Frege, Relativism and Faultless Disagreement

This post is re-presents an article of the same name by Sven Rosenkranz, found in the volume Relative Truth1.


Truth Relativism2 can be an attractive prospect. In aesthetics, in ethics, and elsewhere, there are insoluble disputes, where not only does neither side appear to have epistemic advantage over the other, but it seems quite natural to say that both sides are entitled to their opinions. That is, there seem to be faultless disagreements, where the assertions of each disputant are in contradiction, and yet where each side is correct to assert as they do. Supposing that this is an accurate read of the situation, how are we to make sense of it? Enter Relativism: the simultaneous correctness of both claims is to be explained by the fact that each claim is true relative to the claimant’s perspective. Unfortunately, the hope that Relativism can support the notion of faultless disagreement appears to be forlorn.

Frege on Assertion

As Frege famously argued, stating that some proposition P is true is neither necessary nor sufficient for asserting that P. It is not sufficient, because sometimes we only wish to show that a logical relation exists between P and other propositions, leaving aside questions of their truth (e.g. by conditionalizing on P, or assuming it for the purpose of a reductio); it is not necessary, as P can be asserted without mention of its truth, which is assumed. So, if asserting is not equivalent to stating, what is it? It is the presentation of some proposition as true. By asserting we proceed from the proposition to its truth-value.
Out of this conception of the nature of assertion, falls a norm. If to assert P is to present P as true, then asserting P will be correct just in case P actually has the truth-value ‘true’. So, given the truth-value of a proposition, we can straightforwardly derive the correctness of its assertion. Further, this allows us to derive further conclusions by the laws of logic, for example, we can infer from the correct assertions P and P→Q,  that Q is true and ~Q false, and from this that the assertion of ~Q must be incorrect. In this way we can see how logic acquires its normative force: it laws facilitate the preservation of truth, and thereby ensures the correctness of our assertions3.
We’re now in a position to see why the notion of faultless disagreement is problematic and why a radical proposal like Relativism is appealing. Formally, we define faultless disagreement: A and B faultlessly disagree just in case (i) A asserts P and B asserts ~P, and yet (ii) neither A’s assertion nor B’s assertion is incorrect. Here, condition (i) is meant to capture disagreement, whereas (ii) indicates the faultlessness of both parties to the dispute. Next, we argue4:

(1) A asserts P (assumption: disagreement)
(2) B asserts ~P (assumption: disagreement)
(3) Both assertions are correct (assumption: faultlessness)
(5) B’s assertion is incorrect (from 2, 4)
(6) ~P (from 2, 3)
(7) A’s assertion is incorrect (from 1, 6)
(8) Not both assertions are correct (from 3, 7)

So, given the Fregean view of assertion, it seems that faultless disagreement is impossible: the argument above constitutes a reductio of the concept by showing that the assumption of faultlessness cannot be maintained.

A Relativist Solution?

One way to try to salvage faultless disagreement is to adopt a relativism about truth. According to one development of relativism, the truth of a proposition is relative to a perspective, where perspectives are functions from propositions to truth-values. Perspectives, in some way or another, are intended to provide a standard of assessment for propositions. Different standards of assessment can result in the assignment of different truth-values, thus, different perspectives can assign different truth-values to the same proposition. How does this help us? Rosenkranz explains5:

The lead idea then is that, in the envisaged case, P may be true relative to A’s perspective while ~P is true relative to B’s perspective, even though P ∧ ~P is not true relative to any perspective. Once truth is relativized to perspectives in this way, one cannot simply infer from the fact that P and ~P cannot both be true, that A and B cannot both assert something true. So, it would appear that we can make sense of cases of faultless disagreement after all.

However, recall the grounds for our norm of assertion: the fact that P is correctly asserted iff P is true is to be explained by the identification of asserting P with presenting P as true. Now assume, with the relativist, that both A’s asserting P and B’s asserting ~P are correct, and that this correctness lies in the fact that P is true relative to A, whilst P is false relative to B. In order for this to be the case, we must then think that A’s assertion of P is to be interpreted as presenting P as true relative to A, and likewise B’s asserting ~P as presenting P as false relative to B. Any other interpretation of what A and B are presenting will be inadequate grounds for deriving their respective correctness. But this obviously undermines the claim that Relativism can support faultless disagreement for, if A is presenting P as A-true, and B is presenting ~P as B-true, then they appear to be talking past each other, and not genuinely disagreeing at all.
An example might help bring the point home. Suppose you and I are discussing our favorite foods, and you tell me that “Mushrooms are yum!”, whence I respond “Ugh! How can you eat those things? They’re disgusting!”. Here it appears that we have a genuine disagreement – that both the gastonomic desirability or undesirability of mushrooms are being presented as absolutely true, and that each assertion stands in contradiction to the other. But then you offer a compromise, “Ah, well, what I mean is that mushrooms are yum for me, though I realize they’re disgusting for you“, and I agree to it. Now, upon this interpretation neither of us is incorrect in our original assertions, since we understand each assertion as being presented as relatively true and indeed they are relatively true. However, the price of this mutual correctness is that we no longer disagree over the gastronomic desirability of mushrooms, since in our compromise we have come to see our respective positions as entirely compatible.
Rosenkranz sums up6:

The problem arises because of a certain asymmetry between truth and correctness: whereas propositions are said to be true only relative to a perspective, the correctness of assertions appears to be determined, fully and absolutely, by two interlocking factors: the nature of the relevant assertion as an acknowledgement of P’s being F, and P’s being F. We saw … that even if P is true relative to B’s perspective, this will not yet allow us to speak of the relative correctness of B’s assertion of P as long as that relativity is not reflected in what B presents P as being. But once B is understood to present P as being true relative to his own perspective, his assertion would seem to be correct or incorrect absolutely, depending on whether or not P is true relative to B’s perspective. So even where F-ness is taken to be truth relative to a certain perspective, there seems to be no space left for further relativizing the correctness of an assertion with content.

So it would seem that Relativism is unable to support faultless disagreement any better than Absolutism about truth. Given this is the case, a major motivation behind the view evaporates: a normative toleration in insoluble disputes cannot be achieved by opting for Relativism7.

1 Rosenkranz, ‘Frege, Relativism and Faultless Disagreement’ in Relative Truth (2008), p. 225-37.
2 I take it that all forms of Relativism endorse Truth Relativism. For instance, ethical relativism is a relativism concerning the truth of ethical propositions, and to accommodate this doctrine we adhere to a relativistic conception of truth. The standard way to do this would be let truth be a triadic relation between a proposition, the state of affairs described by the proposition and some further factor, typically a perspective, whereby this last factor is usually irrelevant to truth-values, except in the case of ethical propositions.
3 Such Fregean considerations have historically put pressure on non-cognitivism views, according to which the truth-aptitude of certain sentences is denied. The Frege-Geach problem consists in pointing out that the laws of logic appear to govern the correct assertion of moral sentences (e.g. it is incorrect to say that “Murder is wrong” and “If murder is wrong, then promoting murder is wrong”, but then continue with “However, promoting murder is not wrong”), and that therefore, moral discourse should be understood as factual in nature.
4 Rosenkranz, ‘Frege, Relativism and Faultless Disagreement’ in Relative Truth (2008), p. 227.
5 ibid., p. 228.
6 ibid., p. 232.
7 Rosenkranz doesn’t finish here, going on to argue against the prospect of any solution, but I shan’t follow him in these details.


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