A System for Analyzing the Problem of the Criterion
An introduction in epistemological justification is best served by inquiry based on basic assumptions about knowledge. The first question should be explanatory: 1) What is the problem of the criterion? I will systematize this problem with a sequence of statements below but the criterion can be provisionally answered in two parts: 1.a) The criterion is a justification of knowledge, and 1.b) The problem is determining that criteria. This problem has been pejoratively referred to as "the diallelus" or the problem of "the wheel" or (quite negatively) the "vicious cycle" [1], but I am not necessarily discussing the problem of self-refutation, the BIV paradox, or other variants stigmatized for dogmatic skeptics.
In the systemization of epistemology that I adopt from Steup [2], the criteria is analogous to a method; it is a theory of justification where the method justifies how we know what we know, and that justification theory is itself a theory of knowledge. Although Steup seems to define these terms via some dependency hierarchy, as may be the case for foundationalism, and although I characterize the criterion as methodical, the problem of the criterion has not been, I expect, exhausted by coherentism or particularism. Others classify the criteria as second-order knowledge, or meta-knowledge; and, although this classification better depicts the scope of the problem in general, the system I develop below applies this theory to argumentation, i.e. debate. My application of the criterion, however, yields light on theories for justifying other fields, including science and mathematics.
What I mean by applicable might better be understood by analogy. Take philosophic discussions as examples (including this writer-reader discussion). There seem to be perennial disagreements concerning claims to truth and strength of arguments, and these disagreements appear as verbal conversations, threads posted to online boards, letters of correspondence, etc. I characterize these discussions by the object of their statements, namely, certainty (of truth) and necessity (of form) given by the following disagreements:
α) Advocate A claims that proposition p is true but advocate B claims that p is obviously not true.
β) Advocate A claims that his argument for believing p is stronger than advocate B's (obviously weaker) argument for believing the same proposition p, and vice versa.
Although these generalizations differ with respect to their objects, where the object of (α) is the truth of p while the object of (β) is the argument for believing p, both describe a disagreement nonetheless. They are variations of a theme that narrow the scope of the problem from meta-knowledge to an instance of the problem, namely, philosophic discussions. Thus a discussion is the context of the problem of the criterion in this essay and determines its relevant solutions. Similar disagreements can be found in science and mathematics but I merely make inference to the implications on those fields.
Parameters for Reasonably Solving Problems
The first solution to this problem is trivial: ~1) The problem of the criterion is not a problem. This answer is problematic and will be discussed in the "Answers" section below. For now, lets move forward with a variation of (~1) by a redefinition of the original that follows Carnap's system: 1') The problem of the criterion is a pseudoproblem. [3] To determine whether (1') or even any answer, such as (~1), can actually solve the problem of the criterion, I think Robert Amico judiciously provides parameters within which we can reasonably discuss problems.
Amico identifies relationships between problem-solution and question-answer pairs that he calls “pragmatic presuppositions”, and he defines these. [4] He does not describe every possible relationship or meaning but his framework is reasonable and relevant to discussions so I will extend them contextually and codify them with the label: AmicoVapor's "Parameters for Reasonably Solving Problems" (because "AmicoVapor" sounds like something went wrong at the gas station):
Ω) a problem includes a set of questions, although a problem need not only contain questions because it may include statements that clarify the question(s), i.e. questions are a necessary condition for a problem;
Ψ) a question is not declarative (and exempts rhetorical questions) and cannot be assigned a meaningful truth-value
Φ) a solution is a set of answers; a solution set contains no unanswered questions, i.e. answers are necessary and sufficient conditions for a solution
Π) an answer is declarative and can be assigned truth(-value(s))
Φ is the parameter for determining certainty and has important implications for problems of necessary truth. To illustrate these parameters, consider the comparison of two similar sentences:
p: Knowledge is possible.
q: Is knowledge possible?
