Covid-19, Bayesian Probability, and Kantian Ethics

Here’s something I wrote with an advanced or motivated undergraduate audience in mind: I Have a Sore Throat: am I going to die?I started it in mid March. Brings a lot of stuff about evidence, probability, and ethics that I’m interested in to bear on early pandemic decision making. I was intentionally short with everything, sort of just trying to entice interest by connecting broad philosophical issues together as they pertain to current events. Includes stuff on probability, evidence, the universalizability constraint, and internalism/externailism in epistemology. I would welcome comments and would be flattered if anyone shared with their students.

Alito on the death penalty, and deontic logic.

In a 2015 death penalty case Alito wrote: “Because it is settled that capital punishment is constitutional, [i]t necessarily follows that there must be a [constitutional] means of carrying it out.” I think Alito’s reasoning is formally incorrect.

e = We execute Jones.
p = We cause Jones excruciating pain.

Suppose it is a brute fact that if we execute Jones then we cause Jones excruciating pain: ie, e \rightarrow p.

Introduce PE as a deontic operator for “it is constitutionally permissible that” and OB for “it is constitutionally obligatory that.” These should function as a deontic operators in standard deontic logic (SDL). Alito’s claim is that the following is an inconsistent triad: \{ PE(e), \neg PE(p), e \rightarrow p \}

These would be inconsistent if \neg PE(p), e \rightarrow p \vdash \neg PE(e).

What would an argument for this look like. Maybe the following:

1. \neg PE(p) assumption
2. e \rightarrow p assumption
3. PE(e \rightarrow p) from 2, deontic logic
4. PE(e) \rightarrow PE(p) from 3, deontic logic
5. \neg PE(e) from 1 and 4, modus tollens

I suppose we might have to grant that brute facts must be permissible: ie that step 3 is valid. PE(e \rightarrow p) is true because p \rightarrow e is true in the actual world and hence must be accepted as permissible.

But I don’t think that step 4 is valid. Supposing we grant that P(e) is true, this just means there’s some normatively admissible world, maybe some world where all feasible means of execution does not cause excruciating pain, maybe not the actual world, where e is made true by our action. This is consistent with there being no normatively admissible world where p is made true by our action, including the actual world.

Maybe the thought is that the derivation should go like this:

1. \neg PE(p) assumption
2. e \rightarrow p assumption
3. OB(e \rightarrow p) from 2, deontic logic
4. OB(e) \rightarrow OB(p) from 3, deontic logic
5. PE(e) \rightarrow PE(p) from 4, deontic logic
6. \neg PE(e) from 1 and 5, modus tollens

The reason for doing this is to try to use the distributivity of \rightarrow OB$ (analogue of modal S5) to get get around the problem of the non-distributivity of \rightarrow PE$ in the failed der(a), and into a position to do the modus tollens Alito desires. There is a rule of SDL that says that if a proposition is a theorem then it is obligatory. Maybe this could be used to justify step 3. This would be a mistake; e \rightarrow p is not a theorem. Also, I think that the step from 4 to 5 would be invalid. It would work if  \vdash PE(e) \rightarrow  OB(e) and \vdash OB(p) \rightarrow PE(p), but the former is clearly not a theorem.

If I’ve got this right, I’ve really only shown that two attempts to reconstruct Alito’s thinking are dead ends. This doesn’t show that there is no valid reconstruction, but to me it doesn’t look promising. Alito seems to have confused the condition of there being some normatively permissible world in which e is made true by our action with the condition that the actual world must be a normatively permissible world in which e is made true by our action, but the latter condition is precisely what is made false if the only actual means to e is p and \neg PE(p).

Descartes and the Problem of Error


There is, outside of Plato’s works, perhaps no philosophical work more familiar to the educated public that Descartes’ Meditations on First Philosophy. It is something of a rite of passage to go through the experience, annoying to some and mind-blowing to others, of watching your professor stare at his hands wondering aloud whether they really exist. It is the first meditation, with its emphasis on methodological skepticism that is remembered, and the epistemological project of Cartesian reconstruction that is emphasized. The modern turn in philosophy, on this reading of Descartes, is distinctively epistemological. Accordingly, we are directly acquainted with appearances and ideas, which are mental items, and we must reconstruct, in a way consistent with the constraints of methodological skepticism, our knowledge of the external world and of other minds on an inferential basis. Descartes on this traditional picture is a “Veil of Appearances” philosopher, and his fundamental problem is the epistemological challenge of lifting the veil. If we remember the second or third lecture on Descartes from our undergraduate skeptical hazing, we may recall the Cartesian Circle problem as a fundamental challenge to the project of reconstructing our common-sense knowledge on the basis of appearances and ideas.

This is a familiar and very fun way to read Descartes. It introduces the students to challenge of skepticism, which the mind-blown cohort at least will find simultaneously disturbing and intellectually invigorating, and it affords middle-aged professors the opportunity to date themselves by talking about Total Recall and The Matrix. However, in recent years some scholars have come to question whether the standard epistemological reading of Descartes’ Meditations well captures the author’s intended reading. In this essay, I read Descartes as responding to an argument which I term the “Problem of Error.” I’m not making an historical, scholarly claim about what were in fact Descartes’ most central concerns, just suggesting an interesting reading of the text that centers on the sometimes neglected Meditation IV.

