Edward Feser

Fire, Water, and Numbers

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Fire vs. Water

“All things are water,” says Thales.

“All things are fire,” says Heraclitus.

“Wait,” says David Hume’s Philo. “You both agree that all things are made up of one substance. Thales, you prefer to call it water, and Heraclitus, you prefer to call it fire. But isn’t that merely a verbal dispute? According to both of you, whatever you point at is fundamentally the same fundamental stuff. So whether you point at water or fire, or anything else, for that matter, you are always pointing at the same fundamental stuff. Where is the real disagreement?”

Philo has a somewhat valid point here, and I mentioned the same thing in the linked post referring to Thales. Nonetheless, as I also said in the same post, as well as in the discussion of the disagreement about God, while there is some common ground, there are also likely remaining points of disagreement. It might depend on context, and perhaps the disagreement is more about the best way of thinking about things than about the things themselves, somewhat like discussing whether the earth or the universe is the thing spinning, but Heraclitus could respond, for example, by saying that thinking of the fundamental stuff as fire is more valid because fire is constantly changing, while water often appears to be completely still, and (Heraclitus claims) everything is in fact constantly changing. This could represent a real disagreement, but it is not a large one, and Thales could simply respond: “Ok, everything is flowing water. Problem fixed.”

Numbers

It is said that Pythagoras and his followers held that “all things are numbers.” To what degree and in what sense this attribution is accurate is unclear, but in any case, some people hold this very position today, even if they would not call themselves Pythagoreans. Thus for example in a recent episode of Sean Carroll’s podcast, Carroll speaks with Max Tegmark, who seems to adopt this position:

0:23:37 MT: It’s squishy a little bit blue and moose like. [laughter] Those properties, I just described don’t sound very mathematical at all. But when we look at it, Sean through our physics eyes, we see that it’s actually a blob of quarks and electrons. And what properties does an electron have? It has the property, minus one, one half, one, and so on. We, physicists have made up these nerdy names for these properties like electric charge, spin, lepton number. But it’s just we humans who invented that language of calling them that, they are really just numbers. And you know as well as I do that the only difference between an electron and a top quark is what numbers its properties are. We have not discovered any other properties that they actually have. So that’s the stuff in space, all the different particles, in the Standard Model, you’ve written so much nice stuff about in your books are all described by just by sets of numbers. What about the space that they’re in? What property does the space have? I think I actually have your old nerdy non-popular, right?

0:24:50 SC: My unpopular book, yes.

0:24:52 MT: Space has, for example, the property three, that’s a number and we have a nerdy name for that too. We call it the dimensionality of space. It’s the maximum number of fingers I can put in space that are all perpendicular to each other. The name dimensionality is just the human language thing, the property is three. We also discovered that it has some other properties, like curvature and topology that Einstein was interested in. But those are all mathematical properties too. And as far as we know today in physics, we have never discovered any properties of either space or the stuff in space yet that are actually non-mathematical. And then it starts to feel a little bit less insane that maybe we are living in a mathematical object. It’s not so different from if you were a character living in a video game. And you started to analyze how your world worked. You would secretly be discovering just the mathematical workings of the code, right?

Tegmark presumably would believe that by saying that things “are really just numbers,” he would disagree with Thales and Heraclitus about the nature of things. But does he? Philo might well be skeptical that there is any meaningful disagreement here, just as between Thales and Heraclitus. As soon as you begin to say, “all things are this particular kind of thing,” the same issues will arise to hinder your disagreement with others who characterize things in a different way.

The discussion might be clearer if I put my cards on the table in advance:

First, there is some validity to the objection, just as there is to the objection concerning the difference between Thales and Heraclitus.

Second, there is nonetheless some residual disagreement, and on that basis it turns out that Tegmark and Pythagoras are more correct than Thales and Heraclitus.

Third, Tegmark most likely does not understand the sense in which he might be correct, rather supposing himself correct the way Thales might suppose himself correct in insisting, “No, things are really not fire, they are really water.”

Mathematical and non-mathematical properties

As an approach to these issues, consider the statement by Tegmark, “We have never discovered any properties of either space or the stuff in space yet that are actually non-mathematical.”

