Wednesday, November 2, 2016

Induction Is All We Got


In this piece I shall defend what may appear an unusual thesis, namely that all reasoning is ultimately based on induction, and hence that induction is the only way in which we ever know anything. By induction, I here mean what seems right in light of the doubtable data/experience we have accumulated so far. In everything from logic and mathematics to philosophy and psychology, this is invariably how we evaluate what is true. Or so I shall argue.

How can we be sure that the patterns we have reliably observed in the world so far will also exist in other times or places? How can we justify the assumed uniformity of the world that induction seems to rest upon? How can we trust induction when it cannot be deductively justified? This is the problem of induction in a nutshell.

What is interesting, however, and seemingly universally missed, is that exactly the same problem is staring us in the face when it comes to deduction. Logical deductions are also part of the world, and hence to assume that they will be valid in all times and in all realms is therefore also to assume that the world is uniform in certain ways. It is the exact same assumption, so why is it considered problematic in the case of induction but not in the case of deduction? What is the source of this discrimination?

The answer, I think, is that it just seems true that deduction is universal, and that the opposite claim — that logic is not universal — seems to make no sense. I certainly share this impression, but this does not render deduction wholly undoubtable. We may reasonably have confidence in the statement that logical deductions are universal, but we should be clear that the basis of this belief is itself merely that it seems reasonable to suppose this given that our minds apparently cannot make sense of anything else. More than that, we should also be clear that we then in fact do accept the uniformity of the world (or perhaps assign high probability to this claim being true), and that we do it on the basis that it just seems reasonable.

Another aspect of the problem of induction is that induction merely is assumed to be valid, and that attempts at justifying it always seem circular. Yet again, how does deduction compare? How do we justify deduction? With deductive arguments? That would be circular as well. With brute assumptions? If so, why is it more problematic to assume the validity of induction?

There really is no fundamental distinction. We accept both induction and deduction because they seem right. Deductions seems obviously reasonable and valid while inductive inferences seem fairly reasonable and probably valid. The only difference, it seems, is the degree of obviousness, a difference I shall try to explain below.


Beliefs: All in Memory

One way to realize the conclusion sketched out above is by recalling the fact that all our beliefs reside in memory. And we know that 1) our memory consists of information we have gathered over time, and 2) our memories can be unreliable. There is nothing logically problematic about this; indeed, this is common knowledge. Yet it implies something rather significant, namely that all our beliefs, including those about logic, are doubtable, and that all our beliefs are a matter of what seems right in light of the doubtable data/experience we have accumulated so far.

This applies to all knowledge, whether inductively or deductively inferred (as we shall see, the latter is a subset of the former). Mathematical proofs, for instance, are often claimed to be certain knowledge, yet our knowledge of mathematical proofs is also contained in memory. And since all mathematical proofs we know of are stored in memory, and since memory is fallible, it follows that our belief in any mathematical proof we hold to be valid is, in fact, fallible.

The idea that mathematical knowledge is certain and rests only on deduction is indeed ridiculous. Take for instance the proof of Fermat’s Last Theorem: a small fraction of professional mathematicians actually fully understand this proof, yet in my experience, virtually all mathematicians will say that we know that Fermat’s Last Theorem is true. And this is probably a highly reasonable belief, but let us be clear about how we know it: by trusting the expertise of other mathematicians. And such trust is transparently based on induction; it is not based on deduction. More than that, we know, inductively, that this inductively based trust is fallible.

A famous example would be Alfred Kempe’s proof of the four-color theorem, presented in 1879, which was widely accepted until it was shown to be incorrect in 1890. Another example is Gauss’ proof of the fundamental theorem of algebra, a proof Gauss himself obviously held to be valid, as did many other mathematicians, yet it was not completed until more than a hundred years after Gauss first published it.

So our mathematical knowledge clearly relies strongly on induction, in that we trust others. Indeed, I would argue that, in practice, a majority of the mathematical knowledge any mathematician knows is known based on such trust in others rather than their own deductions. Yet to think that we rely on induction merely when it comes to trusting others in the pursuit of what we call deductive knowledge is to miss the point. For the point is that this applies to all mathematical knowledge, including when we have made all the deductions ourselves. There is no fundamental distinction between when others have made the deductions and when we have made them ourselves. In both cases, we trust conclusions made by fallible minds, stored in a fallible memory.