Given these parameters, there are no answers that solve p because p is declarative statement, so p is the answer. There are answers that solve q because q is a question, or inquisitive statement, and a solution set with at least one answer can be found because of two corollary parameters:
Δ) a problem has one and only one solution
Γ) for every answer given as a solution, each answer must be relevant to a question contained in the problem
Γ is the parameter for determining meaning, including the definitions of necessity and certainty, and it has important implications for the problem of the criterion. Relevancy is a synthetic test for the question-answer relationship and it follows the analytic test of the problem-solution relationship. The synthetic test is semantic but not trivial; its ambiguity in the abstract will be determined when applied to the discussions below. All these parameters codify an analytic approach to philosophy of the kind that mathematicians and physicists are accustomed to, and it prevents us from assigning truth values to statements that do not solve the problem.
Some may foresee these parameters as "setting ourselves up for failure" by precluding us from solving the problem of the criterion. I will admit that this is one of Chisholm's criticisms, but the argument behind this foresight may be weaker than the insidiousness of the problem, and would itself be a problem solved via some criteria [5]. I adopt these parameters because Amico's intention is the same as mine: a solution to the problem of the criterion would dissolve the problem. [6]
The Sextus System
Plato discussed a version of the problem of the criterion [7] and Carnap illuded to it [8] but Sextus Empiricus is credited for writing the original version so I will systematize Amico's interpretation of him [9]. The Sextus System (SS), as I like to call it, intends to extract different consequences of disagreeing based on the arguments and criteria used by the advocates during a discussion. Let us imagine that Sextus watches a thread from an online philosophy community or hears the oral arguments in a Supreme Court case, and he observes a disagreement in the form (α) or (β) from above:
3) Advocate A seems to judge proposition p differently than advocate B
3*) Advocate B seems to judge proposition p differently than advocate A
Sextus rationally doubts the object of the disagreement, p:
RD) observer X rationally doubts proposition p because X is more justified in withholding belief of p than affirming or denying p, i.e. X disbelieves neither p nor p's negation
This kind of doubt is based on Sextus' concept of "equipollent" judgments and is a concept that I think Amico interprets correctly but one that Chisholm misinterprets. [10] RD is not defined as ~(p ∨ ~p), as Chisholm would have us believe, because his (mis)interpretation is irrational by the definition of non-contradiction [11]. Rather, RD is ~~(p ∨ ~p) where the truth of RD has yet been asserted (and is indeterminate, as is the case for 3-valued logics; see Susan Haack below). Others call this their "suspension of (dis)belief" and in this way I understand Sextus is using a passive tool for observing the discussion. This is an important feature of the SS system because it squelches premature accusations that rational doubt is actually claiming truth in disblief and therefore irrational.
Sextus continues observing the discussion using my system; it is a closed system yet describes 16 possible discussions (two advocates of a four argument form, i.e. 24). I skip some trivial discussions to avoid sounding redundant; only two are fundamental to understanding the problem. For example, if advocate A and B seem to judge the proposition p the same using the same argument P, an argument which is justified by the same criteria ƒ, then obviously there is no problem. This example is, what I call, total agreement (Discussion I). The further from agreement the advocates are, the more important our observations.
Discussion III
4) Advocate A judges the truth of p by argument P
5) Advocate A justifies argument P by criteria ƒ
4*) Advocate B judges the truth of p by argument O
5*) Advocate B justifies her argument O by the same criteria ƒ
This kind of disagreement is one that the advocates should be able to (eventually) solve. This is not a problem of the criterion because the same criteria ƒ is used; this disagreement is a problem of argumentation (P versus O) and adjudication of p. I should note the there is also no problem for advocates of the primitive (α) and (β) who, without justification, merely claim that the proposition is true. The system accounts for this via exemption when we say advocate A or B is unreasonable and trivially refutable. However, unjustified true beliefs, or even propositions advocated with neither certainty nor necessity, have serious implications for theories of knowledge (as I reiterate later).
