HOW TO (start a) SEARCH FOR TRUTH

Eric Lormand
University of Michigan
lormand@umich.edu
Draft: December, 2001

 

I.  AIMING FOR TRUTH 

Meet longtime Tarot reader and renowned occultist Renée O’Cards. Wracked with guilt over her epistemic irresponsibility, seized with fear of being deceived by a malignant demon, and prone to escape into sleep and dreams for unknown time periods, she turns to the consolation of First Philosophy. Today, in secure possession of leisure in a peaceable retirement, she opportunely frees her mind from all other cares, is happily disturbed by no passions, and at length applies herself earnestly and freely to Seeking Truth.             Unfortunately, the First Philosophers she meets advise her to accept whatever Method, at root, is easiest or makes her generally happiest.[1] She discards such a merely “pragmatic” search, offering her crass advisors the use of her old client list, since Tarot readers these days get easy money and a loving network of Psychic Friends. Her search is to be purely “epistemic”, based singlemindedly on her aim for Truth.             How should Madame O’Cards … well, she’s discarded her professional name … how should Renée proceed?

             Of course when Renée aims for “truth” she is not on a hunt for the abstract property of being true, itself. She aims for true things. And she aims “for” true things in the sense of aiming to be poised (or inclined) to use them as true, to take advantage of their truth—for instance, to have true beliefs.[2] She can use true beliefs in order to reach more true beliefs. Or in case she ever comes to be disturbed by a passion, potentially she can use true beliefs in figuring out how to indulge it. But this latter merely practical use does not constrain her purely epistemic aims.[3]

             Renée might form true beliefs too easily to satisfy herself, by “covering all the bases”, that is, accepting each candidate belief along with any apparently competing candidates (perhaps she is poised to use each of them as true, but in different circumstances or for different purposes). This would be unsatisfying because she also seeks nothing but the truth—so that there is a truth that p for each of her beliefs that p—and her aimings allow for the alleged possibility of untrue beliefs.

             Similarly, Renée might form some true beliefs too easily to satisfy herself. She might leave out a lot of truths, and there are no true beliefs she isn’t aiming to form. Ideally she seeks the whole truth—a “complete” group of true beliefs, a belief that p for every truth that p.

             I’ll say Renée’s target is “Truth” (capital “T”) as a shorthand in two ways for what she really aims for—a shorthand for true beliefs, and a shorthand for the truth, the whole truth, and nothing but the truth.

             On the other hand, her overall aiming for Truth is not all-or-nothing: it is more satisfied the more true beliefs she has and the fewer untrue beliefs she has. Her basic overall Truth-aim factors into two kinds of aims, each with conditional content. She aims that for each candidate belief that p: if p, then she believes p; and if she believes p, then p.[4] (See the central root of the tree in the Appendix, Aim 1.)

  

II.  AIMING FOR EPISTEMIC RESPONSIBILITY 

Renée’s fear of a falsity-insuring malignant demon makes her fantasize about a truth-insuring benign angel. But perhaps surprisingly, that also scares her! She aims to find truth, proudly, versus being given it, luckily. She aims to be responsible for reaching Truth: to develop a set of sub-aims that she can satisfy, and that lead to satisfaction of her ultimate aim for Truth.                 The problem is that any old aim A leads to Truth if an angel rewards those who aim for A—e.g., by revealing Truth to them on Judgement Day. And any old aim A precludes Truth if a demon punishes those who aim for A—e.g. by massively deceiving them. So even if outcome O is necessary for Truth, aiming for O seems to require betting against demonic punishment for O-aimers. And even if outcome N necessarily precludes Truth, aiming against N seems to require betting against angelic rewards for N-aimers. But Renée has no evidence against such demons and angels.                 Deep inside Renée, however, is a Nordic defiance of the Fates. She does aim for Truth. But if demons punish her otherwise rational sub-aims, she’d prefer to sacrifice Truth, and to reason as if she can satisfy these sub-aims. Nor would she prefer to sell out her reason to angels promising Truth. How heroic!

            Even if conditions don’t allow her to be causally responsible for reaching Truth, Renée resolves to reason responsibly. This is a kind of virtual or representational responsibility: to specify sub‑aims that serve her end-aims if conditions don’t block her from satisfying the sub-aims. Specifically epistemic responsibility is reasoning responsibly in this sense, and doing so based on the sole initial aim for Truth. (Though Renée doesn’t take epistemic responsibility as a means to Truth, her aim for epistemic responsibility is still “based” on her aim for Truth in a second sense: her aim for epistemic responsibility depends on the existence of her aim for Truth. She wouldn’t have an aim for rational responsibility unless she had the aim for Truth.[5]) (See the rightmost root of the tree in the Appendix, Aim 2a.)

 

            Renée has a core ground rule for prideful epistemic responsibility. It constrains her cognitive starting point. She aims “carefully to avoid precipitancy and prejudice” where she “cannot exclude all ground of doubt” (see Discourse on the Methods of Rightly Conducting the Reason, and of Seeking Truth in the Seances; also Aim 2b of the Appendix.) I will suppose that with one kind of exception, Renée is unwilling initially to accept contingent candidate beliefs as (probably or actually) true or (probably or actually) false. She will not accept such candidate beliefs without epistemically responsible reasons, and at the start she doesn’t have such reasons. But as I said there is one kind of exception: beliefs of the form “I think p” about the contents of her (candidate) beliefs and aims. Although it is contingent which beliefs and aims Renée has—just as it is contingent whether she even exists—I will assume she correctly forms contingent self-directed beliefs about them.[6] Also, I will assume she does correctly sort (candidate) beliefs as necessarily true or as necessarily false.[7] I will try to show how she can proceed from there to a justified method of searching for (further) contingent truths. My hope is that this will eventually point to a way to reach the same end from a more meager starting point, one without initial reliance on self‑directed beliefs or beliefs about necessities.

