Assumptions

As far as practicable, I would like to have no unexamined assumptions. Of course, there are practical limits. How do I know I'm not a brain in a vat? I don't. It is the nature of brain-in-a-vat arguments that you do not know they are false, ex hypothesis. All you can really say is, "I don't care. I am going to go forward, developing my ideas, ignoring that 'possibility.'' If it turned out that I was just a brain in a vat, and not a real-live boy, that would be sad, but then, ultimately, not much sadder than being an epiphenomenal consciousness arising in a meat-sack, pursuing my self-conceived goals for a brief period of time before dissolving into a stinking pile of mush. So be that as it may. In the mean time, I've got things to do...

Pondering Truth

When we speak of “truth” do we describe some single entity or quality in the world?  Or is “truth” hypostasized to simplify a complex of relationships between the inner and outer worlds that we do not (cannot?) understand?

Is “truth” an operational concept?  There is no operational difference “now” between a justified belief and a justified true belief (a.k.a. “knowledge”, at least in many philosophers’ systems).  I make the same choices, take the same actions either way.  But there may be an effect on the outcome (or not).  Is “truth” operational in evaluating outcomes, and therefore, perhaps improving the reasons for future beliefs?

Even in evaluating the outcome of past choices, I still don’t “possess truth”.  I only formulate, and attempt to justify, further beliefs (e.g., beliefs about my past beliefs).  In Dewey’s terminology from Experience and Nature, truth does not seem to be something we can “have directly”.

There is a state of the world, and there is a state of my mind (or yours), which is, itself, part of the state of the world.  The state of my mind includes a simplified, impressionistic “image” (in some neural/synaptic medium) of the state of the world – to the extent it is accessible to my imagination.  In that image, the state of my mind figures under such rubrics as “reasons” and “beliefs”.  Based on my state of mind (at any given time), I will make certain choices, and take certain actions.  Partly because of such actions, at some future time the state of the world, and the state of my mind, will be different.  By comparing the current state of my mind (and especially its world-image) to my memory of its prior state, I make judgments about the truth of my previously held beliefs.  I formulate (reasoned) beliefs about my prior beliefs.

Is “truth”, then, just something we invent to explain our relative satisfaction or dissatisfaction with the outcomes of our past endeavors?  The trouble with that idea is that our feeling of satisfaction may be connected to aspects of the outcome which some mythical unbiased observer would be unwilling to call “truth”.  For instance, a racist may desire to join an organization of like-minded individuals.  His belief that African Americans are genetically inferior to “Aryans” may help him in that endeavor, and thereby lead him to be satisfied, but we would not want to call his belief “true” on such grounds.  Then there is the growing body of psychological research indicating that our brains have evolved so as to readily adopt certain beliefs which are adaptive, but not (necessarily) “true”.  An example is the “confirmation bias”, where by our minds tend to disproportionally accept data that confirms what we want to believe, and reject data that disconfirms it.  Another example is the “hyperactive agent detection” that Daniel Dennett discusses in Breaking the Spell (among other places).  Other examples can be found in various papers in Naturalizing Epistemology (Hilary Kornblith, ed.)

It seems there is something actual about the relationship between our mental states and the world state that we are trying to capture with the concept “truth”, which is related to, but not simply reducible to, our degree of satisfaction with outcomes.  I admit, at this point in my life, to be still wondering (persistently) about exactly what it is.

Postscript on Confirmation.  As with many of the musings on Persistent Wondering, this one pretty much starts “where I am” and doesn’t make much of an effort to relate to an audience that may not be starting at the same place.  I apologize for that… but after all, I am portraying myself as a “wonderer”, and making no claims to be a teacher.  (Lame excuse.)

In this essay in particular, though, it seems to me that many people may wonder why I would feel – at all – that “truth” is not directly accessible.  In many (most?) of our everyday interactions with the world, confirmation of our beliefs is direct and immediate, and seems incontrovertible.  I believe I left my keys on the kitchen counter.  I go downstairs – I either find them there, or I do not.