This of course isn’t to say that such trust is unreasonable, yet the nature of this trust should not be missed: it is the core of induction. There is no deductive argument that proves our memory to be reliable. Rather, we merely assume the reliability of memory, and 1) this is an assumption that we cannot not make, 2) it is an assumption that all deduction, indeed all knowledge in general, rests upon, and 3), to repeat the point made above, this assumption is the core of induction.


Let me explain and justify all these claims in turn. To start with 3), to assume that our memories in this present moment are valid is to assume that the information we have stored in memory earlier still applies. This projected extension of the limited information we know is the core of induction. As for 2), it is trivial that all knowledge, including that derived from deduction, rests on the reliability of memory, since that is where all our knowledge is stored. So to say that we know anything about anything is to assume the validity of our memory — or at least the validity of some aspects of it; more on this below. Lastly, 1), the assumption that we can trust our memory is an assumption we cannot not make because our memory is the position from which we see the world. To even doubt this assumption requires trusting it, since one must then at least trust that one doubts.

Yet we know our memory to be profoundly unreliable, don’t we?”

Yes, but it is not entirely so, and that is the point. For in order to even discover that our memory is not (entirely) reliable, we must assume that at least some aspects of our memory are — at the very least those aspects of it that hint that our memory is not entirely reliable. In other words, the discovery of the imperfect reliability of memory rests on its partial reliability.


So believing that we cannot trust any aspect of our own memory is nothing less than logically impossible, since such a belief — indeed any belief — itself resides in memory, and thus rests on its (at least partial) reliability. And given this status of logical inevitability, this trust in memory, which rests upon the validity of induction (again, this was 3) above), should indeed be granted the same status of certainty as other logical conclusions. Indeed, if possible, it should be granted even higher status, since all other beliefs, including purely logical ones, rest upon this. That’s right: all deductive knowledge rests on the reliability of memory, and this reliability rests on the validity of induction. Conclusion: Deductive knowledge rests on the validity of induction.

Indeed, the reason we trust deduction is ultimately inductive. Deductions are also experiments that we run in our heads, albeit experiments that reliably produce the same result. We therefore inductively conclude that they will keep on doing the same. What we usually consider matters of induction — for instance, we have observed a thousand white swans; should we expect the next swan to be white given all that we know about the world, including the fact that there are other birds who are not white? — is just different in that we are in a realm where our information seems a lot more incomplete. It is ultimately of the same form.

This also explains the difference in the status of certainty we ascribe to deduction and induction mentioned above: deduction seems obviously reasonable and valid because the experiment goes right every time, as far as we can tell, while (what we usually call) induction seems fairly reasonable and probably valid because it works well most of the time.

So the reason, I believe, that Hume found deduction more valid than induction, and found induction so much more problematic, was, ironically, because induction recommends the former more strongly. Hume’s objection to induction is really an adventure in self-contradiction — in many ways. For instance, the great man claimed, based on his own brain’s reasoning, that a universal rule cannot be derived from particular instances, yet what is this if not itself a universal rule derived from particular instances (of reasoning)? What is this if not a glaring self-contradiction?


Try as you might, in the realm of belief, there simply is no denying the validity of induction. Again, in order to even express doubts about the validity of induction, one must inescapably rest on what one is trying to doubt, as one then inductively assumes that doubt is a meaningful concept in this moment (it has been so far), that the others whom one expresses one’s doubts to will understand a word of what one says (they have so far), that there still is a problem of induction (it seems there has been so far), etc. Indeed, all beliefs rest on induction, as they rest on the assumption that the justification we have acquired for them in the past still applies in the present, including belief in notions of past, present, and future in the first place, not to mention belief in there being such a thing as logic, truth, and falsehood — the ideas that constitute the entire framework in which discussions about induction occur.

So what justifies induction, then?”

Nothing. In order to even enter the realm of trying to justify something, we have already accepted induction. In asking for a justification for induction, we ask from a position of unacknowledged acceptance of it. Indeed, what justifies the belief that there is a need to justify induction — a belief that itself rests on induction? Nothing. If we believe anything at all, we are already way past the point of accepting induction, knowingly or not. So to the extent we admit of having any beliefs at all, we admit of the validity of induction. We are fundamentally confused about where in our hierarchy of beliefs induction enters the picture. The answer is: underneath it all.


