ISSA Proceedings 2006 – Pragmatic Reflexivity In Self-defeating And Self-justifying Expressions

Arguments that rely on reflexive expressions, specifically self-defeating and self-justifying expressions, are far from rare in epistemology. A good example is Siegel’s objection to the epistemological relativist view that knowledge and/or truth or justification is relative to time, place, culture, or a set of non-neutral standards of evaluation. Of the objections to relativism, Siegel says:
… by far the most fundamental is the charge that relativism is self-referentially incoherent or self-refuting, in that defending the doctrine requires one to give it up… relativism precludes the possibility of determining the truth, justificatory status, or more generally the epistemic merit of contentious claims and theses-including itself… if it (relativism) is true (right or justified), the very notion of truth (or of rightness or justifiedness) is undermined, in which case relativism cannot itself be true (right or justified). (Siegel, 2004, p. 747-748)

The reflexivity in this argument lies in the charge that relativism is self-defeating; that it is inconsistent when applied to itself. In this Siegel follows the tradition reaching at least back to Theaetetus, of making that charge against various forms of relativism. Another classic reflexivity based argument is Copi’s argument for the truth of the principle of non-contradiction or (PNC): the principle that states that contradictions cannot be true. Copi’s argument is roughly that the denial of (PNC) is self-defeating. I suspect that Siegel would make the same argument on behalf of (PNC), as well as similar arguments against various forms of naturalism.
Although proponents often regard reflexivity based arguments as clearly valid instances of reductio ad absurdum, those same arguments often have been condemned as wishful thinking and nonsense. What is often missing from the primary debate in which the arguments figure is a recognition that the way a given thesis is self-defeating is not always a purely logical matter. In an effort to shed light on this contentious form of argument, I will clarify the extra-logical features of self-defeating expressions in a proposed definition of self-defeating expressions. I will then apply that definition in an evaluation of various reflexivity based arguments, including the above examples. I will also explain how self-defeating expressions relate to self-justifying expressions.

To begin, it is imperative to clarify how an expression may be self-defeating. Following Peirce’s ‘logical magnifying glass’ strategy, the signature features of self-defeating expressions may be revealed by examining extreme cases.[i] The Liar sentence is one such extreme self-defeater.

(L) This sentence is false.

Because what (L) says is that (L) itself is false, (L) can be true only by being false. The fact that (L) is true only if it is false is sufficient to qualify (L) as self-defeating.[ii] There are some who might object to the claim that the liar sentence as self-defeating. In White’s preferred sense of ‘self-defeating’, for instance, what gets expressed in a self-defeating expression must be false. According to White (L) is neither true nor false and is therefore not self-defeating. Though the claim that (L) is neither true nor false is not uncommon, it is controversial. In any case it is unnecessary to quarrel with the claim that (L) is not false since, even if (L) is not false, (L) is definitely not true. On a more liberal definition, one that does not require falsity, (L) is self-defeating because (L) can be true only by being not true. The exact nature of the non-truth of (L), may thus be left as an open question. Closely related to (L) is another extreme example, (N).

(N) This sentence is false and p.

Unlike (L), it is clearly not the case that (N) is false only if it is true. For perhaps p is false. However, (N) is true only if it is false; and that is enough to be self-defeating. A preliminary sufficient condition for being self-defeating is therefore (P1).

(P1) If ‘s’ is true, then ‘s’ is false.[iii]

That is, if (P1) is true of an expression of ‘s’, then ‘s’ is self-defeating.
Consider now, an extreme self-defeater that is importantly different from both (L) and (N).

(A) p but I do not assert that p.

Unlike (L) or (N), it is not the case that if (A) is true then (A) is false. Thus, (P1) does not capture what it is to be self-defeating at its most general because (A) does not satisfy (P1) even though (A) is self-defeating. Although the way (A) is self-defeating is not by satisfying the condition (P1), that way is not completely different from the way (L) and (N) are self-defeating. Specifically, although it is not the case that (A) is true only if (A) is false, if (A) is asserted by any speaker of English then what the speaker asserts is false, i.e., (A) can be truly asserted only if it is false. What is different is that the self-defeat arises not merely from the logical features of what is expressed but also the expressing. The act of asserting (A) prevents (A) from attaining the status of a true assertion. An assertion of (A) is reflexively inconsistent in the pragmatic sense that the assertion of (A) is inconsistent with what is asserted.