Now let us hypothesize that advocates A and B return to the discussion with their respective criteria and propositions that had previously supported some agreements in previous discussions (I-IV). Assume criteria g had been originally used by advocate B, and A had previously agreed with its justification. (This swapping of criteria and propositions is clarified by gender: A is a guy and B is a girl):
Discussion XIV
4') Advocate A judges the truth of p by her argument O
5') Advocate A justifies her argument O by her criteria g
4'*) Advocate B judges the truth of p by his argument P
5'*) Advocate B justifies his argument P but by his criteria ƒ
This kind is of disagreement seems insoluble. Each advocate judges the truth of p based on the opposing advocate's argument and criteria, yet these lead to an opposite adjudication of p! Line (5'*) is the most extreme catalyst for the problem of the criterion. Next, Sextus observes advocate A and B continuing their discussion with the intentions of definitively discrediting their opposition by vindicating their adjudication of p. (I skip advocate B's lines below because they are merely the converse of A's, as demonstrated above by (3-5)*):
Type I
6) Advocate A judges the truth of proposition ƒ by argument F
5) Advocate A justifies argument F by the same criteria ƒ
This is a Type I problem of the criterion or, what I call, the question of a necessary criteria. Advocate A justifies his criteria ƒ by introducing the criteria itself as an argument, here noted as F, so that the truth of ƒ is justified by an argument for itself, in the form: if criteria-as-argument-as-criteria, then ƒ is true. This justification is circular and perpetual, aka. a "vicious cycle".
Sextus could also observe another discussion following this form:
Type II
6') Advocate A judges the truth of criteria ƒ by argument F
7') Advocate A justifies argument F by criteria ♠ (the Ace of Spades, let's say)
... ∞
This is a Type II problem of the criterion or, what I call, the question of the criteria's certainty. Advocate A justifies his original criteria ƒ by introducing the criteria itself as an argument, here noted as F, and justifying it by another criteria. This regresses infinitely towards other criteria that justify the antecedent criteria (despite laying down his Ace of Spaces, i.e. we aren't playing Spades).
My systematization of discussions clearly identifies that the problem of the criterion has two primitive questions, P1 and P2:
P1) The problem for Type I disagreements is the question: Why is advocate A certain of ƒ's justification? or, to be reasonably precise: What is certain justification of ƒ?
P2) ... Type II ... : Why is ƒ's justification unnecessary for advocate A? ... : What is necessary justification for ƒ?
Some Answers
By applying AmicoVapor parameters to the original answers (~1) and (1'), given above, and by imagining a discussion of them using my system, SS and RD, we see how these kind of responses are problems of (P1) and (P2). First, the original question (1) satisfies parameters Ω and Ψ. When one asserts (~1) or (1'), parameter Φ is only contigently satisfied -- contingent on the rest of the solution set. As Chishold foresaw, "we can deal with the problem only be begging the question" with follow-up questions: ~1.a) What is "not a problem" and, 1'.a) Why is "a pseudoproblem". [12] The discussion would go something like this:
1) What is the problem of the criteria? (Given)
~1) The problem of the criteria is not a problem. (Assume that this is a relevant and true answer.)
~1.a) What is not a problem?
... (grab some coffee and return later)
~1) The problem of the criteria.
1) What is the problem of the criteria?
Since the solution to (~1.a) includes an answer that leads to the original question (1) one might superficially claim that the answer is relevant (Γ) but the remaining answers in the set demonstrate that the truth-value of (~1) is uncertain (Π) because we had original doubted (1) via RD. Furthermore, (~1) includes as its answers a solution set that includes the set of questions, or the problem set, and this is a violation of set theory codified by Δ. Therefore, one must either satisfy all parameters by "breaking" the problem into two (or more) sets or, since this follows a Type I problem, one needs a solution for (P1). The other, Type II argument is not as easily seen via finite discussions but the perennial topics discussed by philosophers could be, I think, concatenated to reveal this:
1) What is the problem of the criterion? (Given)
~1) The problem of the criterion is not a problem. (Assume that this is a relevant and true answer.)
~1.a) Why is the problem of the criterion not a problem?
~1.a.1) The problem of the criterion is not a problem because it fails to satisfy the criteria of a problem.
~1.a.1.a) Why does the problem ... fail to satisfy the criteria ...?
~1.a.1.a.1) The problem ... fails to satisfy the criteria because the criteria of a problem is the criteria of
... ∞
ergo ad infinitum. I will not analyze whether this Type II argument satisfies all AmicoVapor parameters as we did above but I will admit that it should be difficult for a finite set of parameters to impose limits on an unbound set of answers (see Russell’s Paradox). The consequence of either Type I or II disagreement is insidiously problematic for philosophic discussions. The later type means that necessarily, advocate A will disagree with B, and the former that they will certainly disagree. And if we extend the discussion in time, as was implied above, by saying 'X advocates y at t', then either advocate will always, necessarily or certainly disagree. Hence, the perennial nature of philosophic discussions is, by this analysis, hypothetically fatalistic.