Knowing Good from Bad Induction

To say that reliance on induction is inevitable is obviously not to say that all inductive inferences are valid. So how do we know valid inductive inferences from invalid ones? Via induction, of course.

In a nutshell, we (ideally) assess the truth of a statement in light of all the information we have in our memory — the totality of what we know. This is all we got, and hence all we ever can evaluate truth claims based on. The more the doubtable data points we have accumulated point our beliefs in a certain direction, the stronger those beliefs are, and rightly so.

For example, the claim that the sun will rise tomorrow is a claim that we believe because it fits with, indeed is predicted by, everything we know, from the totality of humanity’s knowledge of physics and astronomy to our everyday experience.
In the same way, we can deem inductive inferences false. For instance, the claim that the sun will always keep rising because it has done that so far is obviously not true, and the way we know this is again via induction: we know of underlying physical principles that “govern” the physical macro patterns that are the dynamics of stars and planets, and these principles, along with astronomical observations of stars elsewhere, imply that the age of our solar system will indeed be finite. That is what all the data points to.

The commonly cited examples of “hard problems” for our (inevitably) inductive reasoning are all problems that arise from paying attention to a too narrow channel of information. For instance, when we say that every swan we have ever seen is white, and therefore all swans must be white, this is simply a bad inference that fails to keep other relevant facts in view, such as the size of our sample, the size of the Earth, and the fact that there are other birds who have a different color, a fact that is relevant when we keep in mind the additional fact that there is a high degree of similarity in patterns across species.

But what if we did not know about these additional facts? Then the inference seems reasonable.”

First, it should be noted that if we were in that position, we would be ignorant to a degree that is hard for us to imagine as creatures who know a lot. Second, if we were in such a position of knowing virtually nothing, we indeed should be very careful to make general conclusions about the world with confidence. If you have seen a thousand swans, and they have all been white, it seems reasonable to expect that the next one you see will be white as well, but it by no means implies that all swans are.

But couldn’t our inductive reasoning be wrong, even when we know a lot and we consider the totality of what we know?”

This is possible, yet, as we know inductively, e.g. from statistics, the more we know, the less likely such mistakes are. It is also worth noting how we know of the possibility of the fallibility of inductive inferences in the first place, namely via induction. We know that apparently solid patterns can break because we have witnessed it before. Nations that seemed strong suddenly fell, people who were right about many things were suddenly wrong, proofs that seemed valid were shown not to be, etc. We have observed this meta pattern of patterns sometimes breaking when we don’t expect it, which has taught us, inductively, to be more open-minded about the possibility of the breaking of even apparently solid patterns. It is always induction that teaches us epistemic modesty.

So it is due to inductive reasoning, not in spite of it, that we seem to have some reason to be agnostic concerning the generality of patterns we consider general, such as whether the cosmos looks the same everywhere across time and space — a question that is currently debated among physicists and cosmologists. What we can say here seems much like what we could say as the ignorant swan observers we imagined ourselves to be above: it seems reasonable that the time and space in the proximity of that which we have observed to unfold in certain law-like ways will also unfold in such ways, but we cannot confidently claim that this applies to all time and space.


The Source of the Problem: A Narrow and Confused View of Knowledge

As mentioned above, a narrow focus on certain data and beliefs about the world, as opposed to a focus on the totality of what we know, is the source of many problems in epistemology, including Goodman’s new riddle of induction and the traditional problem of induction itself. In the case of Goodman’s new riddle of induction, the problem is, in a nutshell, that we have no reason to believe that properties such as grue and bleen exist in light of all that we know about physics, as their existence would essentially require a change in the laws of physics that we have no reason to believe possible. So it is not the case that these two hypothetical properties constitute a deep problem for induction; the suggestion that things could be grue or bleen merely constitutes an extremely unlikely hypothesis about the world.