 

III.  AIMING TO SEARCH

 

            Renée aims to search for Truth. What can she build into this aim, without prejudice about what’s contingently true? She can stick to necessary parts of searching in general, independent of the specific Truth-search: i.e., general facts about searching for food, shelter, justice, peace, love, hate, war, … even falsity. Then she can remain unprejudiced by applying only those general necessary parts to her Truth search.

             In addition to an aiming for X, conducting a search for X requires a stock of possible candidates for X, and a kind of accepting of candidates. Accepting a candidate X can be various things in various searches: acting as if the candidate X is an X, using it for aimings that are satisfied only if it is an X, believing that it is an X, transforming it into an X, etc., or some combination of these. In some cases, acceptance of a candidate for X varies in degree, along one or more dimensions. For example, you may be more or less inclined to trust something you accept as a healthy food, even holding fixed your aiming to eat and your opportunity. Or you may be much inclined to use an accepted shelter to avoid snow but not to avoid bombs. Degrees of acceptance may be precise or rough, quantitative or qualitative.

             A candidate that is not accepted to any degree is rejected. In some cases the target of the search and the acceptance mechanisms of the searcher place no effective limits on how many candidates can be accepted. But in other cases candidates compete for acceptance, because of total limits on the number of acceptances or because the aimings or capacities of the searcher set up specific pairwise tensions among candidates. For instance, you might set up a competition among your candidate charitable recipients, but you’d be less likely to set up a competition among your candidate charitable donors.

             Candidates are accepted (or rejected) according to a test for X, whose reliability may fall anywhere from infallible to routinely misguiding or even necessarily misguiding. If there are distinct mechanisms for testing and for accepting, the immediate results of the test are scores—aimings to accept or reject—that typically in turn cause acceptance outcomes unless something interferes with the acceptance mechanisms. (If somehow there aren’t distinct mechanisms for testing and for acceptance; then the test scores are the acceptance outcomes rather than mere aimings for or causes of acceptance.) Scores have a number of dimensions and a degree of precision to match the search’s various possible dimensions and degrees of acceptance. Without loss of generality, I’ll assume that the higher the score (perhaps above some threshold), the more the candidate is accepted.

             The process by which possible candidates become subject to testing is generation of candidates, which may be blind (e.g., randomly or unthinkingly stumbling upon a candidate) or guided (e.g., creating a candidate by design). Unlike passing or failing a test, which may admit of degrees, generation of candidates is all‑or‑none: a candidate is either tested or it isn’t. In some cases, a test relies on an exhaustive group of possible candidates’ being available simultaneously. The test is applied once to the whole group, and the search halts. In other cases, a test is able iteratively to test possible candidates as they become available, nonexhaustively, perhaps even one candidate at a time. Iteration matters if the test can be modified by provisionally accepted candidates, candidates that are accepted to some degree but are subject to further testing and potential rejection (e.g., if a competing candidate scores higher in subsequent loops through the search steps). In that case, the order in which candidates become available may affect the outcomes on subsequent iterations, by affecting which candidates are provisionally accepted while the search continues. The search is halted when a candidate gets a special (e.g., perfect) test score, or when there are no new possible candidates, candidates that have not already undergone the same test.

             So in the general case, a search for X contains an ordered series of four steps (which may be repeated):

            (GX) Generating new candidates for X.

            (TX) Scoring generated candidates according to a test for being X.

            (AX) Accepting a candidate to the degree it scores highly on the test (absolutely or relative to competing

                        candidates).

            (HX) Halting if a candidate scores highly enough on the test or if there are no new candidates, otherwise

                        looping to (GX).

A method of searching for X is a particular means for performing (GX), (TX), (AX), and (HX)—including a generation procedure, a test, a kind of accepting, and threshold scores for accepting and for halting. (See the leftmost root of the Appendix tree, Aim 3a.)

             Since Renée’s aim for Truth is partially satisfiable by less than the whole truth, she doesn’t aim merely to mount a single search for the whole truth, rejecting candidate groups of beliefs simply because they are incomplete. Instead, she aims gradually to aggregate subsearches, each aimed at finding some (possibly incomplete) truth(s). She aims to subsearch and aggregate until, ideally, her aggregate is complete.[8] (In Renée’s terms she aims “to divide the problem of seeking truth into as many parts as possible” and “to ascend step by step from the easiest parts to the most difficult parts” and “to enumerate these steps so completely … that nothing is omitted”.)  (See Aim 3b of the Appendix.)

             Applying only the necessary parts of searching in general to her search for Truth, Renée aims to mount (sub)searches for truth with the following steps:[9]
            (G_T) Generate new candidate beliefs.
            (T_T)  Score generated candidates according to a test for being true.
            (A_T) Accept a candidate to the degree it scores ….
            (H_T) Halt …, or else loop to (G_T).
In the specific context of (AT), accepting a candidate belief that p is forming a belief that p. If the threshold score for halting is higher than that in the previous step for accepting, Renée may form a belief provisionally without halting the search, and might reject it—destroy it—if another candidate belief scores higher in subsequent iterations of the search steps. Renée’s test at (T_T) may depend on candidate beliefs she accepted provisionally at a prior (A_T) in the same subsearch, or on her aggregated beliefs from prior subsearches.