A useful definition of self-defeating expressions must therefore account for the ways in which acts of assertion undermine themselves. It is useful to consider the related case of Moore’s paradox to see that there are different ways the act may figure into an expression’s being self-defeating.

(M) p but I do not believe that p.

Given that the conveyance of a speaker’s beliefs is a goal or end associated with genuine or sincere assertion, the impropriety of the Moore sentences such as (M) can be described in a way similar to the above description of the reflexive inconsistency of (A).[iv] A successful assertion of (M) should convey that the speaker believes that p but according to what is asserted the speaker does not believe that p. (M) fails to be a successful assertion because the successful assertion of (M) is inconsistent with (M) itself.[v] Acts of assertion have conditions by which they are successful in some respect or not. It is not necessary at this point to state the conditions of successful assertion in great detail; it is enough to note that such success conditions concern belief and truth as they figure in the act of assertion. In the case of (A) and (M), those conditions cannot be met without being undermined. The self-destruction of (A) and (M) has its source in pragmatic reflexivity because it concerns features of the act of assertion in addition to logical features of what is asserted.

The above conclusion echoes O’Connor’s distinction between semantic paradox and pragmatic paradox. According to O’Connor the former arises between sign and what it designates whereas the latter “is pragmatic in that it arises from the relations between signs and their users” (O’Connor, 1951). In the case of pragmatic paradox “the conditions of the action are defined in such a way that their publication entails that the action can never be carried out” (O’Connor, 1948). (P2) incorporates the pragmatic element into a sufficient condition for being self-defeating.

(P2) If the assertion of ‘s’ is successful, then the assertion of ‘s’ is a failure.

Both (A) and (M) satisfy (P2) in the way explained above.
Though many pragmatic paradoxes satisfy (P2), it is still too narrow a condition. The problem with (P2) is that not everything that is self-defeating is an assertion. Consider (D).

(D) Do not obey this command.[vi]

The problem is that (P2) does not apply to (D) yet (D) is self-defeating. (D) is not something asserted, it is a command. Nonetheless, if someone commanded (D), their act of commanding would undermine the possibility of being obeyed. So, commanding (D) is self-defeating. To accommodate this example, (P2) needs to be generalized to other expressive acts than assertion. (P3) is the result of such a modification.

(P3) If the relevant use of ‘s’ is successful, then that use of ‘s’ is a failure.

Determining what use is the relevant one is a matter of determining whether the expressive act is an assertion, command, question, or argument, etc. For instance, the relevant use in the above example is the use of (D) as a command. (P3) defines a sense of self-defeating that applies to many different uses of expressions besides assertions.

Although (P3) is very comprehensive insofar as a great many self-defeating expressions satisfy it, it does not explicitly indicate how the reflexivity of (L), (N), (A), (M), and (D) give rise to their self-defeating uses. The fact that uses of these expressions are reflexive, i.e., refer to themselves, is both obvious and necessary in order for the expressions to qualify as self-defeating. For instance, the reason that (P3) is true of a use of (D) as a command is that such a command ensures its own failure. Nonetheless, it is possible that some use of an expression succeeds only if it fails because it fails, perhaps necessarily, in some non-reflexive way. Consider (ILL) which satisfies (P3) without being self-defeating:

(ILL) and the if red.

It is impossible to use (ILL) in a successful command or assertion, and thus any such use of (ILL) is a failure. However, (ILL) is not self-defeating. The final modification, (P4), clearly indicates that it is the pragmatically reflexive nature of self-defeating expressions that makes them self-defeating.

(P4) If the relevant use of ‘s’ is successful, then that use of ‘s’ is a failure on account of the inconsistency of that use of ‘s’ with the conditions of success for that same use of ‘s’.

Though I have not argued that (P4) is necessary for being self-defeating, it is a fairly comprehensive sufficient condition.[vii] Moreover, a precise condition such as (P4) provides the basis for the evaluation of arguments that involve or concern self-defeating and self-justifying expressions.