What would it look like if we found a property that was “actually non-mathematical?” Well, what about the property of being blue? As Tegmark remarks, that does not sound very mathematical. But it turns out that color is a certain property of a surface regarding how it reflects flight, and this is much more of a “mathematical” property, at least in the sense that we can give it a mathematical description, which we would have a hard time doing if we simply took the word “blue.”

So presumably we would find a non-mathematical property by seeing some property of things, then investigating it, and then concluding, “We have fully investigated this property and there is no mathematical description of it.” This did not happen with the color blue, nor has it yet happened with any other property; either we can say that we have not yet fully investigated it, or we can give some sort of mathematical description.

Tegmark appears to take the above situation to be surprising. Wow, we might have found reality to be non-mathematical, but it actually turns out to be entirely mathematical! I suggest something different. As hinted by connection with the linked post, things could not have turned out differently. A sufficiently detailed analysis of anything will be a mathematical analysis or something very like it. But this is not because things “are actually just numbers,” as though this were some deep discovery about the essence of things, but because of what it is for people to engage in “a detailed analysis” of anything.

Suppose you want to investigate some thing or some property. The first thing you need to do is to distinguish it from other things or other properties. The color blue is not the color red, the color yellow, or the color green.

Numbers are involved right here at the very first step. There are at least three colors, namely red, yellow, and blue.

Of course we can find more colors, but what if it turns out there seems to be no definite number of them, but we can always find more? Even in this situation, in order to “analyze” them, we need some way of distinguishing and comparing them. We will put them in some sort of order: one color is brighter than another, or one length is greater than another, or one sound is higher pitched than another.

As soon as you find some ordering of that sort (brightness, or greatness of length, or pitch), it will become possible to give a mathematical analysis in terms of the real numbers, as we discussed in relation to “good” and “better.” Now someone defending Tegmark might respond: there was no guarantee we would find any such measure or any such method to compare them. Without such a measure, you could perhaps count your property along with other properties. But you could not give a mathematical analysis of the property itself. So it is surprising that it turned out this way.

But you distinguished your property from other properties, and that must have involved recognizing some things in common with other properties, at least that it was something rather than nothing and that it was a property, and some ways in which it was different from other properties. Thus for example blue, like red, can be seen, while a musical note can be heard but not seen (at least by most people.) Red and blue have in common that they are colors. But what is the difference between them? If we are to respond in any way to this question, except perhaps, “it looks different,” we must find some comparison. And if we find a comparison, we are well on the way to a mathematical account. If we don’t find a comparison, people might rightly complain that we have not yet done any detailed investigation.

But to make the point stronger, let’s assume the best we can do is “it looks different.” Even if this is the case, this very thing will allow us to construct a comparison that will ultimately allow us to construct a mathematical measure. For “it looks different” is itself something that comes in degrees. Blue looks different from red, but orange does so as well, just less different. Insofar as this judgment is somewhat subjective, it might be hard to get a great deal of accuracy with this method. But it would indeed begin to supply us with a kind of sliding scale of colors, and we would be able to number this scale with the real numbers.

From a historical point of view, it took a while for people to realize that this would always be possible. Thus for example Isidore of Seville said that “unless sounds are held by the memory of man, they perish, because they cannot be written down.” It was not, however, so much ignorance of sound that caused this, as ignorance of “detailed analysis.”

This is closely connected to what we said about names. A mathematical analysis is a detailed system of naming, where we name not only individual items, but also various groups, using names like “two,” “three,” and “four.” If we find that we cannot simply count the thing, but we can always find more examples, we look for comparative ways to name them. And when we find a comparison, we note that some things are more distant from one end of the scale and other things are less distant. This allows us to analyze the property using real numbers or some similar mathematical concept. This is also related to our discussion of technical terminology; in an advanced stage any science will begin to use somewhat mathematical methods. Unfortunately, this can also result in people adopting mathematical language in order to look like their understanding has reached an advanced stage, when it has not.

It should be sufficiently clear from this why I suggested that things could not have turned out otherwise. A “non-mathematical” property, in Tegmark’s sense, can only be a property you haven’t analyzed, or one that you haven’t succeeded in analyzing if you did attempt it.

The three consequences

Above, I made three claims about Tegmark’s position. The reasons for them may already be somewhat clarified by the above, but nonetheless I will look at this in a bit more detail.