The Problem of Error can be understood as an atheological argument on analogy with the familiar Problem of Evil, and with this analogy in mind it is straightforward to read the fourth meditation, on belief and judgment, as providing a solution to the Problem of Error that is exactly like the familiar free will theodicy. Although they are sometimes presented as such, with the Problem of Error in mind the concerns of the fourth meditation are not an afterthought for Descartes, as they may seem to be on the epistemological reading, but rather they emerge from his social, scientific, and metaphysical context. Descartes’ solution to the Problem or Error involves his infallibilist, antiskeptical epistemology. Accordingly, so long as we stay on the straight and narrow path of clear and distinct ideas, we will never fall into error. I will assess this solution in light of the pattern of scientific of progress since Descartes, arguing that it is unlikely that the path of our groping progress is has been shown by the kind of divine light that Descartes’ “clarity and distinctness” standard was supposed to provide, and compare Cartesian epistemology with ancient skeptical infallibilism and contemporary fallibilist conceptions of knowledge with respect to the attitudes these epistemological programs suggest toward the pervasiveness of error in human life and society.

The Problem of Error

In the Aristotelian scholastic tradition, knowledge (scientia) requires deductive reasoning from absolutely certain first principles. Allowing for disputations over what is deducible, the first principles of the Aristotelian tradition functioned as shared assumptions in the medieval scholastic world. Descartes was an advocate of new scientific ideas that challenged the orthodoxies of Aristotelian science, heliocentrism and mechanism. The new science rejected the first principles of Aristotle. We are not to think that things fall because it is the essence of earthy matter to seek the center of the universe. Indeed, the earth is not the center of the universe. Motion is inertial not intentional. Animate matter is no longer to be distinguished by its possession of an Aristotelian form imparting a vital essences; animals are machines. A scientific revolution, based on the mechanistic conception of the material world, was replacing the Aristotelian framework’s demand for causal explanations that were formal and final, along with material and efficient, with a mechanistic framework demanding only material and efficient causal explanations. The change was momentous beyond our comprehension, and it implied that the greatest minds of the preceding millennia, basing their view of the world on the wisdom of the ancients and the evidence of the senses, were completely in error. How could this be so? And if we were so profoundly wrong once, how can we really expect to be right? What kind of funhouse mirror universe do we find ourselves in?

One might imagine an opponent of the mechanistic revolution arguing as follows:

  1. If mechanism and heliocentrism are true, then we have been systematically wrong for more than a thousand years.
  2. If we have been systematically wrong, then if we are created it is by a deceiver.
  3. Our creator is not a deceiver.
  4. So, by repeated application of modus tollens, mechanism and heliocentrism is false.

Of course, one person’s modus tollens is another person’s modus ponens, and we might equally well imagine, perhaps whispered where enforcers of orthodoxy could not hear, a mechanistic natural philosopher arguing as follows:

  1. If mechanism and heliocentrism are true, then we have been systematically wrong for more than a thousand years.
  2. If we have been systematically wrong, then if we are created it is by a deceiver.
  3. Mechanism and heliocentrism are true.
  4. So, by repeated application of modus ponens, if we are created it is by a deceiver.

I have no evidence that Descartes was responding to any explicit statement of either of these arguments. However, I do think that his Meditations make good sense as a response to the tension between the mechanism and traditional theistic Aristotelianism, which is drawn out by this pair of arguments. Together the arguments, if their shared premises 1.a/b and 2.a/b are accepted, would show that we must either reject the new mechanistic physical science or come to the conclusion that God doesn’t exist or is a deceiver. Descartes does not want to accept either of these conclusions. Premise 1.a/b however is clearly true. Therefore, Descartes must reject premise 2.a/b by explaining how we could have been so wrong for so long and yet be created by a God who is not a deceiver. This is the purpose of Meditation IV.

I have so far characterized Descartes project as largely responding to the mechanistic revolution in science and its implications. And, indeed, in his early thirties Descartes had written a book, Treatise on the World and Light, expounding a heliocentric astronomy and mechanistic physics. The book was completed in 1633, the same year that Galileo’s Dialogue on the Two World Systems was placed on the Index of Forbidden Books and Galileo was charged with heresy. Descartes delayed publication of his book, and material from it was only later revised and published in a different book. It’s no crude speculation to think that he would have been very interested in how, from his point of view, the truth could come to be declared heresy.

However, the question of the source of error may not have been of a purely scientific character for Descartes. Descartes was alive during a time of warfare and strife. For most of his life, the Thirty Years War raged, initiated by Holy Roman Emperor Ferdinand II attempt to reassert Catholic hegemony. Subsequently, the European powers, each pursuing their perceived interests, could not seem to find peace. Although the war was not strictly a religious war between Catholic and Protestant, Catholic France for instance supported Lutheran Sweden against the Catholic Ferdinand II, the conditions for conflict were set by theological divisions, over which some party certainly was in error, and the conflict was exacerbated by erroneous diplomatic and military judgments. Then, as now, the idea that a great deal of human strife is caused by well-meaning errors would have pressed itself upon the observer of world affairs.

This view, that error is the cause of strife, is not expressed in an articulated Cartesian political philosophy, however, because Descartes never articulated a political philosophy. Descartes’ philosophy is generally regarded as asocial and apolitical. The meditator is solitary, in his study, reflecting inwardly. Contemporary philosophers who are interested in ‘social epistemology’, an inquiry based the view that knowledge and justification are social phenomena, contrast their approach with the asocial epistemology of Descartes. In Descartes’ letters to his friend Princess Elizabeth of Bohemia, the mathematician, philosopher, diplomat, and eventual abbess, he disavows interest in politics and defers to her judgment when she seeks his advice on diplomatic affairs. Elsewhere he argues for very conservative views, that politics should be left to appointed rulers, namely kings (There’s not a lot written on Descartes’ political views. I read Quentin Taylor’s “Descartes’ Paradoxical Politics”). I would argue that Descartes’ silence on politics, however, supports my view that he held that error is the cause of strife. His suspicion of populist reformers and the diversity of opinion in politics reflects the view that political engagement tempts us to form opinions that extend beyond our ken, beyond what we can clearly and distinctly perceive to be true. It is enough that rulers should be tempted into error in the relations between states, causing strife, an opinionated populace could only bring about internal strife and civil war. Hasty judgment has something like the tempting status of sin for Descartes; popular democracy, then, besides being a pretty alien idea, may have seemed like something of a brothel to him.