There are two predominant types arguments in which self-defeating statements play a central role: Arguments to the effect that or for the conclusion that some expression is self-defeating and arguments made from or on the basis of an expression’s being self-defeating. Thus, there are at least two avenues by which the above characterization of self-defeating expressions in terms of pragmatic reflexivity informs the evaluation of arguments. First, by identifying a sufficient and comprehensive condition, (P4) provides an effective test for whether a given expression is in fact self-defeating. Second, the specific content and conditions that satisfy (P4), i.e., how the sort of expression and what is expressed result in reflexive inconsistency, constrain what follows from a particular expression’s being self-defeating and thus what conclusions can be supported by an argument from that self-defeating expression. Though distinct, the two sorts of evaluation may support one another.
(P4) facilitates the assessment of a claim or argument for the conclusion that some expression is self-defeating. If the claim that some expression is self-defeating is based on good reasons for regarding (P4) as true of that expression, i.e., (P4) is true when the suspect expression is substituted for ‘the relevant use of ‘s’’, then there is good reason to regard the expression as self defeating. Since many uses of expressions have more or less well defined success conditions, (P4) can be applied to an alleged self-defeating expression with relative ease.
However, there is an interesting problem case.

(SK) No one knows anything.[viii]

Suppose (SK) is asserted. It is not clear that if the assertion is successful, then it fails on account of the success conditions for that assertion and what is asserted in (SK). For although what is asserted is that no one knows anything, it may be argued that knowledge is not a success condition of assertion. After all, if it were, every successful assertion would be true and it is obvious that there are successful assertions of falsehoods. This case is problematic not because it is a counterexample to (P4), though it has been proposed as such, but because it may not be clear under what specific success conditions (P4) is to be applied.

There are at least two ways in which (P4) may be applied to (SK) such that it turns out to be self-defeating. First, although knowledge of what is asserted may not be a success condition of assertion, some knowledge of how to make assertions surely is. One obvious success condition of assertion is that one have some knowledge of how to make assertions. Thus some knowledge is required for the success of an assertion of (SK) and it is this condition that is inconsistent with what is so asserted by (SK). Another point is that there is a clear inconsistency between what is asserted by (SK) and knowledge that (SK). If (SK) is true, then it is unknowable. Thus, (SK) is self-defeating when used in any act whose success conditions include the possibility of knowing (SK). Perhaps assertion in general has knowability as a success condition but perhaps not. On the other hand many important epistemic acts clearly do have knowability as a success condition, such as learning and explaining. For these acts (SK) is indeed self-defeating.

There is an additional way in which an argument may concern self-defeating expressions: namely by being one. A self-defeating argument is not the same as an argument either based on the claim or to the effect that some expression is self-defeating. Moreover, a self-defeating argument is different from other expressions that are self-defeating, such as self-defeating assertions, insofar as it is a different kind of act. To determine whether an argument is self-defeating, (P4) may be applied to the use of the argument as a whole. For example, the use of the following set of statements (IMP) as an argument is pragmatic reflexive inconsistent because (P4) is true of such a use.

(IMP)
1. If this argument is invalid, then Modus Ponens is invalid.
2. This argument is invalid.
Therefore, Modus Ponens is invalid.

Since one of the conditions for successful use of this argument is that it validly support or establish its conclusion, which in this case is that the argument itself is invalid, the argument succeeds only if fails. If a use of (IMP) as an argument is successful, then that argument fails on account of the inconsistency of that use of (IMP) with the success conditions of so arguing. In this way (P4) may be applied directly to complex acts including arguing.
Since (P4) is only a sufficient condition for being self-defeating, the fact that a given expression does not satisfy (P4) does not by itself undermine the claim that it is self-defeating. Even if (P4) is false for a given expression, it is possible that the expression is self-defeating nonetheless. Of course any such accusations of self-defeat must still be based on some reason even if it is not (P4). In any case, the sufficiency of (P4) provides enough of a test to address the second type of evaluation.

The characterization of self-defeating expressions in terms of (P4) allows for the evaluation of the arguments from self-defeating expressions. Here is the argument for the principle of non-contradiction (PNC) from its self-defeating denial in more detail. If one denies (PNC), it could be true that both (PNC) and not (PNC). But if both (PNC) and not (PNC) could be true, one has not denied that (PNC). In denying the law of contradiction one undermines that very same denial. (In the form of (P4): if the denial of (PNC) is successful, then it fails.) Therefore, (PNC), i.e., necessarily, contradictions are false. Such an argument for (PNC) is the model of rationalistic proofs favored by Siegel, Copi, and others and derided by Ebersole and Stack.[ix] The general strategy is to argue that an expression is self-defeating in such a way that entails the desired conclusion. Usually most of the argument is left implicit or is cast as an objection that a thesis is self-defeating. The common form of arguments based on self-defeating expressions is thus as follows.