First, I said there was some truth in the objection that “everything is numbers” is not much different from “everything is water,” or “everything is fire.” One notices some “hand-waving,” so to speak, in Tegmark’s claim that “We, physicists have made up these nerdy names for these properties like electric charge, spin, lepton number. But it’s just we humans who invented that language of calling them that, they are really just numbers.” A measure of charge or spin or whatever may be a number. But who is to say the thing being measured is a number? Nonetheless, there is a reasonable point there. If you are to give an account at all, it will in some way express the form of the thing, which implies explaining relationships, which depends on the distinction of various related things, which entails the possibility of counting the things that are related. In other words, someone could say, “You have a mathematical account of a thing. But the thing itself is non-mathematical.” But if you then ask them to explain that non-mathematical thing, the new explanation will be just as mathematical as the original explanation.

Given this fact, namely that the “mathematical” aspect is a question of how detailed explanations work, what is the difference between saying “we can give a mathematical explanation, but apart from explanations, the things are numbers,” and “we can give a mathematical explanation, but apart from explanations, the things are fires?”

Exactly. There isn’t much difference. Nonetheless, I made the second claim that there is some residual disagreement and that by this measure, the mathematical claim is better than the one about fire or water. Of course we don’t really know what Thales or Heraclitus thought in detail. But Aristotle, at any rate, claimed that Thales intended to assert that material causes alone exist. And this would be at least a reasonable understanding of the claim that all things are water, or fire. Just as Heraclitus could say that fire is a better term than water because fire is always changing, Thales, if he really wanted to exclude other causes, could say that water is a better term than “numbers” because water seems to be material and numbers do not. But since other causes do exist, the opposite is the case: the mathematical claim is better than the materialistic ones.

Many people say that Tegmark’s account is flawed in a similar way, but with respect to another cause; that is, that mathematical accounts exclude final causes. But this is a lot like Ed Feser’s claim that a mathematical account of color implies that colors don’t really exist; namely they are like in just being wrong. A mathematical account of color does not imply that things are not colored, and a mathematical account of the world does not imply that final causes do not exist. As I said early on, a final causes explains why an efficient cause does what it does, and there is nothing about a mathematical explanation that prevents you from saying why the efficient cause does what it does.

My third point, that Tegmark does not understand the sense in which he is right, should be plain enough. As I stated above, he takes it to be a somewhat surprising discovery that we consistently find it possible to give mathematical accounts of the world, and this only makes sense if we assume it would in theory have been possible to discover something else. But that could not have happened, not because the world couldn’t have been a certain way, but because of the nature of explanation.

Kantian and Anti-Kantian Confusion

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I introduced what I called the “Kantian error” in an earlier post, and have since used it in explaining several issues such the understanding of unity and the nature of form. However, considering my original point, we can see that there are actually two relevant errors.

First, there is the Kantian error itself, which amounts to the claim that nothing real can be truly known.

Second, there is an anti-Kantian error, namely the error opposed to the element of truth in Kant’s position. I pointed out that Kant is correct that we cannot know things “as they are in themselves” if this is meant to identify the mode of knowing and the mode of being as such. The opposite error, therefore, would be to say that we can know things by having a mode of knowing which is completely identical to the mode of being which things have. Edward Feser, for example, effectively falls into this error in his remarks on sensible colors discussed in an earlier post on truth in the senses, and more recently at his blog he reaffirms the same position:

Part of the reason the mechanical conception of matter entails the possibility of zombies is that it takes matter to be devoid of anything like color, sound, taste, odor, heat, cold and the like, as common sense conceives of these qualities.  On the mechanical conception, if you redefine redness (for example) as a tendency to absorb certain wavelengths of light and reflect others, then you can say that redness is a real feature of the physical world.  But if by “redness” you mean what common sense understands by it – the way red looks in conscious experience – then, according to the mechanical conception, nothing like that really exists in matter.  And something similar holds of other sensory qualities.  The implication is that matter is devoid of any of the features that make it the case that there is “something it is like” to have a conscious experience, and thus is devoid of consciousness itself.

The implication here is that the way red looks is the way a red thing is. Since the emphasis is in the original, it is reasonable to take this to be identifying the mode of the senses with the mode of being. In reality, as we said in the earlier discussion, there is no “redefinition” because the senses do not define anything in the first place.