  

IV.  AIMING TO METASEARCH

 

            Though Renée aims to search for Truth, she aims first to search for a method of searching for Truth. And not just any old method, of course; her aim, ideally, is to find an ideal method of searching for truth, where what’s ideal is measured by her aim of finding Truth. Or, failing that, it’s best if she finds the best method of searching for truth, the method that is closest to the ideal, where closeness is also measured by her aim of finding Truth. Or, at least, it would be alright if she finds a right method of searching for truth, a method that is better than some other candidate methods she will have considered, and no worse than any others. She aims to mount a “metasearch” for Truth, which is a search for a right (/best/ideal) method of searching for Truth.[10]

             As before, to avoid prejudice she should carry over to the metasearch for Truth only necessary parts of metasearching in general. A metasearch for X follows steps similar to a search for X, but with “a right method of searching for X” substituted for “X”:
            (G_M) Generate new candidates for a right method of searching for X.
            (T_M) Score generated candidates according to a test for being a right method of searching for X.
            (A_M) Accept a candidate to the degree it scores ….
            (H_M) Halt …, or else loop to (G_M).
In this case “accepting” a candidate method is being poised to use the method in searching for X.[11]

             Putting aside issues of feasibility, an ideal method of searching for X—ideal for the aim of finding X, setting aside any other ideals—would meet three specifications, or what I’ll call “X-Specs”:
            X-Coverage: X is among the candidates generated and tested by the search.
            X-Discrimination: X scores perfectly, or better than all possible competing candidates, and so is accepted.
            X-Stability: X remains accepted because its score halts the search or remains higher than any subsequent
                        competitor’s score.
What’s more, an ideal search method—with heavy emphasis on “ideal”—would meet these X-Specs necessarily, no matter how the world is. Such a search method would in every possible circumstance enable one to find X.

             In case no ideal candidate method is feasible, less than ideal methods might at least partially satisfy the root aim of finding X. Other aims aside, one feasible search method for X is better than another feasible search method for X the closer it approximates to the ideal. There are several interesting dimensions of proximity to the ideal case, based on the degree to which they satisfy the aim of “finding” X. One dimension varies the necessity of a perfect method’s meeting the X‑Specs. One method might be better than another in meeting the X-Specs with greater probability given specific actual conditions. Another dimension of proximity to the ideal varies a perfect method’s jointly meeting the three X‑Specs. In some possible condition, imperfect methods might meet only X-Coverage and X‑Discrimination without X‑Stability, or might meet only X-Coverage without X-Discriminating and X-Stability, or might meet none of these.[12] The more X‑Specs a method meets in circumstance C, the better the method is at finding X in C.[13] So if C is the actual or probable conditions surrounding the search, the more X-Specs a candidate method meets in C, and the more probably it meets them in C, the higher its score in the metasearch.

             The crucial problem is how to test whether it is the aimed‑for target X that a candidate method covers, discriminates, or stabilizes on in conditions C. One way to do this is to compare the candidate method’s scores with unquestioned scores already given to candidates for X. For example, if a candidate food has already been scored (accepted to some degree or rejected), it can be used to “calibrate” candidate methods in the metasearch for a right method of searching for food. A method’s own score is higher the closer the match between (a) the food’s actual score and (b) the score a candidate method gives to that candidate food. A second way uses beliefs about general features of food, even if no specific candidate food has already been accepted or rejected. The higher the score a candidate method gives to candidates with those general features, the higher the method’s own score in the metasearch.

 Call the process of calibrating one’s method using already accepted candidates for X, or using substantive beliefs about general features of X, the “Circle of Calibration”. Can one metasearch for X from scratch—without going around this Circle? It seems that one cannot. Usually this circularity is little or no hindrance, because we do already have accepted candidates for X or substantive beliefs about X before we metasearch—usually it’s these morsels that give us the ideas or aims about X in the first place, and usually they go unquestioned.

            Now let’s apply this in the context of Renée’s search for Truth. A metasearch for Truth contains the following four (repeatable) steps:
            (G_R) Generate new candidates for a right method of (sub)searching for Truth.
            (T_R) Score generated candidates according to a test for being a right method of (sub)searching for Truth.
            (A_R) Accept a candidate to the degree it scores ….
            (H_R) Halt …, or else loop to (G_R).
Judged solely by her aim of finding Truth, her ideal method of searching for Truth would satisfy the following three “Truth‑Specs” (special cases of the “X-Specs” listed above), and would do so necessarily:
            Truth-Coverage: If p, then a candidate belief that p is generated and tested.
            Truth-Discrimination: If p, then a candidate belief that p scores perfectly or better than competitors,
                        and so is accepted.
            Truth-Stability: If p, then a candidate belief that p remains accepted because its score halts the (sub)search
                        or remains higher than any subsequent competitor’s score.
(See the trunk of the Appendix tree, Aims 4-6.) Before factoring in the points about less-than-ideal cases and circular calibration, let’s look at Renée’s bold push for the ideal … 

  

V.  CARDESIAN FOUNDATIONS 

Obsessed by her newfound devotion to philosophical rigor, Renée frees up the rest of the week—not one day less!—for finding an ideal truth‑searching method. On the second day she reasons that since she’s thinking, she exists. But this does little to quench her thirst for the whole truth. On the third and fourth day she argues for the existence of a perfect God (who necessarily protects her from massive deception)—basically, if there weren’t such a perfect being, she wouldn’t even have an idea of a perfect being, since she couldn’t have gotten the idea of perfection from thinking about imperfect things. Over the next couple days she tries to build a tower toward the truth, the whole truth, and nothing but the truth, “so help me God”. (For details of this deal with the divinity, see Meditations on Faust Philosophy.)                 Evening of the sixth day, she sees all that she had made, and, behold, it wasn’t very good. Even given the assumption that she exists and thinks, on second thought she realizes her idea of a perfect being could’ve come from combining ideas of imperfection and of negation, each honed from thinking about imperfect beings. And anyway, she realizes that even a perfect God might deceive her—maybe being massively deceived builds character. Nearly a whole week’s edifice of meditations committed to the flames.

             Ah, well. In the absence of an ideal method of searching for Truth, Renée’s now ready to settle for a method that merely approximates the ideal. Comparisons of methods as better or worse can be derived from the general features of X‑Specs. As in the general case, judged by the aim of finding Truth, in circumstance C one method of searching for Truth is better than another the more Truth‑Specs it satisfies in C, and the more probably it satisfies the Truth‑Specs in C. But how can Renée test whether it is truth that a method covers, discriminates, or stabilizes on in a given context? Her search is for contingent truths beyond those of the self-directed “I think p” variety. But initially Renée makes no use of accepted candidates for such truths or substantive (contingent) beliefs about the general features of such truths. This aversion to prejudice seems to prevent her from calibrating methods according to whether they cover, discriminate or stabilize on such truths. So it seems she can’t use the Truth-Specs to assess methods of forming such true beliefs, initially. Perhaps the Truth-Specs will be of use if her subsearches ever get rolling, and she reaches some more useful contingent beliefs. But initially the Circle of Truth‑Calibration is unbroken.