As for the problem of induction itself, a narrow focus is also to blame. Hume made the following claim: “That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction, than the affirmation, that it will rise.” Yet that this proposition “implies no more contradiction” is simply wrong, since it contradicts pretty much everything we know in fields such as astronomy and physics. And if you can contradict all this, why not also contradict history and claim that there never was a guy named David Hume, and that nobody has ever raised any so-called problem of induction? After all, this is certainly “no less intelligible” or plausible than the claim that the sun will not rise tomorrow. Or to take a more traditional inductive problem: why believe that there is any problem of induction in this moment or the next one just because it seems that there has been in the past? Indeed, why not contradict logical conclusions themselves?

This is surely what Hume means: the claim that the sun will not rise tomorrow seems to imply no logical contradiction, yet this dichotomy between logical and physical knowledge is, I would argue, ultimately misguided. First, in ontological terms, there is no evidence for the existence of some separate logico-mathematical world apart from the physical one — mathematical truths are found in and by the human mind, and given that the human mind is physical, it follows that mathematical truths are found in and by the physical. Second, as mentioned above, in epistemological terms, both what we consider mathematical and physical forms of knowledge ultimately share the same inductive basis — they are stored in our memory based on what we have experienced — which is yet another reason not to strongly privilege one over another, as Hume does. In sum, there is no justification for Hume’s narrow focus on, and privileging of, deductive reasoning and knowledge — his belief that only (what we categorize as) logical truths are valid. Again, deductively based beliefs, like all other beliefs, also rest on induction in the first place.


How We Know Things: It Just Seems That Way

How do we know that we are conscious, or that two plus two equals four? The answer, I would argue, is simply that it appears clear from our experience that this is the case. We ultimately have no deeper justification than this.

And this answer actually does not change when we ask more complicated questions, such as how we know that the Earth is round, or what the name of the current president of the United States is. We know because of experiences that have shaped, and in significant ways are now part of, our present experience from which it just seems obvious what the answer is. We may be able to express a long chain of reasons that compel us to hold the belief we hold, yet at the bottom of this elaborate chain, all we ultimately have is a set of conscious impressions of belief. Or doubt, for that matter, if we don’t happen to know the answer, but the basic mechanics are the same: we weigh our experience and read off from it what our state of belief — or doubt — is; itself a fact about the world.

Every chain of explanations must end somewhere, and, when it comes to our knowledge, the rock bottom of this chain is found in our direct conscious sensations. Ultimately, we do not have a deeper justification for what we know than this: it seems that way from our conscious impressions. This form of foundationalism is, I submit, the solution to the so-called M√ľnschhausen trilemma concerning how we justify what we know.

This is not to say that we cannot question and correct our impressions. We clearly can, as the correction of illusions and biases exemplify, yet our knowledge of such corrections is itself a matter of conscious impressions, for instance impressions that inform us about statistics, which help us correct wrong ones. The ultimate justification for our beliefs is still our experience. And this is indeed how we improve our knowledge of the world: new impressions help update and correct old ones, which in turn makes us form better ones, i.e. impressions that represent the world more accurately.

That our knowledge at bottom rests on experience is also not to say that our knowledge rests on a basis of mere assumptions. A good analogy, I believe, is our knowledge of fundamental physical constants, which are also in some sense primitive, in that they are measured rather than derived from something else. We have no deeper justification for believing what the values of these constants are than our measurements, yet this is clearly distinct from merely assuming these values. Similarly, I would argue that we observe — “measure”, if you will — the fact that we are conscious and that two plus two is four; we do not merely assume this (there is clearly a difference: to arbitrarily assume your friend is in the same room as you is quite distinct from seeing that your friend is in the same room as you). And as in the case of the measurement of fundamental physical constants, direct measurements in consciousness can of course be erroneous, yet when we consistently measure the same result time and time again by running the same experiment, we do seem reasonably justified — inductively, as always — in believing the validity of the measurement.


That our conscious impressions are what our beliefs ultimately rest upon may seem somewhat weak and unsatisfying, yet only if we fail to keep in mind that conscious impressions are in fact all we ever deal in when it comes to our knowledge. This includes the sense that conscious impressions constitute a poor foundation for knowledge: this sense is itself just another appearance in consciousness, resting on the exact foundation it purportedly doubts. And if a statement like “I believe this because it seems that way in light of what I experience” sounds like a weak foundation for knowledge, this, I believe, is mainly because we usually only use this kind of language when it comes to matters we are uncertain about, such as immediate unexamined impressions. In truth, however, this “it is what seems true in light of my experience” is in fact what we always do, regardless of our degree of certainty. One’s knowledge of textbook information is also just another conscious impression.