Both mistakes, namely both the Kantian and anti-Kantian errors, imply contradictions. The claim that there is something that we cannot know in any way contradicts itself, since it implies that we know of something of which we know nothing. Thus, it implies that an unknown thing is known. Similarly, the claim that the mode of knowing as such is the same as the mode of being, to put it in Kant’s words, “is as much as to imagine that experience is also real without experience.” In other words, suppose that “the way red looks” is the very way a red apple is apart from the senses: then the apple looks a certain way, even when no one is looking, and thus precisely when it does not look any way at all.

Thus both errors imply similar contradictions: an unknown thing as such is known, or a known thing as such is unknown. The errors are generated in much the way Kant himself seems to have fallen into the error. Either knowledge is possible or it is not, we say. If it is not, then you have the Kantian error, and if it is, it appears that our way of knowing must the same as the way things are, and thus you have the anti-Kantian error.

As I pointed out in discussing consistency, an inconsistent claim, understood as such, does not propose to us any particular way to understand the world. The situation described is unintelligible, and in no way tells us what we should expect to find if it turns out to be the case. Given this fact, together with the similarity of the implied contradictions, we should not be surprised if people rarely double down completely on one error or the other, but rather waver vaguely between the two as they see the unpalatable implications of one side or the other.

Thus, the problem arises from the false dichotomy between “knowledge is not possible” and “knowledge is possible but must work in this particular way, namely by an identity of the mode of knowing and the mode of being.” I said in the linked post that this is “one of the most basic causes of human error,” but it might be possible to go further and suggest that it is the principal cause of philosophical error apart from error caused by trading truth for other things. At any rate, the reader is advised to keep this in mind as a distinct possibility. We may see additional relevant evidence as time goes on.

Truth in the Senses

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Discussing Thomas Nagel’s Mind and Cosmos, Edward Feser says:

Take a stock example of reductive scientific explanation like the reduction of sound to compression waves, color to surface reflectance properties, or heat and cold to molecular motion.  The way these explanations work is by treating the appearance that sound, color, heat and cold present to us in conscious experience as mere appearance, as a projection of the mind that corresponds to nothing in objective, mind-independent reality.  What common sense understands by color, sound, heat and cold — the way red looks, the way a musical note sounds, the way a hot stove feels, and so forth — is held to have no objective reality, any more than the redness a person unknowingly wearing red-tinted contact lenses thinks he sees in all the objects around him really exists in those objects.  Instead, color is for scientific purposes essentially redefined by the method in terms of the surface reflectance properties that cause in us the subjective appearance of color; sound redefined in terms of the compression waves that cause in us the subjective appearance of sound; and heat and cold redefined in terms of the molecular motion that causes in us the subjective appearance of heat and cold.

Thus, as common sense understands color, sound, heat and cold, etc., the reductive method ends up treating the world as essentially colorless, soundless, devoid of temperature, etc.  What the method calls “color,” “sound,” “heat” and “cold” is in fact something different from what the man on the street thinks of when he hears these terms.  The “red” that the method says exists in the material world is just the tendency of an object to absorb certain wavelengths of light and to reflect others.  The “red” that the man on the street thinks exists in the object does not really exist in the object itself at all but only in his perceptual experience of the object.  The “heat” that the method says really exists in the material world is just the motion of molecules.  The “heat” that the man on the street thinks exists in the object does not really exist in the object at all but only in his perceptual experience of the object.  And so forth.

Now, Nagel’s point is not that there is something wrong per se with overthrowing common sense in this way.  It is rather that whatever value this method has, it cannot coherently be applied to the explanation of conscious experience itself.  If the reductive method involves ignoring the appearances of a thing and redefining the thing in terms of something other than the appearances, then since our conscious experience of the world just is the way the world appears to us, to ignore the appearances is in this case just to ignore the very phenomenon to be explained rather than to explain it.  Consciousness is for this reason necessarily and uniquely resistant to explanation via the same method scientific reductionism applies to everything else.  For the application of the method in this case, writes Nagel, “does not take us nearer to the real nature of the phenomenon: it takes us farther away from it.”  To treat the appearances as essentially “subjective” or mind-dependent is precisely to make them incapable of explanation in entirely “objective” or mind-independent terms.