It is useful in this connection to compare the view that I am attributing to Descartes, which in its strongest form could be stated as the view that error is the root of all evil, with Hobbes’ more explicitly political philosophy. For Hobbes, the connection between epistemology and metaphysics and political philosophy is fully articulated in De Corpore and Leviathan. Writing after the bloody, awful English civil war, Hobbes argues that by making certain epistemological mistakes we can be lead into nonsensical metaphysical views over which the body politic can be divided, think especially of controversies over religion, undermining secular authority and creating strife and civil war. According to Hobbes, if we reason correctly and sensically, we will be materialists, reach proper conclusions about human nature, and accept secular political authority out of rational self interest. Error for Hobbes comes in the guise of nonsense, and sound philosophy (empiricist, nominalist, and materialist) is the cure.

The Hobbesian system is entirely motivated by the pressing observation that error is a great cause of strife. I maintain that Descartes’ epistemology and metaphysics are similarly motivated, though his solution is far different. For one, Descartes thinks that a lot of what Hobbes categorizes as nonsense, namely the category of immaterial substance, is perfectly sensible, and indeed clear and distinct. Adopting a broadly empiricist stance, Hobbes aims to strike the root of evil at the connection between language and meaning. Descartes, on the other hand, strikes at the will to believe, locating error not in the understanding but rather in judgement.

Descartes is clearly worried about a broader “Problem of Error” objection to theism. In Meditation I he states his project: to rid himself of error by refounding his beliefs only on what cannot be doubted. He allows himself to doubt even arithmetic, because maybe an evil genius is messing with his mind, or maybe God has made him with a flawed nature so that he is constantly forming erroneous judgments even about the simplest matters, but then he writes:

“And, besides, as I sometimes imagine that others deceive themselves in the things which they think they know best, how do I know that I am not deceived every time that I add two and three, or count the sides of a square, or judge of things yet simpler, if anything simpler can be imagined? But possibly God has not desired that I should be thus deceived, for He is said to be supremely good. If, however, it is contrary to His goodness to have made me such that I constantly deceive myself, it would also appear to be contrary to His goodness to permit me to be sometimes deceived, and nevertheless I cannot doubt that He does permit this.” (Descartes Med I)

The passage betrays a deep anxiety about error, and shows a social dimension to Descartes’ epistemology. The meditator’s self examination is motivated in part by a requirement to hold herself to the standard to which she holds others. But will this lead to radical skepticism? The solution offered in the following meditations is foreshadowed. I must identify a standard to guarantee the truth of my simplest judgments, and hold myself and others to this standard. However, a problem is anticipated. If there is such a guarantee, then why so much error in the world? The answer to this question will show why Descartes rejects premise 2.a/b. In rejecting premise 2.a/b, Descartes will have to explain how it is consistent with God’s goodness that we should sometimes be deceived.

Descartes’ Error Theodicy

As I have suggested, there is a strong analogy between the Problem of Error that I regard Descartes as responding to and the more familiar Problem of Evil. The Problem of Error asks the theist to answer the question, in brief, “If we are created by God, then why are we so prone to error?” while the Problem of Evil asks, in brief, “If we are created by God, then why are we so prone to evil?” Indeed the problems are related. For, one widely accepted response to the problem of evil states that we are prone to evil because God gave us free will and we choose evil over good. This may be the case, but it raises the question why anyone would freely choose evil over good. Have we been made to desire evil? If so, isn’t this a defect in our nature that is the fault of our creator rather than ourselves? Again, why would anyone freely choose evil? Perhaps selfishness is explanation, but then they are not choosing evil, in the sense that their act aims at evil. They are choosing good, aiming at a good for themself and disregarding the good of others. Furthermore, selfishness does not seem a fully adequate explanation. For, often we choose actions that are not even good for ourselves. Selfish acts may be a case in point, as often they enhance our welfare in the short term at the expense of our reputation, relationships, and long term well being. According to one philosophical tradition, tracing to Socrates and continuing through Thomas Aquinas, the will necessarily aims at the good and our freedom consists in our ability to reason about what is good and to guide our actions according to a long term plan for well-being rather than responding to immediate stimuli. Accordingly, if we do choose evil, despite necessarily willing the good, it should be because of an error in our judgment. Following this line of thinking, an answer to the Problem of Error is required to provide a fully adequate free will theodicy. This is what Descartes provides in Mediation IV.

Descartes response to the Problem of Error is deeply engaged with scholastic, Catholic philosophy from Augustine onward. Before describing error theodicy, however, it will be well to note that Descartes does not see the need to provide a theodicy in order to block the logical inference to atheism. Adopting the Augustinian position that an apparent defect in a part of creation does not imply a defective whole, together with the position that an understanding of the whole of creation is inaccessible to finite minds, Descartes infers that there is no logical Problem of Evil or logical Problem of Error. Each problem poses a “why?” question, and it is possible that there are reasons beyond our ken.

“In considering this more attentively, it occurs to me in the first place that I should not be astonished if my intelligence is not capable of comprehending why God acts as He does; and that there is thus no reason to doubt of His existence from the fact that I may perhaps find many other things besides this as to which I am able to understand neither for what reason nor how God has produced them.”

However, Descartes does not rest with this “skeptical theist” response, and indeed only mentions it after beginning to develop a positive theodicy. The shortcomings of this response are worth noting. While it is true that skeptical theism blocks the logical Problem of Evil/Error as an argument for atheism, it does not imply that a philosophical theist should not hope to benefit from a deeper understanding. A philosophical theist, practicing natural theology, hopes to know something of God’s nature and man’s relation to God from observations of our world. The observations of evil and error should be included in the data to be explained. Furthermore, the philosophical theist should hope that a deeper understanding of evil and error can be gained from providing a positive theodicy, and that this understanding will assist us in avoiding evil and error. This is surely Descartes’ goal, and although we are finite and must acknowledge there are purposes we may not understand, this should not deter us from seeking understanding where it is in fact possible.