             But remember that “truth” in Renée’s aims is shorthand for true beliefs. One potential workaround for Renée—and the only one that occurs to me—is to pare away from the Truth-Specs issues about whether the relevant beliefs are true, leaving pared-down Specs about beliefs independent of their truth or falsity. For example, unless there are some candidate beliefs (whether true or false) that a method stabilizes on, it doesn’t stabilize on true beliefs. Unless there are some pairs of competing candidate beliefs (whether true or false) that a method discriminates between (i.e., accepting one and rejecting the other), then it doesn’t discriminate true beliefs from false beliefs. And unless there are some candidate beliefs (whether true or false) that a method covers, then it doesn’t cover true beliefs. Furthermore, if a method is, ideally, to cover truth in all possible conditions, ideally it should be capable of covering any possible beliefs (this also seems to be required for avoiding prejudice). So part of Renée’s aims for Truth-Coverage, Truth‑Discrimination, and Truth-Stability are aims for the following Belief‑Specs:
            Belief-Coverage: Each possible contingent candidate belief is potentially generated and tested.
            Belief-Discrimination: Some candidate beliefs score perfectly or best among their competitors,
                        while other competitors do not score as high, and so the former (and not the latter) are accepted.
            Belief-Stability: Some candidate beliefs remain accepted, because their scores halt the (sub)search, or remain
                        higher than any subsequent competitors’ scores.
(See the branches of the Appendix tree, Aims 7-9.) Does Renée have trouble breaking the Circle of Calibration as it applies to beliefs? She does start out with examples of contingent candidate beliefs—it doesn’t matter here that she doesn’t start out assuming which of them are true, and that she doesn’t start out with them as contingent accepted beliefs. And perhaps she starts out with beliefs about some general features of contingent candidate beliefs—assuming there are features necessary to contingent candidate beliefs, which she keys on to distinguish contingent from noncontingent candidates in the first place. Either way, she may be able to calibrate candidate methods according to whether they meet the Belief-Specs. And when beliefs that are covered, discriminated, or stabilized on happen to be true—even if this is unbeknownst to Renée—satisfying these Belief-Specs satisfies the Truth‑Specs. By carefully clearing out the issues specifically about Truth, we reach ground upon which Renée may be able to build without prejudice. But there is a little more ground‑clearing to do.

             As in the general case, there are a couple legitimate dimensions along which a method can approximate the ideal of necessarily meeting the Belief-Specs. Even short of the ideal, one method is better than another if it actually meets the Belief-Specs while the other merely possibly does. This standard of actuality may be important to Renée eventually, but since she does not start out with prejudiced assumptions about what’s actual versus merely possible, she cannot use the standard initially to discriminate among methods. (She might just wait around until some possible Judgement Day to compare retrospectively how candidate methods “did” in the actual world. But that would be pointless given her aim of finding truth.) Leaving aside whether the methods actually meet the Belief-Specs, one method is better than another if it more probably does so. This standard of probability may also be of eventual use to Renée, but it is of no initial use: she makes no prejudiced assumptions about what’s probable. So initially Renée seems limited to comparing methods according to whether they do or don’t necessarily meet the Belief-Specs.

             Trouble is, as Renée realizes, no method necessarily meets the Belief-Specs, since for each method a possible demon could be bent on punishing users of that method. She also realizes that no method necessarily fails to meet the Belief‑Specs, given possible angels bent on rewarding use of any given method. But here’s a place where Renée’s aim for epistemic responsibility kicks in. She can accept sub-aims for her Belief-Spec-aims in this way: by reasoning about what would necessarily lead to the Belief-Specs if she is able to satisfy the candidate sub-aims. This, finally, requires no more than her permitted cognitive starting point of beliefs about necessities (and possibilities) and self-directed beliefs about her beliefs (and aims). But can she use it to justify aims for one method rather than another?

  

VI.  AIMING FOR COVERAGE

 

            Renée’s aim for Belief-Coverage is an aim that each possible contingent candidate belief is potentially generated and tested. Here is how she can use this aim to assess truth-searching methods with respect to their procedures for generating candidate beliefs.

 TOLERATING NONEXCLUSIVE GENERATION (Aim 10)

             For purposes of filtering all possible candidate beliefs down to the true ones, it might seem that the distinction between generating and testing is arbitrary—being excluded from testing in a generation stage seems equivalent to being included as a candidate but failing in a testing stage. Even a search with the most lenient or inclusive kind of testing phase (“accept all candidate beliefs”) successfully finds truth if a strict or exclusive enough generation phase compensates—if only true candidates are generated. Even a search with the most lenient or inclusive kind of generation phase (“test all possible candidate beliefs”) successfully finds truth if a strict or exclusive enough testing phase compensates—if only true candidates pass the test.

             No matter how the filtering is done, Renée’s aims for epistemic responsibility are satisfied only if she takes responsibility for each bit of filtering. Ideally, she divides the filtering task into the smallest possible filtering processes, orders them from coarsest to finest, keeps track of them all, and in her metasearch evaluates each. Any unevaluated  filtering process is prejudiced, and if it nevertheless succeeds in filtering out false candidates, this is a matter of epistemic luck which Renée proudly aims to avoid.