(Form)
1. That some specific use of ‘s’ is self-defeating entails T.
2. That specified use of ‘s’ is self-defeating.
Therefore, T.

Though rarely stated so explicitly, the merits of the arguments that have this form depend upon the unstated assumption (1). What is entailed by an expression’s being self-defeating, i.e., the truth of (1), depends on how the expression is self-defeating.

When the self-defeating is purely logical the argument is a reductio ad absurdum of what the self-defeating expression expresses. Reflexive inconsistency that is due exclusively to the semantic or syntactic properties of what is expressed entails the negation of what the logical self-defeater expresses. Logical reflexive inconsistency is logical inconsistency. Assuming classical propositional logic: logical inconsistency implies falsity and falsity entails the truth of the negation. Thus, given that the reflexive inconsistency of (N) is purely logical, then an instance of (Form) in terms of (N) is a good argument for not-(N). Of course, not-(N) is a relatively uninteresting conclusion. A likely explanation for the usual implicitness of (1) is that where ‘T’ is the negation of ‘s’ and ‘s’ is logically reflexive inconsistent, as is the case with (N), (1) is a logical truth.
When the self-defeating is not purely logical the assumption of (1) is more significant and the argument is not a reductio ad absurdum. If (2) is true because the expression is pragmatic reflexive inconsistent, then the merit of the argument depends entirely on what is entailed by that pragmatic reflexive inconsistency. What is entailed largely depends on the specifics of the pragmatic reflexivity, i.e., the success conditions of the relevant expressive act along with the semantic and syntactic properties of what is so expressed.
Optimists about this sort of argument would be mistaken to assume without argument an entailment of the favored conclusion T from the mere fact that an expression s is self-defeating. In order for the arguments to carry any weight it must be determined how the expression is self-defeating. The relevant connection between the way in which the expression is self-defeating (e.g., some specific success conditions that figure in pragmatic reflexive inconsistency) and the content of the conclusion, T, must be accurately specified in (1). Otherwise, very little can be concluded beyond the fact, if it is a fact, that the expression is self-defeating.

Although it is often difficult to determine the connection that would make the arguments work, it cannot be assumed without argument that there is no such connection. Pessimists as much as optimists about a given argument from a self-defeating expression must specify the needed connection as well as argue that it does not hold. Not surprisingly, if one assumes that there is no relevant connection between the success conditions for denial and (PNC) or that the connection is not what it must be, one will find the argument for (PNC) worthless. Stack (1983), for instance, regards such arguments as a contemptible means of avoiding a reductio ad absurdum of some cherished belief, in this case the belief that a certain logical law holds. According to his line of criticism, if the principle of non-contradiction leads to the absurdity of denying that one is denying it as in the simple example argument above, then not only is it not a proof of (PNC) it shows that there is something suspect about it.

Logic is then reduced, it self-destructs, it is shown to be internally incoherent. We use logic to discover this of logic. But this does not mean that logic is necessary. (Stack 1983, p. 334)

According to Stack, the fact that the denial of (PNC) is self-defeating does not entail (PNC), but rather that (PNC) is false. If true, this would amount to a serious objection to the rationalist proof of the logical laws of which the argument for (PNC) is a representative example. Moreover, to his credit, Stack does not assume that there is no connection between the self-defeating and the conclusion of the optimist’s argument; he holds that former entails the denial of the latter. However, he does not offer any argument that I can find for this connection. Thus, his objection to the argument is inconclusive.

(P4) along with (Form) model the structure of the standard arguments from self-defeating expressions.[x] This model indicates what must be the case for a use of the argument to be sound, namely that (P4) be satisfied in such a way that (1) is true. In the case of the argument for (PNC), the soundness of that argument depends upon the relation between (PNC) and the act of denial. Suppose, that the act of denial consists partially in the correct application of the logical laws associated with negation such as (PNC). In that case, not only is the pragmatic reflexive inconsistency of denying (PNC) assured but the argument to be made for (PNC) itself is thereby considerably stronger. This is because the supposition about what constitutes the act of denial guarantees that any successful denial entails that (PNC) is true. Thus, the supposition indicates the truth of premise (1) when the argument is cast as an instance of (Form) so that the successful denial of (PNC) entails (PNC). The question then is whether the supposition is true. I am inclined to think it is if for no other reason than we need to distinguish denial from agreement. On the other hand, even if a good case could be made against the supposition, my immediate point is just that such a connection would have to be articulated if the argument or the objection to it is to be any good.
Roughly the same points may be made on behalf of Siegel’s argument against relativism. Suppose the act of defending a theory is partially constituted by the application of neutral standards of evaluation that are not relative to time, place, or culture. In that case, (P4) is satisfied for any defense of relativism and is therefore self-defeating. Now if we cast T in (Form) as the negation of relativism, then (1) is true. This is because the supposition about what constitutes the act of defending a theory guarantees that any successful defense entails the denial of relativism. Not only is the supposition plausible, similar suppositions about the acts of propounding, articulating, and teaching theories are all just as plausible. As long as the argument against relativism pertains to these acts, it is deadly.