Again, following in the Augustinian tradition, Descartes’ account of error is based on a theory of privation of good, rather than actual existence of evil. Prior to his conversion to Christianity, Augustine followed the ancient Manichaean religion, according to which the universe was a site of struggle between a good and evil deity. The philosophical insight, according to Augustine, that lead to his conversion to a monotheistic religion was that it was possible to explain evil without evil actually existing. The idea can be understood on analogy with the relationship between darkness and light. Darkness is real, in a sense, but it does not exist. Darkness is only the absence of light. Accordingly, evil is real, but it does not exist. It is only due to the absence of perfect goodness in created things such as ourselves. In The Enchiridion Augustine writes:

“All of nature, therefore, is good, since the creator of all nature is supremely good. But nature is not supremely and immutably good as is the creator of it. Thus the good in created things can be diminished and augmented. For good to be diminished is evil.”

Following Augustine’s rejection of Manichaeism and insistence that a good creator only creates good, if our creator is good then our nature must be good, and if, as Descartes believes, our nature consists in our capacity for rational judgment, then our capacity for rational judgment should be good. That is, our rational nature should not be such as to lead us into error. That is, we should not have a faculty whose purpose is to produce false beliefs. We may have a faculty of judgment whose purpose is good, to produce true beliefs, but which is incompletely good. Descartes lays out his Augustinian strategy as follows:

“And it is true that when I think only of God [and direct my mind wholly to Him], I discover [in myself] no cause of error, or falsity; yet directly afterwards, when recurring to myself, experience shows me that I am nevertheless subject to an infinitude of errors, as to which, when we come to investigate them more closely, I notice that not only is there a real and positive idea of God or of a Being of supreme perfection present to my mind, but also, so to speak, a certain negative idea of nothing, that is, of that which is infinitely removed from any kind of perfection; and that I am in a sense something intermediate between God and nought, i.e. placed in such a manner between the supreme Being and non-being, that there is in truth nothing in me that can lead to error in so far as a sovereign Being has formed me; but that, as I in some degree participate likewise in nought or in non-being, i.e. in so far as I am not myself the supreme Being, and as I find myself subject to an infinitude of imperfections, I ought not to be astonished if I should fall into error.” (Med IV).

Some constraints on the Cartesian error theodicy should now be apparent. We should have an account over error and its consequent evils that appeals only to the incompleteness of otherwise inherently good faculties. Descartes describes the will as the power to “affirm or deny, to pursue or shun”, and if this power were such that in exercising it I would knowingly choose evil or falsehood it would not be an inherently good faculty. By its nature, the will desires the good and the true, and for it to be any other way would render evil and error incomprehensible. Moreover, Descartes argues at length that this nature is in a sense binary. The will either does or does not seek the good and the true. There is no possibility of degrees. Hence the source of error cannot be located in the will alone. Similarly, the understanding alone should not be a source of error. In fact, Descartes argues that the understanding cannot be a source of error. For, error presupposes that a judgment has been made, but the understanding alone, though it may contemplate ideas, forms no judgments. A judgment comes when the will affirms an idea under contemplation by the understanding. This is a subtle point, but one that can be well understood if we reflect on the difference between entertaining a hypothesis and affirming the truth of a hypothesis. So long as we only entertain hypotheses and ideas, we cannot have false beliefs because we affirm nothing. Unlike the will, the understanding, on Descartes account, admits of degrees of perfection. For instance, we do not have ideas of all things:

“For by the understanding alone I [neither assert nor deny anything, but] apprehend the ideas of things as to which I can form a judgment. But no error is properly speaking found in it, provided the word error is taken in its proper signification; and though there is possibly an infinitude of things in the world of which I have no idea in my understanding, we cannot for all that say that it is deprived of these ideas [as we might say of something which is required by its nature], but simply it does not possess these; because in truth there is no reason to prove that God should have given me a greater faculty of knowledge than He has given me; and however skillful a workman I represent Him to be, I should not for all that consider that He was bound to have placed in each of His works all the perfections which He may have been able to place in some.” (Med IV).

Furthermore, although it is not noted in this passage, some of the ideas we have are incomplete representations of their objects, unclear and indistinct, owing to the nature of the mind’s connection to the material world through spatially situated sense organs, which affords only perspectivally distorted sensory representations. Why this is so, and how we can correct these distortions by employment of our more clear and distinct idea of extended, material substance and the associated science of geometry is the subject of Meditation V.

According to Descartes, the source of error does not reside in either the will alone or the understanding alone, but in the relationship between them. Because the will is complete and unbounded in its desire for goodness and truth, it is subject to over-reach. In the case of error, this over-reach consists in affirming the reality of unclear and indistinct ideas. For instance, employing an example given to illustrate a point in Meditation III, I may affirm that the sun is the size of my thumb because the representations of my thumb derived from my sense organs are unclear and indistinct. Now, in fact, the silliness of making this affirmation is manifest to everyone, which goes to show that we are readily able to correct for the distortions inherent in perspectival perception. However, in more complex cases we can fall into this error very easily, as the mistaken impression that the earth is fixed and the sun in relative motion shows.

