Thursday, September 09, 2004

Modal Redundancy and Iterated Modalities

  • You can't possibly believe that!
  • It must needs be ascertained whether or not Poindexter is in receipt of his severance pay.
  • Actually, I am quite impressed at her contribution to the fund-raising effort.
  • There is a possible world in which I can play chess as well as Victor Reppert.

The above are examples of modal redundancy. In the first two sentences, one can delete 'possibly' and 'needs' without loss of meaning. In the third case, likewise, though it is not as clear: 'actually' may be functioning merely as an intensifier rather than as a modal term. The fourth is a common mistake among some who try to engage in 'possible worlds' talk. 'Can' is either redundant, or a rather more recherche idea is being advanced willy-nilly, namely, that there is a possible world W in which I exist where I have the ability to play as well as Reppert, or perhaps that there is a possible world W*, accessible from W, where I play as well as Reppert.

Now consider these examples:

  • Since it is necessarily true that I am self-identical, it is necessarily true that it is necessarily true that I am self-identical.
  • If it is possible that I be hiking now, then it is necessarily the case that it is possible that I be hiking now.

In these examples, there is no modal redundancy. What we have instead are iterated modalities. Necessarily p is clearly a different proposition from Necessarily necessarily p. To see this, consider the proposition P expressed by '7 + 5 = 12.' P is necessarily true. But what about the proposition P* that P is necessarily true? Clearly P* is true. But is it necessarily true, or only contingently true? I say the former. Even if you disagree with me, you understand what we are disagreeing about, and so commit yourself to a distinction between P and the proposition that P is necessarily true. That suffices to show an absence of redundancy.