Implications beyond the Context of Discussions
By not solving the problem of the criterion, its persistence might imply a plurality of truths and logics inconsistent with traditional theories of knowledge. The primitive questions P1 and P2 are relevant to foundationalism and coherency, respectively. As an advocate of such traditional theories, Chisholm concludes that both foundationalists and coherentists should appeal to a kind of Kantian metaphysics as the source for knowing things because we perceive particular things and are aware of our perception [13]. I argue that this particularism, as Chisholm calls his answer to P2, does not supplant methodism, or the theory of justification that Sextus originally questioned, because it is itself a method that succumbs to the problem of the criterion (by not answering P1). Others (like Mercier) even say ƒ is the “metacriteria”. Indeed, Steup calls these criteria “J-factors” for justifying beliefs and uses them to identify whether the criterion is a form of internalism or externalism. [14] But Chisholm refutes my (and Amico’s) accusation that a priori synthetic beliefs are no more or less justified than any other J-factor [15]. He says, “’Doesn’t this mean, then, that the sceptic is right after all?’ I would answer: ‘Not at all. His view is only on of the three possibilities and in itself has no more to recommend it than the others do. And in favor of our approach there is the face that we do know many things, after all.’” [16]
An alternative to dogmatic epistemologies that define terms to mean that we do certainly know things ‘after all’ necessarily is to remove the parameters that I extended from Amico. But the consequences would be unreasonable and trivially refutable arguments that might better be described as "dogmatic mysticism" - a pejorative usually prescribed to skeptical arguments. Science and mathematics seem to indicate that we do know things 'after all' and my goal is not to undermine their conclusions. To prevent an unraveling of fields that are far more pragmatic than philosophic debate, we should solve the problem within reason. I expect the solution will include answers to the questions:
P1.a) Why is p true?
P2.a) What p is logical?
But since we must answer both questions, in some way simultaneously, to avoid stepping onto the vicious wheel, I think the hypothesis of a plurality of truths and logics should be analyzed. This analysis would include a systematic deconstruction of the traditional, epistemological edifice using Carnap’s construction system from The Logical Structure of the World, although applied in reverse, and modernized tools of Sextus’ scepticism, such as those explored in Deviant Logic by Susan Haack. In particular, I expect these logics to reveal problems in assigning traditional, bivalent truth-values (exclusively T or F) to ambiguous yet meaningful statements, such as the statement of rational doubt (RD) that we employed for the system above (SS).
[1] Chisholm, Roderick. “The Problem of the Criterion”, a lecture by on March 11, 1973 as The Aquinas Lecture: 2
[2] Steup, Matthais. The Stanford Encyclopedia of Philosophy. "Epistemology" at http://plato.stanford.edu/entries/epistemology/ (on Feb. 2, 2007)
[3] Carnap, Rudolf, The Logical Structure of the World (University of California: Berkeley, 1967), 310.
[4] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 11-12.
[5] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 78-79.
[6] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 13.
[7] Plato, The Great Dialogues of Plato. ed. Philip Rouse, “Meno” (Signet Classics: New York, 1999), 40.
[8] Carnap, Rudolf, The Logical Structure of the World (University of California: Berkeley, 1967), 314.
[9] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 35-36.
[10] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 9, 30.
[11] Chisholm, Roderick. Theory of Knowledge (Prentice-Hall: New Jersey, 1966), 57, 59.