Other “facts” are not so easily confirmed or disconfirmed, though.  There are the challenges of philosophical skepticism.  How do I know I am not dreaming?  Or hallucinating?  Or a disembodied brain kept alive in a vat, with my neural inputs manipulated by alien scientists?  Then there is the question of “modeling”.  Complex physical or social systems cannot be grasped by our minds in their complete and detailed totality.  We need to abstract from them, simplify them, in order to understand them.  Do concepts like race, class, culture, the national income “truly” conform to some real world objects, and if so exactly what and how?  How do we indubitably confirm or disconfirm them?  Theoretical physics provides examples, also.  Do the objects of modern theoretical physics – quarks, bosons, photons – “really” exist, or are they just a convenient (not necessarily unique) way of mathematizing experimental results?  Are the relatively abstract and indirect confirmations of physics experiments really of the same class as our confirming (by looking) that our keys are on the counter?

But really, ALL of our knowledge involves some such modeling (abstraction and analysis).  All the objects we conceive involve some level of abstraction – focusing on certain aspects of experience and ignoring others.  Something of this is suggested by Heraclitus’s statement thousands of years ago that “You can never step into the same river twice.”  What exactly is a river?  Is it the specific water molecules?  But they start out in a glacier and end up in the ocean.  Is it the banks?  But they shift with time as soil particles are removed and deposited.  Is it some abstract (fractal?) pattern that encompasses changes over time?  What is the “truth” of the matter?

Our mental states (beliefs and so on) consist in synaptic patterns, roughly, stable-yet-changing patterns of chemical interactions between neurons.  The state of the world consists in the interplay of forces amongst patterned matter and energy, extending strongly or weakly between the various points of the entire universe.  It is not clear that some unique and transparent correspondence can be established between those two things and unambiguously labeled “truth”.  On a conceptual, theoretical level, the question of the truth of our beliefs, their confirmation or disconfirmation, is not at all a trivial one.  Although on the pragmatic level of day-to-day actions, it very often is.

Truth, knowledge, skepticism, and stuff…

A standard philosophical definition of knowledge goes as follows:

(I know A) <=> (I have a justified belief that A) and (A is true)

As I write this essay, I’m in the middle of reading Robert Nozick’s discussion of knowledge and skepticism in Philosophical Explanations.  Nozick uses a very specific concept of “truth tracking” which leads to some very interesting results, but is essentially (it seems to me) just a particular approach to defining justification, one that leads to a coherent (I think), but sometimes quite peculiar conception of knowledge.  I find myself working around a rather different rejection of philosophical skepticism.  What follow are musings, not intended to represent a complete expression of a developed idea.

If some particular skeptical scenario (SK: SK => not-A) were true, then A would be false, and I would not know A.  However, A, so not-SK, and I do know A.  The skeptic’s objection fails, because SK is not true.

Truth is outside my direct experience.  It is not something I have direct access to.  To use Dewey’s language from Experience and Nature, it is not something I “have directly”.  All that I have directly is justification (evidence, inference rules, trusted sources, etc.)  There is no way to operationalize truth; I can only operationalize justification.  One reason that theories of knowledge remain so problematic is that knowledge, vs. justification and belief, has exactly zero influence on our behavior at time t = now().  We try to justify our beliefs, and to act on justified beliefs.  Later, we may come to believe that our prior beliefs were not (properly) justified, i.e., were false.  But at any given moment (outside of certain contexts of philosophical inquiry) the question, “Are my beliefs true, or merely justified?” is never a useful one.  The question, “Is this belief justified?”, however, is (always?) an important one.  Operationally, the question of “truth” always devolves to:  from perspective B (perhaps a later one), do the beliefs held to be justified from perspective A still appear justified?

There is no way to operationalize (general, philosophical) skepticism at all.  Skepticism places all logical possibilities on an equal footing.  All available evidence is discounted, and there is no way to distinguish one possibility from another, to prefer one over the other.  Skepticism cannot give any positive plan of action.

Philosophical skepticism of the sort I am referring to (what Hume referred to as Pyrrhonism) must not be confused with a critical evaluation of our methods of justification.  Critical evaluation of our methods of justification is completely operational and is critical to ensuring that they track truth as closely as possible.