Phenomenological Positivism: Knowledge Built from a Phenomenological Palette

What we do when we model the world is to represent its features with the different colors of the palette of consciousness. Indeed, this is all we ever can do: consciousness is all we ever know, and hence its colors are all we ever can model and represent the world with at the level of our knowledge.

One can fairly consider this account of knowledge a positivist one, although one that is of a distinctly phenomenological and common sensical sort. For given that consciousness is all we ever know, it is obvious that all facts we know are known via a composition of the various states of consciousness available to us, including the set of facts about the “external world” that can be detected and represented with our conscious minds (and things that fall outside of what we can detect with our conscious minds are obviously the things we cannot know).

So although science is often considered beyond unification, and that universal features shared by all sciences seem to have been deemed non-existent by common consensus, it remains trivially true, to me at least, that all forms of knowledge, whether we deem them “scientific” or not, are known in consciousness, and hence that all our knowledge is at least united by this common feature. In a nutshell, our knowledge of the world is a matter of phenomenological models that appear consistent with phenomenologically observed data. And, again, this “appearing consistent with” — or “seeming right” in light of — all the data, is, as a mater of justification, ultimately all we have. This, I submit, does not only apply to science in its usual narrow conception, but to reason in general. For instance, this is also how we (ideally) assess the plausibility of different views in, say, ethics and epistemology: by weighing the data, including arguments and counter-arguments, and assessing what seems reasonable in light of it all (and here it is worth being mindful of the fact that genes seem to play a significant role when it comes to what “seems reasonable”, also in the realm of ethics and politics, and hence to be intensely skeptical of the “immediate seemings” of one’s crude intuitions, and to probe them deeper).

In this way, this account of knowledge and reason actually breaks down the usual empiricism-rationalism dichotomy: all processes of thought and reasoning are also phenomenally observed sensations, and hence not something different from “observations.” They are indeed themselves impressions — more doubtable data — that influence our view and assessment of the world. Rationalism, as in logical reasoning, is just another mode of empiricism and experiment, one that has strengths and weaknesses like all other “experimental devices”.

It is worth noting that this account of our knowledge, and reason more generally, does not amount to mere Bayesianism in any usual sense. For while Bayesian updating surely shares this general feature of being a matter of updating and estimating degrees of certainty based on all available evidence, and while much of our own updating is overtly Bayesian — for instance, many of us have made updates in our views based on formal Bayesian calculations — there is much more to our knowledge and our updating of our beliefs than mere formal calculations with numerical probabilities. Not all available evidence is represented, or even representable, as numerical probabilities; for a person who does not know what it is like to experience, say, sounds and sights, no amount of formal Bayesian calculations is going to shed light on the matter. One must experience these things to know what they are like. Bayesian updating is merely the formal special case of the more general inductive method of estimating what seems right in light of the doubtable data/experience we have accumulated so far.


Do We Have Faith in Induction/Science?

A notion one often hears from religious scholars is that faith in religious claims is no less reasonable than belief in the facts we know from the sciences, since the latter ultimately rest on faith as well: they rest on faith in reason. Yet is this true? In a nutshell, “no.”

Science is the process of learning about the world by observing it. Therefore, one could argue that science rests on the assumption that we can learn about the world by observing it, which is in fact functionally equivalent to the assumption that induction is valid, since learning about the world by observing it requires that patterns that existed in the past still exist today and in the future — the core of induction.

Yet one need not even make this assumption explicitly, since the assumption that we can learn about the world by observing is one that we cannot not make. In order to even express the belief that one cannot learn from experience of the world, one has already learned from such experience, the experience of one’s own belief. (This inevitability makes it just like the assumption that at least some aspects of memory can be trusted, which is in fact also an equivalent proposition: that we can learn about the world by observing it requires that at least some aspects of our memory is reliable, and for our memory to contain reliable information about the world, it must be possible to learn about the world by observing it.)