All of this illustrates the general point: that some very important epistemological arguments turn out to depend on pragmatic rather than semantic or syntactic considerations. Here is an explanation of that point. Epistemology is the study of knowledge and acts that concern it such as inquiring, learning, teaching, etc. Also, epistemology is itself an inquiry and presumably an act of knowledge acquisition. Thus, epistemology is peculiarly reflexive in that it is essentially the very same kind of epistemic act that it purports to be an inquiry into. Thus a great many epistemological theories turn out to be pragmatically reflexive. Moreover, inconsistencies that arise from such pragmatic reflexivity do carry argumentative force in epistemology insofar as the success of epistemic acts entails that certain epistemic conditions hold. I have argued that some of Copi and Siegel’s arguments are actually supported by pragmatic considerations. I have also provided the support for an argument against skepticism in my argument that (P4) holds for (SK), though that support is limited.
It is interesting to note that when an argument from or based on reflexive inconsistency is successful it shows that its conclusion is a self-justifying claim[xi] More precisely, a claim that is supported by an argument from the reflexive inconsistency of its negation is a self-justified claim, in the relevant pragmatic or logical sense. So, if the example argument for (PNC) is correct, then (PNC) may be said to be self-justifying. If Siegel is correct, some form of epistemological absolutism is self-justifying. If my arguments for (SK) being self-defeating are correct, then some form of anti-skepticism is self-justifying. Provided that they are successful, which means at least supporting (1) and (2) of (Form), arguments made on the basis of self-defeating expressions establish self-justifying conclusions.
Like self-defeating arguments, self-justifying arguments are distinct both from other kinds of self-justifying expressions and the arguments for them. A self-justifying claim or assertion is different from a self-justifying argument in the same way that self-defeating assertion is different from a self-defeating argument. This difference is a difference in the kind of act. Self-justifying arguments are also not to be confused with those arguments that purport to show that some claim is self-justifying. As explained above, arguments for self-justifying conclusions are based on their self-defeating negations. Self-justifying arguments, on the other hand, are reflexive with respect to their use as an argument. As such, self-justifying arguments and self-defeating arguments such as (IMP) involve the same kind of act. The difference is that only the latter are reflexively inconsistent. For self-justifying arguments are reflexively consistent in both the logical and pragmatic sense. A self-justifying argument is one whose successful use supports rather than undermines that very use. The following set of statements (C) can be so used in a self-justifying argument.

To summarize these points about self-justification: a self-justifying argument, like a self-defeating argument and unlike a self-justifying claim or assertion, is reflexive with respect to its use as an argument. There are arguments for self-justifying claims but these are not self-justifying arguments. Rather they are based on the reflexive inconsistency of the negation of their conclusion. An argument from a self-defeating claim is an argument for a self-justifying claim.

I will conclude with a restatement of the major points of this paper. In the first section I proposed a useful definition of ‘self-defeating’. The proposed definition (P4) is not perfect but has the following redeeming features. It is a sufficient and fairly comprehensive condition for being self-defeating and it illuminates both the pragmatic as well as the logical features of self-defeating expressions. The notion of pragmatic reflexive inconsistency articulated in the proposed definition proved useful in the evaluation of arguments that involve self-defeating expressions. Arguments could involve self-defeating expressions in at least three distinct ways and the notion of pragmatic reflexivity helps to explain each of these three. First, there are arguments to the effect that some expression is self-defeating. The evaluation of such arguments facilitated by the precision of the proposed definition (P4). Second, there are arguments that concern self-defeating expressions in none other way than by being self-defeating arguments. I explained such arguments in terms of the general concept of pragmatic reflexive inconsistency and demonstrated how (P4) applies to such complex expressive acts as argumentation. Finally, there are arguments that purport to establish some conclusion on the basis of some expression’s being self-defeating. Arguments of this type are very important to epistemology and ultimately depend on pragmatic considerations about various epistemic acts such as denying, defending, propounding, inquiring into, and teaching, etc. I argued that because epistemology is the study of such acts and yet must also perform those acts, epistemology has an inescapable dependence on pragmatic reflexivity.