P.S.  Nozick, I think, expresses an insight similar to mine above about truth and experience when he says (p. 232 in my paperback copy) “We have said that knowledge is a real connection of belief to the world, [which we call] tracking, and… this view is external to the viewpoint of the knower, as compared to traditional treatments, [though] it does treat the method he uses [to track truth] from the inside, to the extent it is guided by internal cues and appearances.”

P.P.S.  Anticipating certain gleeful but misguided reactions to my rejection of “skepticism”, I want to point out a deviation between a common vernacular use of the word “skeptical” and philosophical skepticism, to wit, the phrase: “Skeptical about God.”  Disbelief in God (or even just doubt) is usually based on a belief that you can trust the evidence to lead you to true conclusions about the world.  Doubt about God stems from observing the lack of positive evidence, and disbelief from observing that the available evidence is incompatible with the God hypothesis.  These methods of justifying belief are exactly antithetical to philosophical skepticism, which holds that no amount of evidence is ever sufficient to justify a belief.  Theists, in fact, often (mis-)apply a skeptical argument when they claim that “You can’t prove a negative result,” not realizing that, if true, this argument merely puts their God on exactly the same footing as being a brain in a vat manipulated by alien scientists in the Alpha Centauri system.

P.P.P.S.  (9/7/2013)  I need to correct my statement that Nozick's concept of "tracking" is just a special case of justification.  (He is at pains to distinguish them on p. 267, by which time I was in a position to realize what he meant.)  Tracking, like truth, is external:  our methods really do track truth.  Justification is internal: we believe our methods track truth, and are therefore reliable or justified.

Choice and Determination

If we choose, and our choosing is not pure, unanalyzable magic, then there must be some mechanism, however complicated, by which we make the choice.  Logically, it seems that, either this mechanism must be “deterministic” in the sense that if the mechanism is in exactly the same state, and receives exactly the same inputs*, then it will decide in exactly the same way; or there is some purely random component (e.g. quantum uncertainty) that affects the choice.

Neither of these options “sounds like” free will.  But if this is not free will, and free will is not simply a meaningless concept, or at least irrelevant to the choices we actual can and do make, then there must exist some entity whose choices are being constrained by this process.  That is, there must be some entity that is not “free”.   But if some entity is unfree, what entity is it?  If “you” are not exercising “free will” in these conditions, who are “you”?

We, the material, biologically constructed entities that we are, do make choices, and our choices are made in an effort to further the ends that we have conceived for ourselves.  This much is manifest.  It seems meaningless to me to say that we do not have free will in these choices based on some highly abstract argument that somehow we will never make the choices we don’t end up making.  What does it even mean for us to somehow be “able” to make the choice we do not, in fact, end up making?  I don’t see how that idea can be rendered coherent, except by reference to physical/mechanical potentialities, and epistemic possibilities that are fully compatible with the “deterministic” mechanisms of choice referred to above.    

In any case, other than these organic mechanisms, which make choices in the manner that we, in fact, make them, there is no entity here that can be “unfree”.

Of course, our choices are constrained, by the materials and opportunities available in our environment, by our abilities, physical and cognitive, by our histories, including things that have happened to us and previous choices we have made.  And of course the ends and goals that we conceive are formed by similar internal and external factors.  But for this to mean that our choices, from among the options that seem epistemically possible to us at the given moment, are “unfree”, there would have to be some self, other than the selves so constructed by history, biology, and prior choice, whose freedom was constrained, whose will was being denied, by the choices the biological “we” are making.  I cannot, for the life of me, conceive of what that other self might be.

I conclude that to say that people do NOT have free will makes no sense.  All that is left is to either accept that the way we actually choose represents free will, or to take the question of free will as an ultimately meaningless “pseudo-question”.  But at this point the choice is purely “semantic” in the colloquial sense of “just a matter of words”, and it makes no real, philosophical difference which wording you pick.