Thus, we all implicitly “assume” that we can learn about the world by observing it, whether we are religious or not, and hence making this inescapable “assumption” cannot meaningfully be called a leap of faith. Rather, it is an inescapable fact, as there is no intelligible alternative (indeed, the very possibility of intelligibility of any kind rests on learning from observation in the first place, as claims cannot be deemed (un)intelligible if they cannot be learned in the first place). This makes it wholly unlike actual leaps of faith, i.e. believing in things, such as supernatural events, without supporting evidence. The latter is by no means inescapable.

Indeed, claims about some things being a matter of faith only make sense in a context where we have already made “the leap of faith” of accepting that we can learn about the world by observing it, since whether a claim rests on faith is a matter of whether there exists evidence to support it. And all evaluations of evidence must take place in a realm where we have already assumed the relevance of evidence for propositions about the world — i.e. already made the inevitable “assumption” whose status was in question. In other words, in order to assess whether or not something is a matter of faith, we must “assume” the relevance of evidence in the first place; we must accept that we should go with what seems right in light of the doubtable data/experience we have accumulated so far.

One may object that science rests on much more specific assumptions than merely the possibility of learning about the world by observing it, yet, ideally, this should not be the case. For while it is true that specific methodologies have emerged in the sciences over time, the process of science most generally — that is, learning about the world by observing it — is not committed to any specific methodology in principle, which makes all specific methodologies open for revision. If certain methods are shown to be seriously flawed, as has happened before, these methods should be discarded or updated. And this is indeed how the methods we see employed in the sciences today have developed. Placebo-controlled studies and double blind experiments were not assumed by faith to be the way to “do science” from the outset. Rather, these and other sensible methods of discovery were themselves discovered over years of trial-and-error.

Thus, what works best, both when it comes to theories and methods, is itself to be settled with observation and examination, not faith. Based on the fundamental principle of learning from observation, science continually refines its own method. In this way, the process of observing and learning about the world is a self-correcting and self-optimizing one.


Doubting the Apparently Undoubtable

As noted earlier, inductive reasoning has shown us that we have good reason to maintain humility about our beliefs. We know that our memory is fallible. As mentioned above, even mathematical proofs held to be valid by many have turned out to be wrong, and this risk of fallibility not only pertains to the logical deductions made by others, but also to those made by ourselves — the appearance that a logical deduction is valid can turn out to be wrong upon closer examination. It has happened before.

So it seems that we should maintain at least some degree of doubt even when it comes to logical deductions that we seem to have reason to be completely certain of, which is not to say that it is reasonable to have more than a negligible degree of such doubt in most cases.

Yet the above-mentioned doubts merely amount to epistemological doubts, doubts about whether our faculties of reasoning accurately track the deeper patterns of the world. We could also have doubts of a deeper ontological nature, namely about the stability of those patterns themselves. For instance, will the laws of physics as we know them apply tomorrow? What about logico-mathematical truths?

Do such questions even make sense? After all, don’t questions concerning what happens tomorrow, and hence rest on the concept of time, already presuppose some basic laws of physics, or at least some elements from the physical framework as we know it? And doesn’t the meaningfulness of doubts concerning whether our logical framework will at all apply tomorrow also itself rest on the validity of that very framework, e.g. that things are either the case or not the case? After all, all talk of whether something applies or not — is true or not — already takes place in the realm of, and therefore presupposes the sensibility of, logical thought. So what does it even mean to say that this framework might no longer apply when the very coherence of “applying” rests on this framework? It seems self-refuting.

It does. Yet even so, we do seem to have reason to maintain at least some degree of humility about these propositions, one reason being the aforementioned “epistemological doubt” — we know our memory is not entirely reliable, and hence we should admit of the possibility that deductions of the sort made above have a small risk of being wrong. Indeed, this argument for the sensibility of (at least a small amount of) doubt seems to pertain to all arguments, including itself (and also the most undoubtable of ethical positions we may hold).