Feser is quite right that consciousness cannot be explained in such a way even in principle. I have touched on this point in a previous post. This is why eliminative materialists such as Daniel Dennett effectively deny the existence of consciousness: if the only things that exist are material things as described by modern science, then consciousness cannot even exist, because it cannot possibly be described in that terminology. John Searle, in a reply to Dennett, says:

In spite of its strident tone, I am grateful for Daniel Dennett’s response to my review because it enables me to make the differences between us crystal clear. I think we all really have conscious states. To remind everyone of this fact I asked my readers to perform the small experiment of pinching the left forearm with the right hand to produce a small pain. The pain has a certain sort of qualitative feeling to it, and such qualitative feelings are typical of the various sorts of conscious events that form the content of our waking and dreaming lives. To make explicit the differences between conscious events and, for example, mountains and molecules, I said consciousness has a first-person or subjective ontology. By that I mean that conscious states only exist when experienced by a subject and they exist only from the first-person point of view of that subject.

Such events are the data which a theory of consciousness is supposed to explain. In my account of consciousness I start with the data; Dennett denies the existence of the data. To put it as clearly as I can: in his book, Consciousness Explained, Dennett denies the existence of consciousness. He continues to use the word, but he means something different by it. For him, it refers only to third-person phenomena, not to the first-person conscious feelings and experiences we all have. For Dennett there is no difference between us humans and complex zombies who lack any inner feelings, because we are all just complex zombies.

I think most readers, when first told this, would assume that I must be misunderstanding him. Surely no sane person could deny the existence of feelings. But in his reply he makes it clear that I have understood him exactly. He says, “How could anyone deny that!? Just watch…”

Dennett is obviously wrong about consciousness. But what about color, sound, heat, and cold? Is it true that “reductive scientific explanation” holds that these things are a “mere appearance” that “correspond to nothing in objective, mind-independent reality?”

Feser may be quite honest personally in his description of what he considers to be two opposing views. But it seems to me that he is inheriting this description from a long tradition of putting Aristotle and common sense, on the one hand, into an unnecessary opposition with modern scientific views on the other. I think that this tradition is in essence wishful thinking: this tradition came to be historically through the efforts of people who wished for disagreement between Aristotle and modern science.

I touched on this wish in an earlier post when I said that John Locke’s understanding of secondary qualities “is actually mostly true, and mostly consistent with the philosophy of Aristotle, even though Locke would likely wish that the latter were not the case.” The early moderns did differ from Aristotle regarding the purpose of the sciences, as I pointed out here in the case of Francis Bacon. Having a different purpose requires employing different means. Consequently it was favorable for their purposes to emphasize their disagreements with the philosophy of Aristotle, regardless of how much agreement or disagreement existed in reality when the positions themselves are properly understood. If people could be persuaded to abandon Aristotelian thought and focus on the new science, the purposes of the new science would be more easily obtained.

Let us ask the question directly: if color for example consists in the reflectance properties of a surface, does this mean that colors as we see them are “mere appearances” that have no objective reality? Elsewhere, Feser says that this view implies that “Objectively there are only colorless, odorless, soundless, tasteless, meaningless particles in fields of force.”

The scientist can presumably reply in this way: Color consists in surface reflectance properties. These properties are objective properties of physical objects in the world. So color is an objective property of physical objects in the world.

Feser’s response can be found in the original quotation above:

What common sense understands by color, sound, heat and cold — the way red looks, the way a musical note sounds, the way a hot stove feels, and so forth — is held to have no objective reality, any more than the redness a person unknowingly wearing red-tinted contact lenses thinks he sees in all the objects around him really exists in those objects.  Instead, color is for scientific purposes essentially redefined by the method in terms of the surface reflectance properties that cause in us the subjective appearance of color; sound redefined in terms of the compression waves that cause in us the subjective appearance of sound; and heat and cold redefined in terms of the molecular motion that causes in us the subjective appearance of heat and cold.

Of course, the scientist would say that when a person wears red tinted contact lenses, the physical objects around him do not have the properties that constitute red, and consequently it is true that the objects are not objectively red. But other objects like red apples and the like do have those properties, and so they are objectively red. The two cases are not the same. Feser is replying by saying that whether he wants to or not, the scientist is denying the existence of red as we know it.

According to Feser, “what common sense understands by color” is something like “the way red looks,” and it is this to which, according to him, the scientist is denying objective existence. This is to say, if it true that red bodies have a certain way of reflecting light, and this fact is all there is in the body which explains why red bodies look red, Feser would say that this means that “the body is red” is a false statement. This is necessary for his position to be true: “the body is red” has to be actually false in the sense that we normally understand it, since he made the comparison with red tinted glasses, where in fact it is false that the body is red.