*The conditions of the mechanism being in “exactly the same” state and receiving “exactly the same” inputs  are considered only to focus on the logical argument.  They are both, in practical reasoning, impossible.  The universe is far too complex for it ever to be put back in the same state twice, and as for our “mechanism”, it is altered by every experience, and therefore can never be in the same state twice.  Even settling for “highly similar” is dubious.  Most significant human choices are, neurologically, a chain (actually a highly “parallel” web) of micro decisions, each of which potentially alters decisions further down the line, possibly in a binary manner (on/off – no shades of gray).  The end result, it seems to me, must show sensitive dependence on initial conditions, whether the component steps do, or not.  (They may.)  Thus even “similar” inputs to a brain in a “similar” state can lead to widely different outcomes.

Note:  I wrote most of the above text while I was reading Ch. 2 in Daniel C. Dennett’s book “Elbow Room: The Varieties of Free Will Worth Wanting”, a book which I have subsequently completed.  I think my views on this, as on many other topics, are broadly compatible with Prof. Dennett’s.

Similarity and Natural Kinds

Preface:  I’ve been reading “Naturalizing Epistemology” by Hilary Kornblith, Ed., which reprints a couple of papers by W.V.O. Quine, “Epistemology Naturalized” and “Natural Kinds”, along with papers by others that relate to questions raised by Quine in those essays, or raised by others in response to those essays.  The present post was inspired by ideas in the first few essays in that book.

“Similarity”, I think, arises from replaceability.  Two objects are similar to the degree to which you could replace one with the other without salient change in the state-of-affairs under analysis.  Obviously “salient” and even “change” are terms in need of further analysis.

Perceptually, we have “hardwired” (innate) and “softwired” (learned) structures in our brains (primarily – with some functionality distributed elsewhere in our somas) to identify different kinds of similarity.  Hardwired structures include things like edge detectors and angle detectors.  Softwired structures are built up from such.  Questions that can be asked include:  How would such features have come to evolve?  Why are they so apparently efficacious?  Just how reliably efficacious are they?

The nature of organisms suggests categorization of environmental factors on the basis of their effects on the organism.  Some factors encourage growth or reproduction.  Some limit these or produce death or extinction.  With complex organisms, some factors have these effects on a part of the organism, only, and may have very different effects (or little effect, at all) on other parts – stimulating production of this hormone, while retarding production of that, for example.  Replaceability of these factors with respect to their organic effects is the basis of categorization, and the source of similarity.  The salience of change can be suitably quantified in each case (e.g., rate of cell reproduction or hormone production).

Since they derive from our interactions with the world, our categories and sense of similarity relate closely to the world.  But there is still an element of subjectivity.  All categories are relative to an analysis.  Some categories may be relatively stable across all conceivable analyses we may do.  These we tend to characterize as “natural kinds”.  But even natural kinds such as species can have fuzzy edges for certain analyses.  (Exactly where, on the evolutionary tree, does a particular species begin?)  An intelligence arising from a very different history (a silicon-based life form, say, or a spontaneously evolving “artificial” intelligence) might cleave the world very differently than we do.  But in some categories (mineralogy, biological lineages) if it made an analysis at all, there would probably be considerable correspondence with our own.  Natural kinds are not meaningless, nor arbitrary, but neither are they perfectly precise.

Starting from Zero

I’ve never read Hegel, but I recently reread Russell’s chapter on Hegel in A History of Western Philosophy as background to some early Marx we were reading for the Democratic Socialists of America Boston local’s reading group. Per Lord R, Hegel starts from the idea that “the Absolute” is “pure being”, deduces that this means it has no qualities, and finds this self-contradictory because to have no qualities is to be nothing. This is the antithesis – “The Absolute is nothing” – and leads to the first synthesis: “The Absolute is Becoming.”

What struck me is that Hegel thinks he is starting from zero, using only one premise – that reality cannot be self-contradictory – but of course he really is applying many premises: that there is something that may reasonably be thought of as “absolute reality”, that “pure being” is a meaningful concept, which entails having no attributes, that to have no attributes (or qualities) is to be nothing, that the union of being and being nothing is becoming.