             Without loss of generality, any filtering process can be treated as part of her test for truth rather than part of her initial generation phase, as can any process of evaluating candidate filters. Collapsing these into her test for truth, the only way she can avoid prejudice is to have a test that can work even given a maximally inclusive or lenient generation phase, because if she excludes possible candidates from generation, without even giving them a “hearing” and without even having evaluated such exclusions, her method is prejudiced. So she aims to find a test that is not a mere rubber‑stamp, but which leads to truth even given a non-exclusive generation phases. Her ideal test “tolerates” non‑exclusive generation. Her purely epistemic search isn’t disturbed by passions for saving time and effort, so she has no initial countervailing reason to opt for an exclusive generation phase.[14]

 TOLERATING NONEXHAUSTIVE GENERATION (Aims 11-12)

             It might seem that an ideal generation procedure for Renée, given that she is not in a hurry, is to generate every possible candidate belief, and then test them all together as a batch. That would be an ideal generation phase, but equally, an ideal test would tolerate a less-than-ideal generation phase. If Renée generates a candidate that she does not bother testing, that would be a kind of prejudice. So Renée aims ideally for testing each candidate she generates. If her test requires a batch of candidates to be generated before it can be applied to any of them, she might unluckily halt (e.g., die, or otherwise get bogged down endlessly) in the middle of a generation phase. So the further her test is from requiring exhaustive generation, the less she relies on luck and the more she takes responsibility for testing each generated candidate. She aims ideally for a test that can work at each iteration with small batches of competing candidates, even applying to them one-by-one, immediately upon generation. Only if she has such a test, and uses it that way, can she necessarily test each generated candidate. So her ideal test would tolerate one‑by‑one generation phases.

 TOLERATING RANDOM GENERATION (Aim 13)

             Now if a nonexhaustive set of candidates is to be tested without prejudiced exclusivity, then an ideal test for Renée would work even if candidates are generated randomly, at least from among the possible candidates not already put to the same test.[15] So, epistemically responsibly, she aims ideally for a test that can tolerate random generation. (This aim could be satisfied even if Renée actually has an exclusive or exhaustive or nonrandom generation phase; she can be proudly responsible so long as her test does not rely at the start on such generation.)

  

VII.  AIMING FOR DISCRIMINATION

 

            Renée’s aim for Belief-Discrimination is an aim that some candidate beliefs score perfectly or best among their competitors, while other competitors do not score as high. Here is how she can use this aim to constrain the general features her scoring factors should have. When she is done, she will be in position to start her metasearch.

 NONNEUTRAL SCORING FACTORS (Aim 14)

             Renée aims ideally to have some factors or other that raise or lower scores; otherwise, all beliefs get the same scores. No nonneutral factors, no (responsible) discrimination among competing beliefs.

 ROBUST SCORING FACTORS (Aim 15)

             It’s possible for there to be truths that are independent of the (perhaps random) order in which Renée generates candidates. Since she aims to discriminate even such truths, she aims ideally for a test that can give the same scores to the same candidates in the same conditions, no matter the generation order. Ideally, acceptable candidate beliefs are robustly acceptable, across variations in generation.

 SEMANTICALLY RELEVANT SCORING FACTORS (Aim 16)

             Let C be a (contingent) true candidate belief that p. Suppose Renée were to score C only by using features that are completely independent of whether C is true. Also suppose that the independence holds in both directions—that C’s truth or falsity is completely independent of the features Renée uses. Despite the mutual independence, such features could be contingently correlated with C’s truth or falsity. But at the start of her search, Renée has no beliefs in such contingent correlations. At best she is epistemically lucky if she discriminates whether C is true, using only such features. So at least initially she aims to score C using features that are in a dependence relation with C’s being true or with C’s being false.

             Now suppose that Renée were to score C only by using features that are in a merely contingent dependence relation with C’s truth or falsity. Then similarly, at least initially when she lacks beliefs in such contingent connections, she could at best be lucky if she discriminates whether C is true. So at least initially, she aims ideally to score C using features that are in a necessary dependence relation with C’s truth status.

             What sorts of features could she use, initially? Whether C is true depends necessarily on (i) C’s having the content that p, and on (ii) whether p. Given her contingent self-directed beliefs about the content of her (candidate) beliefs, she may be able to use (i), and other contingencies to which (i) stands in a relation of necessary dependence.[16] But beyond this, feature (ii) is no help: prior to accepting C, Renée cannot make use of (ii), and at the start of her search, she cannot make use of any other contingency even if it is in a necessary dependence relation with (ii). So Renée aims to score C, at least initially, using features on which C’s content necessarily depends or which necessarily depend on C’s content. In general, initially she aims ideally to use scoring factors that are necessarily semantically relevant. This aim steers her away from initial reliance on intrinsic “hardware” features of beliefs (physical parts, size, etc.), and away from extrinsic physical or causal features of belief (physical location, contingent or context‑dependent use, etc.). These don’t have the kind of necessary connection to content that might enable epistemically responsible discrimination.[17]

 NONRANDOM SCORING FACTORS (Aim 17)

             First, consider a tempting but unsuccessful argument against random scoring: it seems that random scoring either prevents discrimination (when scores for all competitors happen to match) or else makes Renée merely epistemically lucky to discriminate (when scores for all competitors happen not to match). The loophole in this argument is that discrimination can be assured, responsibly, by assigning scores randomly except for scores that are already assigned. (This is akin to drawing lots randomly “without replacement”—one draws a different lot each time.) A better way to motivate an aim for nonrandom scoring is via the aim for semantically relevant scoring: genuinely random scoring depends on no specific features at all of the beliefs scored, and so depends on no features that are semantically relevant to the specific beliefs scored.

