Paradox and Relativism
H. Muhammad Legenhausen
Professor of philosophy, The Imam Khomeini Education and Research Institute, Qom
First Published in: University of Tabriz- Iran, Philosophical Investigations
Vol. 11/ No. 21/ Fall & Winter 2017


Since the time of Plato, relativism has been attacked as a self-refuting theory. Today, there are two basic kinds of argument that are used to show that global relativism is logically incoherent: first, a direct descendent of the argument Plato uses against Protagoras, called the peritrope; and, second, a more recent argument that relativism leads to an infinite regress. Although some relativist theories may be formulated in such a way as to be susceptible to these arguments, there are other versions of relativism that are impervious to these charges of incoherence.

First the arguments against relativism will be stated. Next, a radical form of global relativism with assessment sensitivity is introduced, RR. Finally, it is shown how RR can be defended against the challenges of the peritrope and the regress. No attempt is made to defend RR as a plausible theory; however, the usual attempts to show the logical incoherence of radical forms of global relativism fail.

Keywords: Relativism, Paradox, peritrope, infinite regress, global relativism, Plato


In the Theatetus, Plato has Socrates refute the relativism of Protagoras. The argument is convoluted, and has been judged to be flawed by several commentators. In a justly famous reconstruction and defense of the Platonic argument against relativism, Miles Burnyeat (Burnyeat 1976) argues that the self-refutation argument (dubbed the peritrope by Sextus Empiricus) must be completed by a regress argument. In order to escape self-refutation, the relativist is forced into endless qualifications of his assertions as being true for him, and the thus qualified assertions are still only true for him, and likewise the doubly qualified assertions require further qualification without end. (Also see (Fine 2003), 194, where it is argued that although there is a regress argument that can be made against the position Plato attributes to Protagoras, that position is not global relativism, but infallibility.)

While Burnyeat sees the regress argument as constituting an essential, if only implicit, part of the self-refutation argument, others have claimed that relativism is susceptible to two independent challenges, one based on self- refutation and the other on an infinite regress.

Paul Boghossian provides a more recent rejection of relativism that considers both the self-refutation argument and the regress argument. Boghossian agrees with the traditional objection to relativism, that is, that it is incoherent; but he admits that the self-refutation argument is inconclusive. Instead, he charges relativism with absurdity because of the infinite regress to which it leads: “…it is absurd to propose that, in order for our utterances to have any prospect of being true, what we must mean by them are infinitary propositions that we could neither express nor understand.” (Boghossian 2006, 56).

Other writers seem to concur with Boghossian that variations on the original turning of the tables against Protagoras does not quite clinch the argument (Fine 1998) and (Fine 2003). This leads many to suppose that the best strategy against relativism is to use some version of the regress argument; and, furthermore, many of these same writers explicitly state that their favored version of the regress argument shows that something goes wrong with assertion when relativism is accepted. A version of the regress argument against relativism seems to motivate Nagel’s insistence on unqualified beliefs and assertions in (Nagel 1997). A more explicit regress argument is used against the relativist in (Williamson 2015, 29).

To this charge, one might respond that what is needed is a relativistic theory of assertion. This is exactly the response given by John MacFarlane:

Boghossian’s relativist takes a speaker who utters “snow is white” to have asserted that according to her world-theory, snow is white. But the relativist need not, and should not, hold that to put p forward as true for oneself is to put forward the claim that p is true for oneself. The point of “for oneself” is not to characterize the content that is asserted, but to characterize what the relativist is doing in making her assertion: putting its content forward as true for herself. (MacFarlane 2014, 33).

By shifting from content to force, from what one is saying to what one is doing in a speech act, the regress in the analysis of content is avoided. The shift away from content relativism also enables MacFarlane to respond to another common objection to relativism: the charge that relativism makes disagreement impossible because there is no common content about which parties disagree.

A number of explanations have been offered show how disagreement retains its depth even when truth or assertion is taken to be relative to the contexts of assertion and assessment. Here, we restrict ourselves to few points about disagreement that will be useful when we consider how some varieties of radical relativism are immune from the peritrope and the regress arguments.

First, MacFarlane distinguishes a number of different forms that disagreement can take that fall short of objective contradiction (MacFarlane 2014), Ch. 6. Karl Schafer builds on MacFarlane’s work by considering aims of assertion and aims of conversation that can shape the norms governing speech acts and forms of discourse in various contexts (Schafer 2012).