NOTES
[i] C.S. Peirce sought to uncover the important features of assertion by examining extreme or magnified instances of assertion such as oaths. This is the strategy of the logical magnifying glass that I follow here. See The Collected Papers of C. S. Peirce 5.546. Hilpinen (1998) is a detailed account of Peirce’s logical methodology and resultant theory of assertion.
[ii] Since (L) is false only if it is true as well, (L) is perhaps self-justifying as well as self defeating. As I discuss in connection with White’s definition, this may rule (L) out as purely self-defeating but it will still count as self-defeating on my attempted, more inclusive, definition. I will discuss the relation between self-justification and self-defeat in more at the end.
[iii] It may be observed that a material conditional reading of (P1) threatens to reduce the proposed definition to the condition that ‘s’ is false. Since this would make mere falsity a sufficient condition, such a reduction would ruin any hope of a definition of self-defeating expressions. I thank Michael Shaffer for forcefully making this point at the 2006 ISSA Conference on Argumentation. I intend the conditional in this and subsequent definitions to be read non-materially. However, I cannot here defend a specific semantic account of counterfactuals or normal conditionals etc., since it is beyond the scope of this paper to address all the issues that arise for such conditionals.
[iv] Instead of putting the matter in terms of goals I could just as well describe the same point about assertion in terms of rules, e.g., successful assertions are those that conform to the rule: assert only what you (the assertor) believe. I use the formulation in terms of goals in a neutral way.
[v] I realize that even if one allows that assertions of (M) entail that the speaker believes that (M) other, more controversial principles concerning belief must be assumed to derive a contradiction. These include at least a principle of distribution of belief for believed conjunctions and some principle concerning the iteration of belief. I ignore those issues here because I am only concerned to point out the necessity of referring to the connection between belief and the act of assertion, i.e., that it must be assumed that an assertion of (M) conveys belief that (M) in any explanation of the impropriety of such an assertion.
[vi] Michael Veber, in conversation, came up with this example in a more realistic but less obvious form: “Don’t take my advice.”
[vii] It should also be noted that my definition of pragmatic reflexive inconsistency in terms of (P4) is consistent with the recent work of Ingvar Johanssen. Johanssen (2003) provides a detailed explanation of, not just semantic and pragmatic self-defeaters, but of various sub-types of the pragmatic variety. In particular, he makes a distinction between performative contradictions, which are self-defeating on account of the content of a given use of an expression and its conditions of success, and anti-performatives, which are self defeating on account of what is shown by a given use of an expression and its conditions of success. For example (A), above, is an example of a performative contradiction whereas (H) and (!) below, are anti-performatives.
(H) I’m always very humble.
(!) I never raise my voice! (Yelled at audience)
According to (P4), both (H) and (!) are pragmatic reflexive inconsistent, even though such expressions differ from (A) in the way indicated by Johanssen. I will not pursue Johanssen’s classification any further than noting that my analysis in terms of (P4) leaves open the possibility of further distinctions among types of pragmatic reflexive inconsistency. The points I make will be relevant to both the performative and anti-performative types of pragmatic reflexive inconsistency.
[viii] I owe this example to a fruitful discussion with Kirk Ludwig at the 2005 meeting of the Florida Philosophical Association. Ebersole also argued that this example shows a shortfall in the notion of pragmatic paradox defended by O’Connor.
[ix] The argument against Protagorean relativism gleaned from Plato’s Theaetetus and Descartes “Cogito” argument are perhaps the most well-known historical examples of arguments from self-defeating expressions. For one other, more recent example see: Bonjour(1998), for the objective epistemic value of a priori justification.
[x] (P4) together with (Form) model the structure of arguments like Siegel’s argument against relativism. Harvey Siegel’s agile and prolific use of this form of argument is not only a large part of the impetus for this paper but is also the source of the use of the term ‘harvpoon’ as a general name for that type argument.
[xi] The notion of self-justification I discuss is not very robust: I simply mean that the expression contains the resources for its own support.

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