 

 VIII.  A METHOD FOR RENÉE’S METASEARCH

 

            Renée aims to find nonneutral scoring factors, ones that raise or lower scores of candidate beliefs. Since the main point of finding factors is to score contingent candidates, and since she doesn’t start out with any accepted contingent beliefs (beyond the “I think p” sort):
            Ideally, the right factors should adjust the scores of contingent candidates
                        even in the absence of previously accepted contingent candidates.
She can also apply her structural aims for ideal generation and scoring as follows:
            Ideally, the right scoring factors should outscore competitors robustly,
                        independently of order of generation. (from Aim 15)
            Ideally, the right scoring factors should outscore a competitor even if tested one versus one. (from Aim 12)
Also, since Renée doesn’t start out with any accepted scoring factors, she aims to make a first acceptance (perhaps provisionally), so
            Ideally, the right scoring factors should outscore competitors
                        even in the absence of previously accepted scoring factors.
These general features provide ways to score candidate scoring factors.

             To check for these features Renée aims to reason about a variety of possible testing contexts (with different orders of generation, different batches of competitors, and different previously accepted beliefs). What are her resources? Given the aim for epistemic responsibility, she only needs to reason about how the tests would proceed in these contexts if their component individual aims are satisfied. (So no fair meddling demons, meddling angels, and unluckily falling anvils.) And without prejudice, she can use beliefs about what is or isn’t necessarily true or false if the tests proceed as aimed. Here’s how she could responsibly proceed.
             Step One (Generating): Think of some candidate factors—it doesn’t matter how Renée does this … randomly, or exhaustively, or by focusing on necessarily semantically relevant dimensions characterizing all or many candidates.
            Step Two (Minimal Testing): For each candidate factor F, consider a minimal testing context in which F is the only generated factor, tested alone. There are three “basic” candidate aims about how candidate factor F applies (overall, or at first):
            F_Virtue = F raises scores;
            F_Vice = F lowers scores;
            F_Neutral = F doesn’t affect scores.[18]
Score these aims by whether under the minimal conditions they necessarily insure or preclude responsible coverage, discrimination, or stability (of belief). F_Neutral’s score is lowered because in the absence of other factors, it (necessarily) precludes (responsible) discrimination. Accepting F_Neutral in this context would leave Renée without any way to pull apart the scores of competing beliefs. So if either F_Virtue or F_Vice outscores the other, it wins this three-way competition, so F is provisionally acceptable as a scoring factor in the minimal testing context.

             Step Three (Robust Testing): For each provisionally acceptable factor F from Step Two, consider whether F would be robustly acceptable in more elaborate testing contexts, especially when other surviving factors have been previously accepted (so the aim of having some scoring factor does not automatically lower F_Neutral’s score), when F itself has been previously accepted, or when F is considered not alone but in competition or in conjunction with other factors. Strengthen or weaken acceptance of F to the degree it is or isn’t robustly acceptable.

             Step Four (Contingent Testing and Iterating): Start the search for (more of the) Truth (i.e., the aggregation of subsearches for incomplete truths), if at some point enough provisional scoring factors are in place to enable some contingent candidate beliefs to be provisionally accepted over competitors. Adjust the factors accepted in the metasearch as may be required in light of the ongoing search (and the provisional metasearch). This could be done by generating new candidate scoring factors (as in Step One), then by considering nearly minimal testing contexts (as in Step Two, except that the new candidate scoring factors are tested one‑by-one in the context of Renée’s actual search—her provisionally accepted scoring factors and provisionally accepted beliefs), then by testing robustness of the scoring factors within this provisionally growing context (as in Step Three). Renée has no need to halt her metasearch until she halts her search; the two can run in parallel. All that’s required to start the search are provisional, rather than final, results from the metasearch.

  

IX.  AIMING FOR STABILITY

 

            Renée’s aim for Belief-Stability is an aim that at some point a perfect or best (discriminating) score for a candidate belief halts the (sub)search, or remains higher than any subsequent competitor’s score. Here is how she can use this aim to give purely epistemic (provisional) support to some more-or-less familiar candidate virtues often considered to be merely pragmatically supportable, at best.

SIMPLICITY (Aim 18)

             Step One (Generating): Renée would not responsibly satisfy her aim for necessarily semantically relevant scoring factors by scoring beliefs according to abundance of spatiotemporal parts or other intrinsic physical features. But she might responsibly satisfy this aim by scoring beliefs according to abundance of some kind of semantic “parts” or determinants. What sort of determinants could a belief have that necessarily affect its content (in a way that potentially affects its truth or falsity)? She might get the idea of scoring a belief in terms of its amount of involved concepts, conjuncts, or disjuncts. Beliefs do have different contents if determinants such as these have different contents. However, one problem is that amount of conjuncts and disjuncts can be varied without varying content: e.g., Renée’s (candidate) belief that p is equivalent to her belief that p and (p or q), or her belief that p or (p and r) or (p and s). Perhaps this can be avoided by counting only mutually independent conjuncts and mutually independent disjuncts. Another problem is that amount of involved concepts can be varied without varying content: Renée’s belief that o is a square may be equivalent to her belief that o is an equilateral rectangle, but the former may involve more concepts than the latter (if her concept square involves these other two concepts but not vice versa). Perhaps this can be avoided by counting only her most basic concepts; ones that do not involve other concepts, as her concepts are organized.[19] For brevity, let’s lump all these considerations under the label “simplicity”—a candidate belief (or group of beliefs) is simpler the fewer basic concepts it involves and the fewer mutually independent conjuncts/disjuncts it involves.[20]

             Step Two (Minimal Testing): In the minimal testing context, a basic aim of treating complexity as a virtue (or in other words, treating simplicity as a vice) would preclude responsible stabilizing. Suppose Renée were to raise the scores of more complex competitors. Then her (sub)search would never responsibly stabilize, since for any candidate there is always a more complex candidate, a candidate involving more (uses of) basic concepts or more conjuncts or more disjuncts. If it does stabilize, it does so merely “luckily”, e.g., if Renée is hit by an anvil, or if her generation phase illicitly excludes the more complex candidates in a prejudiced way.[21] So Complexity_Vice (or in other words, Simplicity_Virtue) wins, provisionally. (Recall that a scoring factor F is ideally robust enough to be supportable in a minimal testing context, and F_Neutral can only be competitive in a minimal testing context if neither F_Vice nor F_Virtue outscores the other.)[22]^,[23]

 PARSIMONY and ANALOGY (Aims 19-20)

             Step One (Generating): By definition, a (candidate) belief that p is “committed” to particular contingent entities or kinds of entities E such that, necessarily, E exists if p. Renée might responsibly satisfy her aim for semantic relevance by considering amount of such commitments as scoring factors.[24] Also, a belief (or group of beliefs) has greater “parsimony” the fewer particular entities it is committed to.[25] And the fewer kinds of entities a belief (group) is committed to, the greater “analogy” it exemplifies—the more similar to one another are the particular entities it is committed to.