Finally, Lionel Shapiro considers how norms of assertion and retraction are governed by assumptions about the views of one’s conversation partners (Shapiro 2014). All three writers, MacFarlane, Schafer, and Shapiro, defend forms of relativism that relativize truth or assertion to contexts of utterance and contexts of assessment. All three avoid relativism about content as found in indexical contextualism. MacFarlane and Shafer focus on non-monadic truth, that is, truth relative to a context of utterance and a context of assessment, while Shapiro considers how the norms governing assertion are relative to contexts of utterance and assessment regardless of one’s position on non-monadic truth. In what follows, by relativism (unless otherwise indicated), I will mean some such form of assessment relativism. Later we will consider an implausibly radical version of relativism, RR.

Most relativists moderate their relativism along two lines: (1) relativism is restricted to some specific areas of discourse, e.g., normative discourse; and

(2) perspectives or conceptual frameworks are restricted to those that are coherent, although accounts of coherence vary. Contemporary assessment relativism emerges as a hypothesis to explain the norms governing various types of discourse. There is no a priori defense of a relativism that applies to all statements.

The first of the above lines of moderation is sometimes discussed as a move from global to local relativism. This distinction is not sufficient to remove all ambiguity. One might be a global relativist in the sense that one holds that all areas of discourse are governed by norms that are sensitive to contexts, but deny that these norms yield results that would differ from non- relative ones for some of the assertions made in any given area. Let’s say that relativism is global when it covers all areas of discourse and that it is general when, in a given area of discourse, it holds that all assertions or their truth are governed by context sensitive norms or conditions.

Although the empirical basis of inferentialism would be receptive neither to global relativism nor to a completely general local relativism, if the peritrope or the regress argument are to have a chance at refuting relativism,

it would be best to take relativism to be both global and general. So, even if contemporary relativists tend to favor some moderate form of relativism that is neither global nor general, we should begin with global general relativism in order to examine the logical point that there is something about the doctrine that causes it to defeat itself or to metastasize (Swoyer 2014) through some sort of infinite regress.

There two more ways in which relativism might be moderated to avoid the peritrope and regress. First, sensitivity to a context or being relative to a perspective can be given two interpretations. Global relativism can only be self-refuting if it adheres to what I will call context contingency:

The Context Contingency Thesis (CCT): For all propositions, p, p is true relative some contexts and is false for others. (Compare Kölbel’s (GR) in (Kölbel 2011, 21.)

CCT is formulated here for global general relativism. Restrictions could be placed on the universal quantifier to generate forms of CCT for local and non-general forms of relativism. CCT is to be distinguished from the claim that truth is not monadic because the parameters relative to which propositions are true or false must be taken into consideration. Context dependency may be defined as follows:

The Context Dependency Thesis (CDT): For all propositions, p, p is true only with respect to parameters.

CDT denies that truth is monadic, that is, it denies that it is proper to claim that p is true. One can only say that p is true relative to some parameters or contexts. CDT does not imply CCT, for even if truth is relative to contexts, the contexts might be such that for some range of propositions, those propositions are true relative to all possible contexts of utterance and assessment.

The most plausible forms of relativism will be local and will not be general. However, for the sake of investigating the logical point of whether relativism is a self-defeating position and whether it involves a vicious regress, we will define radical relativism, RR, to be global and general. Relativisms that endorse CCT are also implausible; but, again, for the sake of argument, we will stipulate that RR endorses CCT. This is a very extreme form of relativism, and one that is not defended by even the most strident cultural relativists, and would certainly be dismissed immediately by those who seek to find evidence in linguistic practices for any sort of relativism, whether a kind of contextualism or a kind of assessment sensitivity. If the peritrope and the regress argument have a chance of refuting relativism, they should be able to refute this sort of radical relativism.

Finally, some writers consider it an essential feature of relativism that all contexts are equal. They hold that it is inconsistent with the entire tradition of moral relativism, for example, to hold that some moral perspectives are morally preferable to others. Contexts should be “metaphysically on a par” (Coliva and Moruzzi 2012, 57). Max Kölbel writes: “Again, privileging some perspectives … goes against the basic commitments of the relativist.” (Kölbel 2011, 23). This is highly disputable; and it is precisely this disputable point that allows RR to be defended against the peritrope and the regress.

A common error made by many critics of relativism is that they assume that any privileging of perspectives is inconsistent with relativism. Once we understand how rankings of perspectives can be accommodated by even very radical relativists, such as those who might propound RR, it is not difficult to see how the charges of self-refutation and infinite regress can be deflected.

