claim could assert the certainty of P, given that P is known. The sentence would then read: If I know that P, then P is certain. This seems perfectly fine.

But there is an alternative meaning: that knowing P implies the necessity of P. A claim is necessary if it is impossible for it to be false. There are two kinds of necessary truths. The first are made true by virtue of the meaning of the terms involved. These truths are called "De Dicto," and examples are "Bachelors are unmarried," and "Unicorns have one horn." These are frequently called "analytic truths," following Kant. The other kinds of necessary truths are more controversial. These are called "De Re," and are somehow necessary in virtue of the object itself, and not merely the description. If there is no de re necessity, then all non-analytic truths are not necessarily true. Primary examples of de re necessity: Gold has 79 protons, gold is atomic. These are not analytic because they were discoveries, and analytic truths are not. If true, they are necessarily true. But we could be wrong, we might have made an error in discovery.

Be that as it may, there are several examples of claims that are not necessary. "Hanno exists," "Hanno's phone number is 555-1212." Notice then what happens. If the initial claim is true, then the claim "If I know Hanno exists, then necessarily, Hanno exists." Well, I do know that Hanno exists. It follows that Hanno necessarily exists. That cannot be right, since my existence is surely contingent on many factors. Just because I know my phone number does not mean I could not have had another, or no phone number at all.

Now, if the second reading of the initial claim were right, knowledge all by itself would imply the necessity of everything known. If some being knew everything, then everything would be necessary. But knowledge by itself does not imply the metaphysical necessity of everything, but merely the epistemic necessity (certainty).

But if we follow the grammar of the initial claim, we can see the error. The necessity does not apply to the proposition, but to the implication. The third way of reading the initial claim is: It follows necessarily that if I know P, then P. This is not a claim about certainty, nor is it a claim about the necessity of P. It is a claim about the necessity of the connection between the antecedent and the consequent, between "I know P" and P. On this reading, I can know Hanno exists, and grant the first claim. But what follows is merely that Hanno exists. My existence is no longer necessary, and the rest of the world can breath a sigh of relief.

It then follows that even if some being knows everything, it does not follow that everything that happens happens necessarily. That may still be true, but it does not follow merely from the state of knowledge.


BECK said...

how was your day?
i liked your blog
you are fantastic!!!

really nice blog
fabulous fantastic
take care
see you

Hanno said...

Gosh, thanks for the comment!

tr said...

So, in the second interpretation, the implication is the main connective, and the necessity box attaches to the consequent. In the third interpretation, the necessity box is the main connective and attaches to the entire conditional. Is that right?

Lee said...

Oh god this all goes way over my head.

Hanno said...


Right. Its a matter of scope, but I don't have symbols here, so I can't show it.

Lee- uh, sorry. I tried to make it accessible, though the post came out of a philosophy club meeting 3 weeks ago.

Rob said...

Hanno, your talk of the number of protons in an atom of gold makes me think of your lectures on Locke. Thinking of Locke makes me think of the corpuscular atomic theory. And you know what, you were right...corpuscles does sound like something gross.

Hope that was insightful.

Hanno said...


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