             Step Two (Minimal Testing): Parsimony is provisionally acceptable as a virtue for reasons similar to simplicity. Raising the scores of less parsimonious competitors precludes stabilizing (since there is always a way to “multiply entities” further) unless Renée gets lucky. So Parsimony_Virtue wins. In the same way, rewarding candidates for positing more “kinds” of entities, laws, or processes (etc.) is also a never‑stabilizing method (barring luck). So (provisionally) the more analogous to one another the posited entities, laws, or processes, the better.[26]

 CONSERVATISM (Aim 21)

             Step One (Generating): Given an old belief and a new candidate belief, whether they match in content is of course necessarily fixed by their contents. So Renée might satisfy her aim for semantically relevant factors by scoring candidates according to amount of matching with previous beliefs. A candidate belief with the same content as a previous belief is “conservative”. And a group of candidate beliefs is more conservative the more contents it shares with previous beliefs.

             Step Two (Minimal Testing): The minimal testing conditions in Step Two cannot quite test conservatism; for conservatism can be treated as a vice or a virtue only when there is a previous belief. But Renée can still test conservatism in an unprejudiced way by imagining a testing context in which she has previously accepted an arbitrary contingent belief that p, subject to two provisos for avoiding prejudice. She must suppose she has accepted the belief that p without prejudice (minimally, as a result of prior testing) and she must not use any features specific to p in testing conservatism (e.g., p should not itself entail whether conservatism is a virtue). In this nearly minimal testing context Renee (re)considers the belief that p along with some rival candidate belief that q (e.g., that not p). Absent any other reasons for choosing one rival over the other, favoring nonconservative (/nonmatching) beliefs over conservative (/matching) beliefs means never stabilizing, but instead oscillating forever between believing that p and believing that q, unless luckily hit by an anvil. (First the belief that q would be the nonmatching belief, then after it is accepted the belief that p would be the nonmatching belief, then the belief that q again, etc.) So Conservatism_Virtue wins in the nearly minimal testing context.[27]

             Step Three (Robust Testing): Though conservatism is supportable in minimal testing conditions, it doesn’t fare well in the context of the other provisional scoring factors. Renée considers a context in which simplicity (alone) is previously accepted as a virtue, and she considers adding conservatism as a scoring factor. The three candidate aims Conservatism_Virtue, Conservatism_Vice, and Conservatism_Neutral seem equally simple—as do the three corresponding beliefs, one for each aim, that it should be accepted. Conservatism_Vice would still preclude responsible halting, as in Step Two, but this is no longer sufficient to support Conservatism_Virtue, because Conservatism_Neutral’s score is no longer lowered (since Renée already has a scoring factor). So Renée should weaken her acceptance of conservatism as a virtue (but without increasing any inclination to treat conservatism as a vice).[28]

 

X.  PROSPECTS FOR RENÉE’S SEARCH

 

            I leave open which other scoring factors, if any, Renée can provisionally accept, prior to her search for contingent truths. These depend on her ingenuity (if any) in generating candidate factors (subject to constraints such as semantic relevance), on the impact (if any) of Coverage and Discrimination as well as Stability, and on the existence of further Specs (if any) derivable from her root aims. But since ideas for such elaborations are scarce, I will end by illustrating how Renée’s search might proceed given what has been supported so far.

 UNIFICATION AS EXPLANATION

             Simplicity, conservatism, and kin are typically cast as criteria to be used in inference to the best explanation. But they are supportable independently of aims for explanation. Renée can treat them as criteria to be used in inference to best beliefs, whether or not these have “explanatory power”. If explanatory power is a virtue at all, perhaps it is a merely contingent virtue (to be supported as Renée aggregates contingent truths).

             Or perhaps some form of explanatory-power virtue is derivable from the provisional virtues above. For example, suppose Renée has a group of independent old beliefs, o in number. And suppose she considers a group of independent new beliefs—n in number—from which the old beliefs can be deduced. If n is less than o, accepting the new beliefs is a way of reducing the conjunctive simplicity of her overall theory. Though the number of beliefs increases—by n, or by even more if the new beliefs have further new entailments—this is not relevant to measuring simplicity. More relevantly, the number of independent beliefs decreases—from o down to n. The old beliefs have been “unified” by the new beliefs, and such unification is often considered a key to explanation. This process of unification, in pursuit of the aim for simplicity, is Renée’s key hope for being able to introduce concepts and beliefs that “go beyond” her initial concepts and beliefs.

CANDIDATE BELIEFS AS DATA 

            Renée avoids prejudice by avoid prejudging contingencies beyond self-directed “I think p” beliefs. She can start with beliefs about necessities and possibilities, and self-directed beliefs about these beliefs. But where p is contingent (and not itself of the form “I think q”), Renée doesn’t initially form the belief that p and so doesn’t initially form the belief that she believes p. However, she may without prejudice initially form the candidate belief that p, and so the genuine belief that she has a candidate belief that p. Ultimately, this is her only source of “data”.