If one’s moral relativism is general, and one affirms a context sensitive form of relativism, like that of MacFarlane, then assertions about the relative moral worth of different perspectives will be true or false only relative to a context of utterance and a context of assessment. There is nothing inconsistent with relativism about taking contexts or perspectives to be metaphysically or morally differentiated as long as the propositions through which the ranking is asserted are considered to be relatively true. What goes against the basic commitments of the relativist is the assignment of an absolute ranking to give some perspectives a privilege, not rankings relative to perspectives.

Indeed, the claim that all contexts are absolutely equal, that is, that they are equal independent of any context, would be no less against the basic commitments of the general relativist than an absolute ranking, for the general relativist holds that any claim can only be true relative to some contexts, regardless whether the claim is used to assert the privilege of some perspectives or their equality. Under normal circumstances, beliefs are accepted and assertions are made from a context of assessment in which the assessor assumes her own perspective to be privileged. Indeed, without the privileging by the assessor of the context of assessment over the context of utterance, there could be no rationale for retraction of past assertions; and assessment sensitive relativism is founded on observations about norms of retraction. (MacFarlane 2014, 13, 108).

The key to MacFarlane’s assessment sensitivity theory is that all perspectives are not treated as equals. Contexts of assessment trump contexts of assertion. Shapiro shows that assessment relativism can be seen as holding an intermediate position between absolutism and indexical contextualism. The absolutist position is that whatever is true from one perspective must be true from all perspectives. The indexical contextualist holds that truth from any given perspective is irrelevant to truth from another. Assessment relativism holds that the norms governing assertion determine that assertions have a force that is directed toward a select range of possible contexts of assessment. T

he relation between a context of assertion and a context of assessment toward which the assertion is directed, R, can be used in a manner analogous to the accessibility relation between possible worlds familiar from Kripke’s semantics for modal logic. Steven Hales has shown that the peritrope can be wielded against radical forms of relativism in which R is reflexive, symmetrical, and transitive, as in S5. (See (Hales 1997) and the discussion in (MacFarlane 2014, 30.) Our relation R, however, need not be symmetrical or transitive (and one might even contemplate non-reflexive contexts of assertion). Hence, the peritrope will fail when directed against assessment sensitivity theories, even when such theories are coupled with extremely radical forms of relativism, like RR.

As for the regress argument, this depends upon the need to qualify one’s assertions, with the assumption that without such qualifications they must be absolute. What Shapiro shows, however, is that unqualified assertions can be understood as having a limited scope of direction that is given implicitly through the context of the conversation in which the assertion is made and the norms governing assertion and retraction relative to that context. Endless qualifications are unnecessary because the norms governing assertion and assessment are implicit in their own contexts.


Boghossian, Paul. 2006. Fear of Knowledge: Against Relativism and Constructivism. Oxford: Oxford University Press.

Burnyeat, M. F. 1976. “Protagoras and Self-Refutation in Plato's Theatetus.” The Philosophical Review 85(2):172-195.

Coliva, Annalisa and Sebastiano Moruzzi. 2012. “Truth Relativists Can't Trump Moral Progress.” Analytic Philosophy 53(1):48-57.

Fine, Gail 1998. “Relativism and Self-Refutation: Plato, Protagoras, and Burnyeat.” Pp. 137-164 in Method in Ancient Philosophy, edited by Jyl Gentzler. Oxford: Oxford University Press.

Fine, Gail. 2003. Plato on Knowledge and Forms. Oxford: Oxford University Press.

Hales, Steven D. 1997. “A Consistent Relativism.” Mind 106(421):33-52

Kölbel, Max 2011. “Global Relativism and Self-Refutation.” Pp. 11-30 in A Companion to Relativism, edited by Steven D. Hales. Chichester: Wiley- Blackwell.

MacFarlane, John. 2014. Assessment Sensitivity: Relative Truth and Its Applications. Oxford: Oxford University Press.

Nagel, Thomas. 1997. The Last Word. Oxford and New York: Oxford University Press.

Schafer, Karl. 2012. “Assessor Relativism and the Problem of Moral Disagreement.” The Southern Journal of Philosophy 50(4):602-620.

Shapiro, Lionel. 2014. “Assertoric Force Perspectivalism: Relativism without Relative Truth.” Ergo 1(6):139-168.

Swoyer, Chris. 2014. “Relativism” The Stanford Encylopedia of Philosophy. Retrieved April 19, 2015 (

Williamson, Timothy. 2015. Tetralog. Oxford: Oxford University Press.