Second, certain drastic changes, such as changes in certain otherwise lawful physical patterns, do not seem inconceivable; indeed, some cosmological theories predict such changes. Therefore, the claim that at least some apparently solid facts about the world may suddenly change cannot be ruled out deductively, it seems. Might the very fabric of existence suddenly change in radically unexpected ways, thereby perhaps altering physical and mathematical truths as we know them? (Again, on a physicalist view of the world, physics and mathematics cannot be separated, which means that what we may call the uniformity of mathematics depends on at least some degree of uniformity of [what we consider] physics). It seems extremely unlikely, but we cannot exclude it with total certainty.

Lastly, it also seems conceivable that we could have new experiences — on a sufficiently exotic drug, for instance — that would suddenly make the so far inconceivable seem conceivable, and thereby make apparently valid deductions and brute facts appear invalid and untrue. Again, the only justification we have for believing what we believe is, ultimately, that “it just seems true.” And while it may be inconceivable to imagine, say, that mathematical truths could suddenly change, it does not, strangely enough, seem inconceivable that such an apparently inconceivable claim could seem conceivable in a radically different state of mind. And if it can seem right in another state of mind, how can we maintain absolute certainty that that state of mind is more wrong than our own present one is? It seems we can’t.

In sum, it seems that even when it comes to the most outrageous of claims, claims we cannot even make any sense of, some small degree of uncertainty about their status still seems in place, although the appropriate degree may be very small indeed. Everything can reasonably be doubted to some degree. Or so it seems.

[A small side note: In terms of practical implications, this small window of doubt might help one soften up painful certainties, such as certainty in fatalism. For while it might be tempting to some to think about the world as being an unalterable multi-dimensional structure that we cannot change in any strong sense, one must admit that this view could in fact be wrong, and hence that trying to change the world for the better indeed might have some chance of making a difference even in a very strong sense. Either way, it seems like one does not lose anything by trying one’s best.]


Inconsistent Skepticism

Our conscious experience seems to represent a world “out there” that is independent of our own minds. But how do we know this representation is at all accurate? How do we know the truth is not rather some well-known skeptical conjecture — for instance, that our experience is all a dream or a computer simulation?

I think there is a lot to be said against skepticism of this sort, the most important one being that it is inconsistent. Knowledge of dreams and simulations is itself found in our experience, and hence to consistently doubt the validity of our experience requires us to doubt the validity — i.e. the meaningfulness and sensibility — of these notions themselves. Yet in our entertainment of skepticism of this sort, these notions themselves are somehow exempt from skepticism. They stand beyond scrutiny, while virtually all other appearances we know of, and all other beliefs we hold, do not.

What can justify such inconsistent skepticism? Nothing, as far as I can see, especially given that claims of the sort that all we experience could be a dream or a computer simulation seem extremely dubious to say the least. Take the claim that our entire experience is a dream. Does anything we know of actually suggest this in the slightest? Not to my knowledge. The state of our consciousness in our dreams is radically different from our waking state. Indeed, within a dream it is even possible to realize that one is dreaming, as many of us have tried; something similar never happens in our waking state. The only thing that remotely hints that our experience could be a dream is an argument from analogy: Given that our experiences in dreams can seem to convincingly represent the world, yet still turn out to be mere dreams, could our waking state that seems to convincingly represent the world not be a mere dream too?

If dreams were anything like our waking state, this would indeed seem reasonable. Yet the truth is that they are not.

This “the appearance is different” fact may seem to say precious little, yet only if we miss the significance of differences in appearances. By analogy, imagine that you are on holiday in Istanbul. You remember planning the journey, traveling there, being there for the past five days, and presently you are watching the Sultan Ahmed Mosque while feeling the unbearable summer heat. Now, how do you know that you are not, in fact, in Oslo? Well, just about every single appearance in your consciousness suggests that you are not, and hence you are not in much doubt. And reasonably so.

Yet is this really analogous to the difference in appearance between our dreaming and waking state? Not quite, as I would argue that this analogy actually fails to do justice to the actual difference between our waking and dreaming state, a difference that is far greater than the difference between a waking experience of Istanbul and Oslo respectively. Hence, I would argue that we have no more reason to suspect that our present experience is a dream anymore than we have reason to suspect that we, say, live in a completely different city than we thought. Yes, the world, including the basis of our experience, may well turn out to be very different from what we expect in many ways. Yet the specific claim that our experience of the world is a dream — something that takes place in the brain of a sleeping person — is, I would argue, extraordinarily implausible in light of all that we know, especially the enormous difference between the character of our waking and dreaming state.