[12] Chisholm, Roderick. “The Problem of the Criterion”, lecture on March 11, 1973: The Aquinas Lecture: 37
[13] Chisholm, Roderick. Theory of Knowledge (Prentice-Hall: New Jersey, 1966), 60-61
[14] Steup, Matthais. The Stanford Encyclopedia of Philosophy. "Epistemology" at http://plato.stanford.edu/entries/epistemology/ (on Feb. 2, 2007)
[15] Chisholm, Roderick. “The Problem of the Criterion”, lecture on March 11, 1973: The Aquinas Lecture: 22
[16] Chisholm, Roderick. “The Problem of the Criterion”, lecture on March 11, 1973: The Aquinas Lecture: 38
In the systemization of epistemology that I adopt from Steup [2], the criteria is analogous to a method; it is a theory of justification where the method justifies how we know what we know, and that justification theory is itself a theory of knowledge. Although Steup seems to define these terms via some dependency hierarchy, as may be the case for foundationalism, and although I characterize the criterion as methodical, the problem of the criterion has not been, I expect, exhausted by coherentism or particularism. Others classify the criteria as second-order knowledge, or meta-knowledge; and, although this classification better depicts the scope of the problem in general, the system I develop below applies this theory to argumentation, i.e. debate. My application of the criterion, however, yields light on theories for justifying other fields, including science and mathematics.
What I mean by applicable might better be understood by analogy. Take philosophic discussions as examples (including this writer-reader discussion). There seem to be perennial disagreements concerning claims to truth and strength of arguments, and these disagreements appear as verbal conversations, threads posted to online boards, letters of correspondence, etc. I characterize these discussions by the object of their statements, namely, certainty (of truth) and necessity (of form) given by the following disagreements:
α) Advocate A claims that proposition p is true but advocate B claims that p is obviously not true.
β) Advocate A claims that his argument for believing p is stronger than advocate B's (obviously weaker) argument for believing the same proposition p, and vice versa.
Although these generalizations differ with respect to their objects, where the object of (α) is the truth of p while the object of (β) is the argument for believing p, both describe a disagreement nonetheless. They are variations of a theme that narrow the scope of the problem from meta-knowledge to an instance of the problem, namely, philosophic discussions. Thus a discussion is the context of the problem of the criterion in this essay and determines its relevant solutions. Similar disagreements can be found in science and mathematics but I merely make inference to the implications on those fields.
Parameters for Reasonably Solving Problems
The first solution to this problem is trivial: ~1) The problem of the criterion is not a problem. This answer is problematic and will be discussed in the "Answers" section below. For now, lets move forward with a variation of (~1) by a redefinition of the original that follows Carnap's system: 1') The problem of the criterion is a pseudoproblem. [3] To determine whether (1') or even any answer, such as (~1), can actually solve the problem of the criterion, I think Robert Amico judiciously provides parameters within which we can reasonably discuss problems.
Amico identifies relationships between problem-solution and question-answer pairs that he calls “pragmatic presuppositions”, and he defines these. [4] He does not describe every possible relationship or meaning but his framework is reasonable and relevant to discussions so I will extend them contextually and codify them with the label: AmicoVapor's "Parameters for Reasonably Solving Problems" (because "AmicoVapor" sounds like something went wrong at the gas station):
Ω) a problem includes a set of questions, although a problem need not only contain questions because it may include statements that clarify the question(s), i.e. questions are a necessary condition for a problem;
Ψ) a question is not declarative (and exempts rhetorical questions) and cannot be assigned a meaningful truth-value
Φ) a solution is a set of answers; a solution set contains no unanswered questions, i.e. answers are necessary and sufficient conditions for a solution
Π) an answer is declarative and can be assigned truth(-value(s))
Φ is the parameter for determining certainty and has important implications for problems of necessary truth. To illustrate these parameters, consider the comparison of two similar sentences:
p: Knowledge is possible.
q: Is knowledge possible?
Given these parameters, there are no answers that solve p because p is declarative statement, so p is the answer. There are answers that solve q because q is a question, or inquisitive statement, and a solution set with at least one answer can be found because of two corollary parameters:
Δ) a problem has one and only one solution
Γ) for every answer given as a solution, each answer must be relevant to a question contained in the problem
Γ is the parameter for determining meaning, including the definitions of necessity and certainty, and it has important implications for the problem of the criterion. Relevancy is a synthetic test for the question-answer relationship and it follows the analytic test of the problem-solution relationship. The synthetic test is semantic but not trivial; its ambiguity in the abstract will be determined when applied to the discussions below. All these parameters codify an analytic approach to philosophy of the kind that mathematicians and physicists are accustomed to, and it prevents us from assigning truth values to statements that do not solve the problem.