Descartes, having discovered in Meditation II the criterion of clarity and distinctness through the contemplation of his knowledge of his own existence, argues that by restraining the will we can stay on the straight and narrow path of truth. He is not immodest in the concluding remarks to Meditation IV:

“I have not gained little by this day’s Meditation, since I have discovered the source of falsity and error. And certainly there can be no other source than that which I have explained; for as often as I so restrain my will within the limits of my knowledge that it forms no judgment except on matters which are clearly and distinctly represented to it by the understanding, I can never be deceived; for every clear and distinct conception is without doubt something, and hence cannot derive its origin from what is nought, but must of necessity have God as its author—God, I say, who being supremely perfect, cannot be the cause of any error; and consequently we must conclude that such a conception [or such a judgment] is true. Nor have I only learned today what I should avoid in order that I may not err, but also how I should act in order to arrive at a knowledge of the truth; for without doubt I shall arrive at this end if I devote my attention sufficiently to those things which I perfectly understand; and if I separate from these that which I only understand confusedly and with obscurity. To these I shall henceforth diligently give heed.”

There is much to recommend in the resulting Cartesian ethics of belief. Imagine for a moment a world in which we all, fearful of propagating error and causing the consequent evils, refrained from sharing memes and news on facebook without first subjecting them to the utmost scrutiny. Would adherence to this standard cure the body politic of some of the viruses infecting our discourse? Imagine a world in which the avoidance of error that results from the misuse of our faculties was as great an anxiety as is the avoidance of sin. The standard is very high, and one wonders whether, if we refrained from believing anything of which we are not certain, we should believe anything at all. If I didn’t share anything on facebook unless I could prove that it was not created by an evil demon (or Russian spy), would I share anything at all? Should we, perhaps, find tranquility in this world of strife only by extinguishing our beliefs, as the ancient Pyrrhonian skeptics advised? “Don’t read the comments” goes the popular advise. Perhaps one ought only to read the comments in order to employ the Modes of Agrippa in trolling others, with the goal of thereby eliminating their own beliefs.

I have suggested that there may be a Cartesian suspicion of democracy motivated by the recognition that political passions render us especially prone to hasty judgment based on hazy impressions, but ultimately Descartes thinks intellectual elites need not embrace Pyrrhonism, and so he needs a positive account of how infallible justification is possible after all. This standard of clarity and distinctness is therefore integral to Descartes error theodicy, and we should say a bit more about the role it must play for him. When an idea has the mark of clarity and distinctness that mark must be subjectively accessible upon reflection, so that it can be used as a guide to avoiding error, and it must be such as to guarantee the reality of the object corresponding to the idea. Descartes supposes himself to have discovered such a mark in contemplating his own existence, which cannot be doubted even if I entertain the hypothesis that I am being systematically deceived by an evil genius. This mark is also supposed to apply to my idea of God, and this is the foundation for his proof of God’s existence in Meditation III. Finally, my possession of clear and distinct ideas is supposed to guide my theoretical reasoning about the material and mental worlds and the relationship between them.

Do we have clear and distinct ideas?

The questions thus arise whether any of our ideas possess the mark of clarity and distinctness which they must have for Descartes’ error theodicy to go through, and whether enough of our ideas have this mark to afford a sufficiently rich set of beliefs under the constraint of a Cartesian ethics of belief. Answering the “any” question would take us into an assessment of the arguments of Meditations II and III. For my part, I find the arguments unconvincing. I do not clearly and distinctly perceive that the self is an immaterial substance or that the premises of the conceivability arguments are true, and I do not clearly and distinctly perceive that an idea with as much objective reality as my very limited conception of God must be caused by an object having infinite formal reality. I’m not even sure I understand the talk of quantities of reality on which Descartes’ ontological argument turns. But I do not intend, in the present context, to go deep into the weeds to establish my views on Meditations II and III, each of which would require a paper length commentary in their own right. So, presently, I will only defend the claim that the standard of clarity and distinctness, if it permits any belief at all, will permit only a very small set of beliefs and would preclude much of the kind of theoretical knowledge that Descartes believed it would allow.

Let us begin with Descartes own beliefs about extended substance. According to Descartes, the new mechanistic science is warranted by the understanding’s clear and distinct grasp of the nature of res extensa, extended substance or matter. In grasping the nature of matter clearly and distinctly, Descartes thought, we can arrive by reason at a vindication of the view that there can be no such thing as empty space, supporting the contention that “nature abhors a vacuum”, known also as the horror vacui thesis. This thesis, incidentally, is partly related to the overall cosmology endorsed in Descartes embrace of Augustinian/Thomistic theodicy. Empty space would, accordingly, be non-existent, but if it is non-existent it cannot be extended. Hence only matter can have extension and all space is full of matter. As a proponent of horror vacui, Descartes opposed the atomistic mechanism of Galileo, favoring instead a plenist corpuscularism. According to this view, all motion and alteration of motion, ultimately all of the purely material properties of the world, were to be explained by appeal to patterns of motion of an all-present plenum of matter, and the cause of a change in motion of one part of the plenum would be explained by pressure on it exerted by a neighboring region with which it was in contact.

This is heavy stuff, but I want to highlight just one component of Descartes view in order to make a broader point about the standard of clarity and distinctness. Descartes thought he knew, clearly and distinctly, that a force could only be exerted on an object by surface contact. This is because he believed that he grasped, through the operation of the understanding, clearly and distinctly the nature of material causation. This view is involved in his rejection the Aristotelian account of gravitation in favor of a mechanistic account. According to the Aristotelian view of causation there were different sorts of material in the world which each had a natural place, and their attraction to that place explained their motion toward it, as if a dropped cup desires to go to its home, the center of the universe. With the rejection of geocentrism, this view was no longer tenable. Descartes came to believe that it was based on a confused application of concepts appropriate to understanding the interaction of mind and matter to the interaction of matter alone, a confused theory embraced by the overeager will. Restraining himself to only what he took himself to clearly and distinctly perceive, Descartes offered a theory of gravitation that appealed to vortices of matter swirling around and pushing the cup downward.