Even stronger skepticism seems justified in the case of the claim that all we experience is a computer simulation, one reason being that we simply have no evidence that computer simulations can mediate conscious minds like our own in the first place — at least no more evidence than we have for believing that, say, tomatoes can (indeed, tomatoes are in many ways far more similar to human brains in physical terms than computers are). Another good reason to be intensely skeptical is that so-called ancestor simulations are in fact impossible.

A similar degree of skepticism seems apt in the case of the claim that all we experience is the result of a brain in a vat. According to what we know from fields such as physics, chemistry and biology, there is, as Daniel Dennett shows in Consciousness Explained, no way to produce an experience like ours by stimulating a brain in a vat. And if we dismiss such knowledge, we might as well dismiss our belief in the existence of brains in the first place — itself a belief about physics and biology that we do not seem justified in granting a more privileged status than we do other solid facts found in the canons of physics and biology.

And since we are dealing with various skeptical hypotheses, it seems worth pointing out that skepticism about the existence of other minds is on no firmer ground, as it indeed has the exact same epistemic status as doubting the existence of brains does. The existence of brains is only known through our own conscious experience, an experience that, according to what is known in that experience itself, is mediated by a physical brain. Based on this, we draw an inferential arrow that connects our experience to physical brains. We go from experience to physical brain. Therefore, drawing an arrow from brain to experience — whether one’s own or that of others — which is really just to draw the exact same arrow in the opposite direction, is no more problematic. Conclusively, doubting the existence of other minds is really no more reasonable than doubting the existence of one’s own brain.

One may argue that there is a difference when we are talking about different brains from our own, yet one could say the same about one’s future or past brain, which is also different from one’s present one. If one believes that one’s own future brain will be conscious — a brain that is similar yet still different from one’s present one — then how can one maintain that the brains of other beings that are also similar, yet different from one’s present brain are not conscious as well? Similarly, if one believes that one’s ever-changing brain has mediated conscious states in the past, why should the different brain states of others not mediate consciousness as well? To believe they do not is simply inconsistent.



The problem with skeptical conjectures such as the dream and the simulation hypothesis is, again, that they hold that virtually all the appearances we know from our experience are false, yet the appearance of the possibility that the basis of our experience is something radically different from what we thought — yet still something that we know of from our experience, such as the notion of a dream or a simulation — is not subjected to such doubt at all (in spite of an absence of good reasons for believing in such possibilities in the first place). In other words, these conjectures rest on arbitrarily constrained skepticism.

More than that, these skeptical hypotheses also seem to undermine themselves. For if we accept the premise that our experience indeed is a simulation or a dream, what reason do we have for believing that the worldview we are able to draw from it, including any conclusion about dreams and simulations, has any validity beyond our own simulation or dream? If we are living in a dream or a simulation, it seems that what we think we can say with any certainty about the world, including about dreams and simulations, is likely to be wrong to an unimaginable degree, since it is all based on pure dream or simulation itself. Conclusively, accepting any of these conjectures seems to force us to doubt them strongly, even to make it difficult to make sense of them. And being self-undermining is not a virtue of a conjecture.


Again, what we do when we assess the truth of a proposition is, ideally, to judge its plausibility in light of the totality of what we know. And this is exactly what we fail to do when we deem skeptical conjectures of this sort likely. We go with peculiar arguments, propositions, and concepts, and then doubt everything else, thereby ignoring that the meaning, even the coherence, of these arguments and concepts rest, in subtle and not so subtle ways, on all this other knowledge that they supposedly imply we should doubt, thereby inadvertently destroying their own foundations.

Keeping the totality of our knowledge in view and applying our skepticism consistently leads us, I maintain, to a relatively common sense view of the world, at least when it comes to the basics of the basis of our experience. What we know about the world hints that our experience is mediated by a biological brain just as strongly as our experience hints that the Earth is round; nothing really suggests it is not. In my view, we have no good reason to believe that what we experience is, or even could be, a dream or a simulation, while a very great deal — including consistent thinking based on what we know — strongly suggests it is not.