What do we mean when we say that something is red? We don’t just mean that it looks a certain way, because we know that sometimes things appear to be a color which they are not, as in the case of the tinted glasses. We don’t mean that it looks some way; we mean that it is that way. Take something that looks red. If we say that it is actually red, we mean that it actually is the way it looks.

All this is true, but it causes Feser to fall into error. “This is actually red” no more describes the nature of red than “this looks red” does. We know how red things look, because we experience it directly. But this experience is not a description. It is not something that can be true or false, so that we can say “surface reflectance is a false description of this experience.” It is a sensible experience, not a claim to truth or falsehood, and we consider sensible experiences accurate when they do not mislead us. Red tinted glasses do mislead us, and so we consider those experiences “false”, and say that the things are not really red. But even if color consists in surface reflectance properties, the experience of color never misled us. It never said, “This is not a reflectance property,” because it never said anything at all. It was not a statement but a sensation.

In order to determine whether something is actually red, we do not turn sensation into a description and check whether the thing matches that description. This is probably not even possible. We simply recognize that “this is actually red” when it looks red to a normal person in normal circumstances. And this is true regardless of what is present in the body that causes red things to look red to us, whether that is the properties of the surface or something else. Thus the scientist has no need to deny the objectivity of color, nor to deny his physical explanation of color.

Feser may actually have a different concern about objectivity, not merely whether statements about color are true or false. Are the distinctions in question natural distinctions, or are they essentially arbitrary from an objective point of view? Is the line between blue and green a natural one, or do our senses make that distinction in a basically arbitrary manner? Locke and others called certain qualities “secondary” because it seemed to them that the distinctions in question were basically arbitrary. We have good evidence that at least in some cases, they were right. An object feels hot or cold depending on the current condition of the one who feels it, without having to change from “being objectively hot” to “being objectively cold.” While the evidence is less conclusive in the case of color, something similar appears to be the case there. The line between different colors is in a different place for different people, as is most evidently the case in colorblind persons, and much more are the dividing lines in different places for different species of animal. This means that we have some reason to believe that green and blue things are objectively distinct, but that this objective distinction is much like the objective distinction between persons who are under six feet tall and persons who are over six feet tall. The distinction itself is objective, but the choice of distinction is basically arbitrary, if the thing is considered in itself.

 

 

 

 

 

 

Edward Feser on Naturalism

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Edward Feser, discussing David Hart on natural law, says, “For Darwinian naturalism, as Hart points out, gives us a view of the mind on which it floats entirely free of truth.  Any belief or argument whatsoever could seem absolutely indubitable even if it were completely wrong, if this were conducive to survival.” He takes this as an argument against Darwinian naturalism, which means that he thinks the claim, “Any belief or argument etc.” is either false or implausible.

It is not entirely clear why he thinks this, given that either he agrees, or at least does not disagree, with the biological theory of evolution. However, it may be that, holding that the intellect is immaterial, he believes that it is not subject to the process of natural selection. But this cannot be true. It is evident that whatever the exact relationship between the mind and the body, there is certainly some relationship, and the null hypothesis is basically always false. Consequently, whether or not the intellect is immaterial, there will be bodily causes that influence a person’s tendency to be certain or uncertain about things, with the result that the claim, “Any belief or argument whatsoever could seem absolutely indubitable etc.”, will surely have at least some truth.

It is also clearly true from experience. For example, in Muslim societies, most of the population are extremely convinced that Islam is true, even though this is completely wrong, but very conducive to survival, since even in the present day the death penalty continues to be used against apostates from Islam.

Obviously Islam has not existed long enough for natural selection to have much effect here, however, so in fact this particular case is probably part of a more general situation where agreeing with the people around is “conducive to survival”, both in the literal sense, and in the sense of producing economic and social advantages.

Nor does this imply that the mind “floats entirely free of truth”, since in most cases wrong beliefs about the world are harmful, and true beliefs helpful. If there is a pit of spikes in front of me and I believe that there is not, this is not conducive to survival at all. It does imply that the mind is not perfect and that there is a need to reflect on its work and frequently correct it. The possibility of self-reflection provides possibilities for progress in truth, even given the existence of such mental flaws.