The theory is fascinating, clever, bold, and probably not true. By the end of the 18th century, following Newton, many physicists were willing to accept forces acting at a distance between two bodies, a position that was anathema to the pure mechanism of Descartes. This view, of course, was by the early 20th century replaced with a view that gravitational motion is explained by the curvature of space-time. Notably, this relocalization of the causes of inertial change could have been embraced by Descartes as a sort of vindication, though not of his swirling vortices. Nevertheless, notwithstanding space-time curvature and gravitation, non-locality is now widely accepted by physicists who believe in quantum entanglement. Our intuitive ideas about how matter should behave are widely thought to be radically unreliable at subatomic scales. Even among defenders of locality, few would be so bold to, in light of modern physics, claim that their position is clearly and distinctly perceived to be true.

Descartes’ new foundations for science had preserved much from the Aristotelian ideal of scientae. According to this classical ideal, we have to get the first principles right by applying the standard of clarity and distinctness, and we must proceed inerrantly through deductive methods from there. But Descartes’ new foundations like Aristotle’s old ones faltered and crumbled. Science is messier than scientae. Science involves probabilistic and inductive reasoning, through statistical methods and inference to the best explanation. The philosophy of science involves extensive debate over what counts as a “best” explanation. The philosopher of science Karl Popper claimed that the progress of science occurs through a process of conjectures and refutations. We begin with conjectures that are fascinating, clever, bold, and probably not true, then we subject these conjectures to the tribunal of experience by designing rigorous experiments with the aim of falsification. Those conjectures that survive rigorous testing become candidates for belief, but the basis is always fallible and uncertain. Popper’s vision of science has been challenged in its details by philosophers who insist that no theory can be strictly falsified in the way that Popper imagined, but this only makes things worse for the classical, infallibilist scientae, because, accordingly, we are unable to be certain not only of claims that our theories are true, but also of claims that they are false.

Jamesian Ethics of Belief

If there is nothing, or very little, that we can be certain of, ought we then refrain from all belief? If the overriding norm governing the ethics of belief is to avoid error, then, supposing the lessons from the history of science above, ought we after all join with the ancient skeptics? I think that if we were completely honest with ourselves about the requirement of absolute certainty we would believe very little indeed, and this would include the elimination not just of beliefs about theoretical science, but also dearly held beliefs of many on religious matters, beliefs that guide decision in our personal lives, and beliefs that ought to guide decision in political matters. A standard which forbids belief altogether is entirely useless for the task of setting a standard to which I should hold myself and others. A more useful standard, more suitable to our fallible nature, can be found in William James’s essay “The Will to Believe.” James writes:

“There are two ways of looking at our duty in the matter of opinion–ways entirely different, and yet ways about whose difference the theory of knowledge seems hitherto to have shown very little concern. We must know the truth; and we must avoid error–these are our first and great commandments as would-be knowers; but they are not two ways of stating an identical commandment, they are two separable laws. Although it may indeed happen that when we believe the truth A, we escape as an incidental consequence from believing the falsehood B, it hardly ever happens that by merely disbelieving B we necessarily believe A. We may in escaping B fall into believing other falsehoods, C or D, just as bad as B; or we may escape B by not believing anything at all, not even A.

Believe truth! Shun error!-these, we see, are two materially different laws; and by choosing between them we may end by coloring differently our whole intellectual life. We may regard the chase for truth as paramount, and the avoidance of error as secondary; or we may, on the other hand, treat the avoidance of error as more imperative, and let truth take its chance.”

If we were to walk the Pyrrhonian path of withholding belief where any possibility of doubt could be shown we would perfectly satisfy the aim of “Shun error!” but we would fail completely to “Believe truth!” We could satisfy the demand to “Shun error!” trivially, by having no beliefs at all. At the other extreme, we could satisfy the demand to “Believe truth!” by believing every single proposition. We would necessarily thereby believe the contradictory of every proposition we believe, hence necessarily believing many falsehoods, but we would nevertheless believe all conceivable truths. Jamesian ethics of belief requires that we balance the two extremes. We should be willing to believe and act upon our well tested conjectures, but we should also be vigilant in sussing out sources of bias and error in our thinking. When, for instance, we recognize selection bias and motivated thinking as a source of another’s error, we should reflect whether we have fallen into the same patterns ourselves. Those who know their Aristotle will notice an interesting twist here. The Jamesian ethics of belief directs us to find the mean between skepticism and credulity.


I should have something to say now about whether the Problem of Error is resolvable from the standpoint of a Jamesian ethics of belief. I think that it is, but that the solution will now look more like a soul-building rather than a free will theodicy. James permits us, in a way that is forbidden by Descartes, to take chances in belief, but with this should come certain civic as well as epistemic virtues. If I am convinced, for instance, that I know my beliefs are true beyond all possible doubt, I am equally convinced that I have nothing to learn from unbelievers and that there is no possibility that future evidence should cause me to change my beliefs in the future. We should be very wary of the dogmatism of such true believers. Instead, we should enter the civic arena with a measure of humility and openness that is especially lacking in those who take themselves, often on the basis of accepting a tacit Cartesianism in politics, to have figured out the first principles once and for all. Tolerance of diversity of opinion, responsiveness to evidence, curiosity about opposing viewpoints, ideological flexibility, and favoritism towards adaptable policies are all hallmarks of the virtuous, yet politically engaged believer.

hermeneutical injustice

Work on testimonial and hermeneutical injustice strikes me as an example of philosophy at its most socially relevant, and it’s a topic I’m beginning to work into my Intro to Philosophy course. In this post I just want to share a couple of podcasts I recently listened to that really deepened my understanding of these issues.