It seems there is a basic flaw in a philosophy which tries to start from zero, or from some very small set of premises, building up from these by synthesis; to wit, that we cannot do it. We always, in fact, have to start with a lot. Descartes’ radical doubt leads, perhaps, to “cogito ergo sum” (more precisely, perhaps, “...something is”, but to go further, he needs to introduce more premises, “undoubting” certain things. He selects premises that purport to justify the undoubting – clear and distinct ideas, and the goodness of God – but this is basically B.S., not justified by his method, as stated.

Really, what we do, always, is to start with everything we know, or think we know, and start juggling it about. We apply reasoning (rules of inference) that feel right to us and (perhaps) we try to codify these into a system of logic. We apply various tests in doing this. What tests depends on the person and what he or she brings to the process. Examples are empirical tests (how well do these premises and this logic predict future experience) and faith-based tests (do these premises and this logic lead to conclusions that conflict with “revealed” scripture?) We can apply tests, at any time, to some of our a priori beliefs about facts, and or to our rules of inference, but each test involves accepting other facts and rules, at least temporarily and contingently. We can never test the whole shebang.

This process is irreducibly ad hoc and messy, which is no doubt what has led many philosophers to reject it, and to try and find a purer and simpler alternative. But they were deluding themselves.

The actual process “works”, more or less, because our sensual and reasoning faculties have evolved by natural selection. If they failed badly at the task of extracting meaning from the universe, we would have become extinct, or at least these faculties would have. But this is no guarantor of “ultimate knowledge”, whatever that is. Aspects of our reasoning system may be selectively neutral, such that there is no effective, general difference in survival rates from reasoning one way or the other. These aspects, then, would not be fine tuned by natural selection. Like blue eyes and brown eyes, both may survive indefinitely in the species. I suspect this may be particularly true of the ways we construct abstract structures of meaning to explain our experience to ourselves.

Different ways of knowing can also serve the same person better or worse under different conditions. Something like what I called “faith based” learning is certainly the most satisfactory way of learning for a child, who will learn much too slowly if she must test every new factoid empirically, rather than trusting the wisdom imparted by her elders. In fact, realistically most of what we learn throughout all our lives, we learn from others whom we trust, either because of their social position as teachers, authors, or what-have-you, or simply because we believe they have no reason to lie. In complex situations, we have to apply other tests – such as when we find that the “experts” don’t agree with each other. And empirical experience is the ultimate arbiter, to which faith, for any reasonable person, must bow. Galileo’s telescope trumps the Pope.

Episteme

I have two fundamental epistemological premises: that the evidence of my experience is the best available (really only available) data I have for learning about the world, and that most people who study, think, speak and write about the world are not intentionally lying. These seem to be pragmatically a minimal set. I don’t see how one can practically set forth on the project of learning without them.

Note that the use of the words “most” and “intentionally” in the second premise imply two corollaries: some people are lying, and some people may be unintentionally stating mistruths. (In fact, I might argue that we are all unintentionally stating mistruths to a greater or lesser extent, but that would be more of a theorem than a premise.) Also, saying experience is the “best available” data doesn’t imply that it yields infallible insight.

The two premises do not form a complete (i.e., sufficient) set. All they really say is that I can trust what I experience, and what people tell me about what they experienced (including second or third hand, etc. reports) – but with a grain or two of salt. They don’t say anything about how to come up with that grain of salt, or to know how many grains to apply. They don’t, in other words, tell me how to distinguish the veracity of conclusions I draw from these sources, or how to distinguish between competing theories. They don’t specify any rules of inference, at all.