Some may foresee these parameters as "setting ourselves up for failure" by precluding us from solving the problem of the criterion. I will admit that this is one of Chisholm's criticisms, but the argument behind this foresight may be weaker than the insidiousness of the problem, and would itself be a problem solved via some criteria [5]. I adopt these parameters because Amico's intention is the same as mine: a solution to the problem of the criterion would dissolve the problem. [6]
The Sextus System
Plato discussed a version of the problem of the criterion [7] and Carnap illuded to it [8] but Sextus Empiricus is credited for writing the original version so I will systematize Amico's interpretation of him [9]. The Sextus System (SS), as I like to call it, intends to extract different consequences of disagreeing based on the arguments and criteria used by the advocates during a discussion. Let us imagine that Sextus watches a thread from an online philosophy community or hears the oral arguments in a Supreme Court case, and he observes a disagreement in the form (α) or (β) from above:
3) Advocate A seems to judge proposition p differently than advocate B
3*) Advocate B seems to judge proposition p differently than advocate A
Sextus rationally doubts the object of the disagreement, p:
RD) observer X rationally doubts proposition p because X is more justified in withholding belief of p than affirming or denying p, i.e. X disbelieves neither p nor p's negation
This kind of doubt is based on Sextus' concept of "equipollent" judgments and is a concept that I think Amico interprets correctly but one that Chisholm misinterprets. [10] RD is not defined as ~(p ∨ ~p), as Chisholm would have us believe, because his (mis)interpretation is irrational by the definition of non-contradiction [11]. Rather, RD is ~~(p ∨ ~p) where the truth of RD has yet been asserted (and is indeterminate, as is the case for 3-valued logics; see Susan Haack below). Others call this their "suspension of (dis)belief" and in this way I understand Sextus is using a passive tool for observing the discussion. This is an important feature of the SS system because it squelches premature accusations that rational doubt is actually claiming truth in disblief and therefore irrational.
Sextus continues observing the discussion using my system; it is a closed system yet describes 16 possible discussions (two advocates of a four argument form, i.e. 24). I skip some trivial discussions to avoid sounding redundant; only two are fundamental to understanding the problem. For example, if advocate A and B seem to judge the proposition p the same using the same argument P, an argument which is justified by the same criteria ƒ, then obviously there is no problem. This example is, what I call, total agreement (Discussion I). The further from agreement the advocates are, the more important our observations.
Discussion III
4) Advocate A judges the truth of p by argument P
5) Advocate A justifies argument P by criteria ƒ
4*) Advocate B judges the truth of p by argument O
5*) Advocate B justifies her argument O by the same criteria ƒ
This kind of disagreement is one that the advocates should be able to (eventually) solve. This is not a problem of the criterion because the same criteria ƒ is used; this disagreement is a problem of argumentation (P versus O) and adjudication of p. I should note the there is also no problem for advocates of the primitive (α) and (β) who, without justification, merely claim that the proposition is true. The system accounts for this via exemption when we say advocate A or B is unreasonable and trivially refutable. However, unjustified true beliefs, or even propositions advocated with neither certainty nor necessity, have serious implications for theories of knowledge (as I reiterate later).
Now let us hypothesize that advocates A and B return to the discussion with their respective criteria and propositions that had previously supported some agreements in previous discussions (I-IV). Assume criteria g had been originally used by advocate B, and A had previously agreed with its justification. (This swapping of criteria and propositions is clarified by gender: A is a guy and B is a girl):
Discussion XIV
4') Advocate A judges the truth of p by her argument O
5') Advocate A justifies her argument O by her criteria g
4'*) Advocate B judges the truth of p by his argument P
5'*) Advocate B justifies his argument P but by his criteria ƒ
This kind is of disagreement seems insoluble. Each advocate judges the truth of p based on the opposing advocate's argument and criteria, yet these lead to an opposite adjudication of p! Line (5'*) is the most extreme catalyst for the problem of the criterion. Next, Sextus observes advocate A and B continuing their discussion with the intentions of definitively discrediting their opposition by vindicating their adjudication of p. (I skip advocate B's lines below because they are merely the converse of A's, as demonstrated above by (3-5)*):
Type I
6) Advocate A judges the truth of proposition ƒ by argument F
5) Advocate A justifies argument F by the same criteria ƒ
This is a Type I problem of the criterion or, what I call, the question of a necessary criteria. Advocate A justifies his criteria ƒ by introducing the criteria itself as an argument, here noted as F, so that the truth of ƒ is justified by an argument for itself, in the form: if criteria-as-argument-as-criteria, then ƒ is true. This justification is circular and perpetual, aka. a "vicious cycle".