The first is an episode of the podcast “Examining Ethics” that looks at the Me Too movement through the lense of testimonial and hermeneutical injustice. The episode contains a nice overview and discussion of both testimonial and hermeneutical injustice. Check out that link to the website

The second podcast is an episode of Radiolab that tells Dana Zzyym’s story. Their story really makes powerfully clear how restricting hermeneutical injustice can be with respect to self understanding. Dana is hermeneutically liberated by the discovery of the concept “intersex” and by uncovering undisclosed facts about their medical history, at the age of 50. They describe the euphoria of “breaking the binary.” The podcast does not use the terminology of “hermeneutical justice” but I think Dana’s story is a very clear case of its liberating power.

Some of the scholarly discussion of hermeneutical injustice has centered around whether the examples given by Miranda Fricker, who pioneered work on the idea, were well chosen and described. Fricker’s discussion centered on the concept of “sexual harassment”, and some commenters criticized her characterization of victims of sexual harassment who lack this vocabulary as not understanding that they have been harmed, or incompletely understanding, or otherwise bewildered. The suggestion that such individuals are restricted in understanding their experience, because dominant conceptual frameworks are descriptively impoverished, fails to recognize the individual and collective agency of oppressed persons and subordinate groups, according to critics. I have read a little in this area (I was asked to comment on a terrific paper by Margaret Owens, a Georgia State grad student, at the Midsouth Philosophy Conference last spring), but not everything, so I hold only tentative views on this criticism; while the criticism does strike me as importantly highlighting various means of hermeneutical resistance, my tentative view is that it depends on an uncharitable reading of Fricker. On a more charitable reading the discussion seems more like a friendly amendment than a criticism.

In any event, what struck me about Dana’s case is how clear an instance it is, in their own description, of the bewildering effect of hermeneutical injustice, as discussed by Fricker. One of the things that’s so terrific about podcasts like Radiolab is their potential to help a cis white guy like myself better understand issues like these. I’m just so grateful for anything that opens my mind and increases my ever-imperfect understanding.

pragmatic encroachment, thick credence, and portfolio diversification

For some time, I’ve had the idea that a theory of “thick credences” that are rationally sensitive to both evidential and practical factors can be helpful in clarifying some fundamental issues in epistemology as well as useful in economic modeling. Over the past week, I’ve been working on a revision of a paper on pragmatic encroachment (the thesis that non-evidential factors, such as the stakes in a decision, should properly influence what a subject knows) that applies a theory of thick credences, which model degrees of belief using imprecise probabilities. According to proponents of thick, as opposed to sharp, credences, a degree of belief should have an upper and lower bound, rather than one specific value. For example, if I told you an urn has some proportion of red balls between \frac{1}{4} and \frac{3}{4}. If you have thick credences your degree of belief a ball drawn randomly from the urn will be red could be an interval, [\frac{1}{4}, \frac{3}{4}] naturally, but if you have sharp credences you’ll need to commit to a precise value, probably \frac{1}{2}. In the case where you have the thick credence we write \underline{C}(r) = \frac{1}{4} and \overline{C}(r) = \frac{3}{4} for the lower and upper credence. The thesis I defend in my paper is that the thickness of a credence is something that can rationally dilate or contract depending on practical circumstances. In this post I want to expand on an example from the paper, using an objection to pragmatic encroachment that was put forth by Baron Reed as a launching off point, that I think gives a nice rational psychology of portfolio diversification. I am not claiming that this is better than other accounts, just that it’s nifty. Some of this post is word for word from the paper I’m working on, but I’m going to fill in more detail than the paper demands.

Here is Reed’s objection to pragmatic encroachment:

I have a broker who is extremely reliable at picking stocks. She tells me that a biotech stock, BXD, is a good long term investment and that she can move a fourth of my assets into BXD stock. Given her testimony, I know that it will go up in value, so I agree. An hour later, she tells me that she can now move another fourth of my assets into BXD. I know it will go up in value, so I agree again. An hour later, the same thing happens. When she calls me for the fourth time, she offers to move my remaining assets into BXD. But she also points out that I would then have all of my assets tied up in a single stock, which is a very risky thing to do. The stakes have become too high, and so it’s not rational for me to buy more shares of BXD. Given RKP, this means that I no longer know that the stock will go up in value. I no longer have the knowledge that would permit me to keep the stock, so I tell my broker to sell all of it in favor of other investments I know to be safe. After an hour, she calls back to remind me that BXD is an excellent long term investment. Having sold all my shares, this is no longer a high stakes proposition for me. I reflect that she is reliable in her stock tips, and I again come to know that BXD will go up in value. So, I take her up on her offer to move a fourth of my assets into BXD. And so on.

B. Reed. “Practical matters do not affect whether you know.” In J. T. M. Steup and E. Sosa, editors, Contemporary Debates in Epistemology, 2nd. ed. Wiley-Blackwell, 2013.

The case Reed presents is complicated in ways that the following toy example will simplify, but I think that the example illustrates a kind of doxastic equilibrium for pragmatically dilating thick credences that dodges the worry that pragmatic encroachment will make you a money pump for your broker. Reed’s idea is that if one can lose knowledge that BXD is a good bet just by having the magnitude of one’s investment in it increase, then one will become a money pump for broker’s fees. I wish to argue, on the contrary, that appeal to pragmatic dilation of thick credences can offer a fine-grained account of the rationality portfolio diversification.

Consider the following scenario. I have on offer two gambles. Gamble A costs $0.95 and pays $1.00 if p is true. Gamble T costs $0.95 and pays $1.00 if q is true. Accordingly, if I know the odds corresponding to the probability \frac{95}{100} to be advantageous in each case, I should buy into each prospect. \frac{95}{100} is a  kind of threshold. If I have a sharp credence below that threshold, for either proposition, then I shouldn’t take the corresponding bet; above, I should. If I have a thick credence, I claim that if my lower bound falls below that threshold, then I don’t believe that it’s a good bet, and my epistemological claim is that whether such beliefs are knowledge is a function of stakes.

