More on the Prefix Paradox

Posted on June 30, 2010
Filed Under Heidegger, Peirce, Philosophy | Leave a Comment

I’ve been thinking a bit more about the Prefix Paradox from the other day, as I don’t think I really put into words well my objections.

First, I think when considering it one ought distinguish between belief, assertion, and judgment. The most interesting aspects of the “paradox” are in my mind the epistemological ones. And the key issue that enables the paradox is basically the claim that it is irrational to believe contradictory things. In the comments I raised the pragmatic response that vagueness entails that the principle of contradiction doesn’t hold.

I think it best for clarity’s sake to put the paradox in the proper form. Let’s exclude belief as what really is at issue is what one ought believe. That is it is not fundamentally about beliefs or assertions but judgments. (I recognize that in common language we often conflate these three) Judgements considered epistemologically are concerned with the idealized judgments from a given set of evidence. That is they are fundamentally an example of ethics in that they deal with when we should form a judgment. (By implication this is taken to be about when we should believe, but that’s a bit trickier in practice) The question then becomes how to deal with contradictory justified judgments.

My assertion is that the logic of judgments is fundamentally different from the logic of say existence. Our judgment about general claims violates the law of the excluded middle whereas our judgment about vague claims violates the law of contradiction. (Peirce ends up developing the issue in terms of a game-theoretic model for judgment making)


Before I deal with why I think this, let me add that I think the logic of assertions is somewhat different from the logic of judgments. That is because offering an assertion is a kind of taking responsibility. Yes, making judgments also involves this taking up of responsibility. But the way the two are manifest ends up being different. I think though that what is key to discerning the logic of judgments is in recognizing the role of responsibility (which is obviously tied to the ethical aspects of epistemology).

To ask when one should make a judgment is thus to fundamentally ask a question about responsibility. To say that two contradictory judgments shouldn’t be held is to assert that it is irresponsible to hold to contradictory judgments. However what the paradox of the prefix demonstrates, I think, is that it is very responsible to do this. The standard approach to epistemology is a claim that it is irresponsible to hold inconsistent beliefs – that is that ones own beliefs ought be fully coherent. One other “solution” to the paradox is to assert it fundamentally equivocates. That is one dealing with attempting to eliminate errors while recognizing we don’t always eliminate errors. I personally think this once again merely gets at the issues of responsibility but merely avoids the problem by avoiding the question of judgment. The fact is that we do make the judgments that the paradox presents and we do recognize it isn’t irrational to do so. This is only a problem for those who think rationality inherently entails the same laws as reasoning about existence does.

Put in more Heideggarian terms, the question is about withdrawal or absence. When we reason is our reasoning parasitic on a particular conception of being in terms of pure presence. Pure presence entails the law of the excluded middle and non-contradiction. If there is absence in what we reason about, that is our conception of being as cognizability in its broadest sense, then the nature of logic changes. Put an other way logic inherently has metaphysical foundations. Put a little less aggressively: one has to use the right logic for the right objects.

Related posts:

  1. Paradox of Expressibility
  2. Meta-Coherence
  3. Knowledge and the Dogmatism Paradox
  4. God and Completion
  5. The Instability of Philosophers’ Judgments
  6. Cantor’s Paradox

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