Sextus could also observe another discussion following this form:
Type II
6') Advocate A judges the truth of criteria ƒ by argument F
7') Advocate A justifies argument F by criteria ♠ (the Ace of Spades, let's say)
... ∞
This is a Type II problem of the criterion or, what I call, the question of the criteria's certainty. Advocate A justifies his original criteria ƒ by introducing the criteria itself as an argument, here noted as F, and justifying it by another criteria. This regresses infinitely towards other criteria that justify the antecedent criteria (despite laying down his Ace of Spaces, i.e. we aren't playing Spades).
My systematization of discussions clearly identifies that the problem of the criterion has two primitive questions, P1 and P2:
P1) The problem for Type I disagreements is the question: Why is advocate A certain of ƒ's justification? or, to be reasonably precise: What is certain justification of ƒ?
P2) ... Type II ... : Why is ƒ's justification unnecessary for advocate A? ... : What is necessary justification for ƒ?
Some Answers
By applying AmicoVapor parameters to the original answers (~1) and (1'), given above, and by imagining a discussion of them using my system, SS and RD, we see how these kind of responses are problems of (P1) and (P2). First, the original question (1) satisfies parameters Ω and Ψ. When one asserts (~1) or (1'), parameter Φ is only contigently satisfied -- contingent on the rest of the solution set. As Chishold foresaw, "we can deal with the problem only be begging the question" with follow-up questions: ~1.a) What is "not a problem" and, 1'.a) Why is "a pseudoproblem". [12] The discussion would go something like this:
1) What is the problem of the criteria? (Given)
~1) The problem of the criteria is not a problem. (Assume that this is a relevant and true answer.)
~1.a) What is not a problem?
... (grab some coffee and return later)
~1) The problem of the criteria.
1) What is the problem of the criteria?
Since the solution to (~1.a) includes an answer that leads to the original question (1) one might superficially claim that the answer is relevant (Γ) but the remaining answers in the set demonstrate that the truth-value of (~1) is uncertain (Π) because we had original doubted (1) via RD. Furthermore, (~1) includes as its answers a solution set that includes the set of questions, or the problem set, and this is a violation of set theory codified by Δ. Therefore, one must either satisfy all parameters by "breaking" the problem into two (or more) sets or, since this follows a Type I problem, one needs a solution for (P1). The other, Type II argument is not as easily seen via finite discussions but the perennial topics discussed by philosophers could be, I think, concatenated to reveal this:
1) What is the problem of the criterion? (Given)
~1) The problem of the criterion is not a problem. (Assume that this is a relevant and true answer.)
~1.a) Why is the problem of the criterion not a problem?
~1.a.1) The problem of the criterion is not a problem because it fails to satisfy the criteria of a problem.
~1.a.1.a) Why does the problem ... fail to satisfy the criteria ...?
~1.a.1.a.1) The problem ... fails to satisfy the criteria because the criteria of a problem is the criteria of
... ∞
ergo ad infinitum. I will not analyze whether this Type II argument satisfies all AmicoVapor parameters as we did above but I will admit that it should be difficult for a finite set of parameters to impose limits on an unbound set of answers (see Russell’s Paradox). The consequence of either Type I or II disagreement is insidiously problematic for philosophic discussions. The later type means that necessarily, advocate A will disagree with B, and the former that they will certainly disagree. And if we extend the discussion in time, as was implied above, by saying 'X advocates y at t', then either advocate will always, necessarily or certainly disagree. Hence, the perennial nature of philosophic discussions is, by this analysis, hypothetically fatalistic.