Now suppose I have the following testimony. Aldo asserts `p‘ and Tomis asserts `q‘. How shall I allocate funds to each prospect? Assuming that I take Aldo and Tomis to be equally reliable, it may seem clear that I should divide my purse evenly, but what if, perhaps knowing Tomis a bit more personally, I take him to be a bit more reliable. In this circumstance, maybe I should put my entire purse on q, according to decision-making with sharp credences C(p) and C(q). Assuming \frac{95}{100} < C(p) < C(q), I regard each gamble as desirable, but it seems that I should regard Gamble T to be more desirable in virtue of my greater confidence in Tomis, in virtue of which Gamble T will always have higher expected utility than Gamble A.

I think the conclusion that greater confidence in Tomis implies not diversifying is counter-intuitive. I think we can describe a pragmatically dilating thick credence that nicely captures the intuition that I should somehow split my purse. I assume that in the situation described above, absent any independent evidence for \neg p or \neg q, I should have \overline{C}(p) = \overline{C}(q) = 1. Taking Tomis to be more reliable than Aldo (but both to be sufficiently reliable that Gamble A and Gamble T are initially desirable) and before putting anything into either prospect, I should have \frac{95}{100} < \underline{C}(p) < \underline{C}(q) < 1. I am suggesting that \underline{C}(p) and \underline{C}(q) should be decreasing functions of S_A and S_T, the stakes invested in Gamble A and Gamble T, respectively. Accordingly, my greater confidence in Tomis would be reflected by the inequality \underline{C}_{S_A}(p) < \underline{C}_{S_T}(q) when S_A = S_T, but when S_A < S_T the hypothesis of stakes-sensitive pragmatic dilation allows that inequality to be reversed so that \underline{C}_{S_A}(p) > \underline{C}_{S_T}(q). If my purse is large enough, and I can buy as much as I want, my uniquely preferred portfolio \{S_A, S_T\} is the one that satisfies the condition \underline{C}_{S_A}(p) = \underline{C}_{S_T}(q) = \frac{95}{100}.

The forgoing presentation is perhaps a little symbol-laden but the idea is intuitive. I have no reason to think either is wrong, so my upper credence on their testimony is 1, but I know reliable people sometimes are wrong, so my lower credences are below 1. My higher confidence in Tomis is reflected in my having a higher lower credence in q, initially. Since I’m more confident in Tomis, I’ll start by buying Gamble T, but as I get more and more of my purse into T my credence in q gradually dilates and the lower bound on my credence in q gradually falls below my lower bound for p. At this point, investing in Gamble A becomes more advantageous than investing in T, by my lights. There’s going to be a set of pairs of stakes \{S_A, S_T\} where there’s a sort of equilibrium, adding more on either end of the scale tips the balance if it’s not matched (not necessarily “pound for pound”, however) on the other side. If I put enough into each prospect, I will reach a moment where each lower credence falls to the threshold \frac{95}{100} and I should invest no further in either gamble.

We can be more exact by actually defining the lower credences as decreasing functions of stakes. Each function should be defined over the domain [0, \infty] and restricted to the range [0, 1]. Given these constraints, the following functions are somewhat natural, though of course not uniquely entailed.

  • \underline{C}(p) = 0.97 - 0.97(1 - \frac{1}{S_A + 1})
  • \underline{C}(q) = 0.99 - 0.99(1 - \frac{1}{S_T + 1})

These are nice, but a slight adjustment makes the x-axis more reasonable as a representation of dollar stakes. So I came up with:

  • \underline{C}(p) = 0.97 - 0.97(1 - \frac{1}{\frac{S_A}{10^6} + 1})
  • \underline{C}(q) = 0.99 - 0.99(1 - \frac{1}{\frac{S_T}{10^6} + 1})

Graphing these next to each other gives the following, where the y axis represents the lower bounds on the thick credences in p and q and the x axis represents the stake invested:


If you draw a horizontal line that intersects both the red and blue lines, you’re in a kind of equilibrium, corresponding to the levels of investment indicated on the x axis below those points of intersection; increasing your stake in either gamble immediately makes the other one more desirable. Until your lower credences fall below 0.95 each gamble is believed to be desirable to you and you should be buying, not selling. At the unique equilibrium defined by \underline{C}_{S_A}(p) = \underline{C}_{S_T}(q) = \frac{95}{100}, you should be neither buying nor selling. So the money-pump dynamic implied by Reed’s objection does not arise. Moreover, we have a nifty account of why and how funds should be allocated even to prospects one is less confident of than others in a portfolio. Obviously, a lot will depend on how lower credences are defined as dilating functions of stakes. The function given in the toy example given above is not plausible for someone that doesn’t have \approx $65,000 to invest. Furthermore, any actual portfolio allocation problem is going to be way more complicated because there will be a distribution of possible outcomes, not an all or nothing gamble, and dependencies on far more propositions than just one. And, there are obviously other frameworks for incorporating risk aversion into a portfolio through diversification. I’m not trying to claim too much here, but I think it’s nifty, and it answers Reed’s objection, and maybe it’s a framework that could be pushed further.

simple math and shy discovery

Let’s try this again.

The blog’s been inactive since 2011, when I finished grad school and stopped using it for brainstorming. I’ve made all the past posts private because they’re old ideas. I’m hoping to post about philosophy at a pace of about once every couple of weeks and to get reactions to some of my half-baked ideas. I have thoughts to share, but producing research quality output is difficult with my teaching load. Blogging seems like a good way to start working toward some drafts to send to conferences.

I might share some political thoughts too; no hot takes.

I think I’ll probably have some very general things to say about the role of teaching and learning in colleges and universities and the value of the liberal arts.

If I accidentally take a nice photograph while camping and hiking with my family, I may share those.

Possibly, I’ll share a recipe that I’ve developed.

I’ll occasionally share music I like, starting with this.