             Her key hope for going beyond this data is to find distinctive groups of such data that can be unified by theoretical candidate beliefs. If she generates all possible candidate beliefs at once, or generates each through a method of reasoning of which she is already aware, then perhaps she will not be able to find such groups. But if some of her generation processes are partial and spontaneous instead, perhaps she will. She must hope to unify (or in a sense, explain) why she most frequently or readily considers candidate beliefs with such contents, why her candidate beliefs are similar and different in these or those ways. Maybe her spontaneous patterns of candidate beliefs are products of reliable perception, and maybe they’re products of unreliable seances or Tarot or dreams or demonic meddling. A method that automatically accepts all spontaneous beliefs seems prejudiced, as does a method that automatically discriminates some from others for acceptance, but a method that automatically rejects all of them prevents Renée from going beyond her starting point at all. May the most virtuous hypothesis win.[29]

 EVALUATIVE TRUTH

             Renée’s epistemic reasoning is filled with evaluations, beliefs about which candidate aims and beliefs she should accept. But these are all hypothetical evaluations, evaluations made true in part by her basic aim for Truth. From her starting point, without prejudice, can she reach justified categorical evaluative beliefs, evaluative beliefs that are true no matter what aims are in place? If Renée’s only data are her beliefs about which candidate beliefs she has, then she has no categorical evaluative beliefs as data (even if some of her candidate beliefs are themselves categorically evaluative).[30] Perhaps categorical evaluative beliefs can help explain (or at least unify) her nonevaluative beliefs about which candidate beliefs she has, but at the moment Renée can’t think of how they might (or how they might do so better than nonevaluative competitors). So suppose she has no “data” relevant to justifying categorical evaluative beliefs.

            It might appear that she is stuck. But this is one place where it matters that her provisional method is that of general inference to the best beliefs rather than specific inference to the best explanation. Her aim isn’t for accepting the most virtuous available belief that might explain or unify data. It’s to accept the most virtuous available belief, period. If no candidate evaluative beliefs unify any data, they are all in effect tied at unifying zero data, so this “other thing” is “equal” and the candidates can be scored using the other factors. Of competing categorical evaluative beliefs that equally explain nothing, she should accept the simplest (or most parsimonious or analogous).

             Immediately (but as always, provisionally), simplicity favors “universalist” evaluative beliefs over “particularist” ones. For example, “everyone should do no harm” trumps “everyone should do no harm to white people, but should do harm to black people” … and similarly trumps other corresponding principles of racism, sexism, ageism, patriotism, religionism, speciesism, etc., as well as egoism. It also trumps relativism of the “weak people but not strong people should do no harm” sort. Whatever their intuitive or pragmatic repulsion or allure, these particularist evaluative views are provisionally epistemically irrational in the same way as beliefs in invisible leaf-blowing leprechauns; they present a cost in simplicity (or parsimony) without presenting a gain in explanation (or unification). Problem is, simplicity alone does not favor one universalist principle over another. Why shouldn’t everyone do no help rather than doing no harm?

             Suppose Renée considers these three candidate universalist evaluative beliefs:
            (A) Ideally, every aim should be satisfied.
            (B) Ideally, some aims should be satisfied and others should be frustrated.
            (C) Ideally, every aim should be frustrated.
Candidates (A) and (C) seem simpler than candidate (B), but equally simple to one another. However, (C) seems to harbor a paradox in a way that (A) does not. If that air of paradox can be spun into a reason to reject (C), then (A) is supported.

             The paradox is formal if, as seems plausible, an evaluative belief that X should exist is itself an aim for X (see note 3 for this suggestion). In this case (C) is an aim that every aim be frustrated, which when applied to itself would require its own frustration. An aim for X that requires its own frustration is a self-contradictory aim against X. And when that aim is an evaluative belief that X should exist, it is a belief entailing that X should not exist. So (C) is a self‑contradictory belief entailing that not every aim should be frustrated. (C) cannot be true, so (A) wins.

             Once Renée reaches belief (A), it itself becomes evaluative “data” subject to explanation (or unification). Why is universal aim-satisfaction ideal? Suppose Renée considers these three candidate evaluative hypotheses:
            (A1) Each aim should be satisfied (so in the aggregate, all should be).
            (A2) Some aims should be satisfied, others are neutral (so the aggregate goes above and beyond “duty”).
            (A3) Only the totality of aims should be satisfied (so the ideal is all-or-nothing).
(A1) is simpler than (A2) and (A3), in not drawing distinctions among aims. It also explains (A) in a way that is most analogous to the way basic universal facts are explained in the nonevaluative realm. The totality of mass is subject to gravity because each bit of mass is subject to gravity, not because gravitation is partial or all-or-nothing.[31]

             When aims conflict, which aims should be satisfied? Traditional utilitarian theories would appeal to some notion of  aim “strength”, but Renée doesn’t yet see any way to support this: e.g., “stronger aims are more important” seems no more simple than “weaker aims are more important”. Instead, she applies the conflict resolution procedure latent in (A1): if each aim should be satisfied, then the more aims that are satisfied, the better. Squashing a roach, or picking a grape before its time, might frustrate a few aims of the roach or the grape. For all we know, those aims may be extremely strong (it is life or death for the roach and the grape, and the roach is intensely singleminded if minded at all). Psychologically more complex beings have more aims that would be frustrated by killing them, so (A1) favors the life of a psychologically more complex being over the life of a psychologically simpler being, intensity or strength aside. But the interests of groups of simpler beings could outweigh the interests of a more complex being.[32]

             So (A1) is where Renée gets, provisionally, when she tries to think about evaluative matters from scratch, without prejudice, and without relying on potentially demon-induced evaluative “intuitions”. As her methodological metasearch and nonevaluative search develop, she might be led elsewhere. Maybe new beliefs about basic nonevaluative facts will open up new analogies that favor other basic evaluative facts. Maybe a version of conservatism friendlier to intuitions will turn out to be supportable. Maybe she will reach a contingent belief that certain thinkers’ judgments are signs of truth across the board, and maybe they will happen to counsel against (A1). Meanwhile, you might aim to stay away from her. But I expect she’ll be preoccupied by Seeking Truth for too long to do you any harm.