Implications beyond the Context of Discussions
By not solving the problem of the criterion, its persistence might imply a plurality of truths and logics inconsistent with traditional theories of knowledge. The primitive questions P1 and P2 are relevant to foundationalism and coherency, respectively. As an advocate of such traditional theories, Chisholm concludes that both foundationalists and coherentists should appeal to a kind of Kantian metaphysics as the source for knowing things because we perceive particular things and are aware of our perception [13]. I argue that this particularism, as Chisholm calls his answer to P2, does not supplant methodism, or the theory of justification that Sextus originally questioned, because it is itself a method that succumbs to the problem of the criterion (by not answering P1). Others (like Mercier) even say ƒ is the “metacriteria”. Indeed, Steup calls these criteria “J-factors” for justifying beliefs and uses them to identify whether the criterion is a form of internalism or externalism. [14] But Chisholm refutes my (and Amico’s) accusation that a priori synthetic beliefs are no more or less justified than any other J-factor [15]. He says, “’Doesn’t this mean, then, that the sceptic is right after all?’ I would answer: ‘Not at all. His view is only on of the three possibilities and in itself has no more to recommend it than the others do. And in favor of our approach there is the face that we do know many things, after all.’” [16]
An alternative to dogmatic epistemologies that define terms to mean that we do certainly know things ‘after all’ necessarily is to remove the parameters that I extended from Amico. But the consequences would be unreasonable and trivially refutable arguments that might better be described as "dogmatic mysticism" - a pejorative usually prescribed to skeptical arguments. Science and mathematics seem to indicate that we do know things 'after all' and my goal is not to undermine their conclusions. To prevent an unraveling of fields that are far more pragmatic than philosophic debate, we should solve the problem within reason. I expect the solution will include answers to the questions:
P1.a) Why is p true?
P2.a) What p is logical?
But since we must answer both questions, in some way simultaneously, to avoid stepping onto the vicious wheel, I think the hypothesis of a plurality of truths and logics should be analyzed. This analysis would include a systematic deconstruction of the traditional, epistemological edifice using Carnap’s construction system from The Logical Structure of the World, although applied in reverse, and modernized tools of Sextus’ scepticism, such as those explored in Deviant Logic by Susan Haack. In particular, I expect these logics to reveal problems in assigning traditional, bivalent truth-values (exclusively T or F) to ambiguous yet meaningful statements, such as the statement of rational doubt (RD) that we employed for the system above (SS).
[1] Chisholm, Roderick. “The Problem of the Criterion”, a lecture by on March 11, 1973 as The Aquinas Lecture: 2
[2] Steup, Matthais. The Stanford Encyclopedia of Philosophy. "Epistemology" at http://plato.stanford.edu/entries/epistemology/ (on Feb. 2, 2007)
[3] Carnap, Rudolf, The Logical Structure of the World (University of California: Berkeley, 1967), 310.
[4] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 11-12.
[5] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 78-79.
[6] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 13.
[7] Plato, The Great Dialogues of Plato. ed. Philip Rouse, “Meno” (Signet Classics: New York, 1999), 40.
[8] Carnap, Rudolf, The Logical Structure of the World (University of California: Berkeley, 1967), 314.
[9] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 35-36.
[10] Amico, Robert. The Problem of the Criterion (Rowman & Littlefield: Maryland, 1993), 9, 30.
[11] Chisholm, Roderick. Theory of Knowledge (Prentice-Hall: New Jersey, 1966), 57, 59.
[12] Chisholm, Roderick. “The Problem of the Criterion”, lecture on March 11, 1973: The Aquinas Lecture: 37
[13] Chisholm, Roderick. Theory of Knowledge (Prentice-Hall: New Jersey, 1966), 60-61
[14] Steup, Matthais. The Stanford Encyclopedia of Philosophy. "Epistemology" at http://plato.stanford.edu/entries/epistemology/ (on Feb. 2, 2007)
[15] Chisholm, Roderick. “The Problem of the Criterion”, lecture on March 11, 1973: The Aquinas Lecture: 22
[16] Chisholm, Roderick. “The Problem of the Criterion”, lecture on March 11, 1973: The Aquinas Lecture: 38