I’m afraid all I can say about making distinctions is, “It’s ad hoc.” I am no Descartes, to offer a single unified answer to the question of how to distinguish true ideas from false ones. Certainly, I do not believe that because I can hold some idea “clearly and distinctly” that it must be true (although it might suggest truthfulness prima fascie). Instead, it’s more a matter of how well does an idea “fit in” with the other body of ideas I have constructed, over time, from the same evidence. “Consistency”, in a word. But how do I decide if an idea is consistent? Certainly not the idea of the excluded middle. I am quite convinced that it is possible for a thing to be both A and not A. The clearest examples come from human emotions: do I want to spend a month’s vacation in Venice this year, even though the press of work before and after will be terrible, it will cost a lot of money, my Italian is rusty, and I will have to find a house-sitter and/or worry about my pets and everything else in my house? I do, but I don’t. Fuzzy logic may offer better (if inherently less certain) models. But I am convinced that real antinomies can also be supported, as matters of fact (at least as humans perceive fact) in the real world, as well. Or at least, I’m not convinced that they can’t.

Ad hoc. I know it when I see it. Maybe. More or less. (I do, but I don’t.) Kind of like Descartes, perhaps, except I substitute “vague and fuzzy” for “clear and distinct”?

This could be depressing, if, like many philosophers past, I desired the nature of my mind (or soul) to approach some ideal of perfection – to make me like a god. But I don’t believe in gods. Rather than being depressed at failing to approach a fictional divinity, I prefer to celebrate the humanness of it all. Because this messy, ad hoc, but often very effective process of distinction is the stuff of life, after all, and quintessentially human, if only because humans, by and large, do it exceptionally well. Not that we do it infallibly – there are a lot of people in the world who are dead certain of things about which I am certain they are dead wrong. But by and large, in the billions of tiny, every day distinctions and decisions we make over the course of our lives, we do mostly pretty well.

We do this, of course, because we’ve been programmed that way by natural selection. Our brains have evolved to do a job, and they do it rather well (just as flies fly very well, and frogs do an excellent job of catching them). We have certain decision making processes built into our equipment. By studying our thinking in a natural scientific sort of way, it is possible to get clues as to what they are. Philosophers, I think, who have tried to set rules of thought start with some biological rule and then codify it – so clarity and distinctness counts, biologically, as evidence, and so, on some level, does the excluded middle. But we can’t stop there. We move on to fuzzy logic, paradigmatic categories... and who knows how far beyond?

My guess is that, as in most things, the brain works by having a bunch of rules, without any necessary regard as to whether they are consistent in any a priori theoretical sense. Different rules are stimulated by a particular experience, others suppressed, memory of past experience and feedback loops are brought into play, until the system “settles” in some state (“settles” is a relative term for a system that is constantly in motion), and we feel that this “makes sense” or doesn’t. This is what I mean by “consistent” with the rest of my body of knowledge. It is, in fact, the biological basis of, in a sense the definition of, “consistency”. The rules exist because, at some time in the past, they have been found helpful in negotiating the world – they have been empirically proven. They may be “hard coded” rules, proven in the dim historical past of our heritage, but, again like most things in the brain, the “hard coded” rules can be modified, and new rules created, by our individual experience. And such learned rules may be passed on to subsequent generations via the “Lamarckian” evolutionary process represented by our culture and its systems of education.

Thinking in this natural historical way about distinction and rules of inference, etc., may not “prove” validity, in the sense that philosophers have traditionally sought such proofs. But it may give pretty damn’ good evidence of empirical functionality. And, I would argue that this empirical, matter-of-fact kind of “proof” is most suitable to our real-life existence as human beings in a material world, even if it fails for some fictional existence as souls aspiring to a divine one. If philosophy is the pursuit of the “good” and if good must be good for something, then this is the kind of knowledge and truth that is “good for humans”.

Laplace’s demon

Reading the discussion of “Deterministic and Stochastic Processes”, in Elliott Sober’s book, The Nature of Selection, has me musing on Laplace’s demon. The brilliant 19th Century mathematician Pierre-Simon Laplace was convinced (despite his own pioneering work in probability) that the world was at root deterministic. His famous expression of this, as cited (in translation) in Sober is:

“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it – an intelligence sufficiently vast to submit these data to analysis – it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain, and the future, and the past, would be present to its eyes.”

This hypothetical vast intelligence has come to be known as “Laplace’s demon”.

Is Laplace’s demon, i.e., some being which could know everything there is to know about the universe, even theoretically possible? (In a philosophical sort of definition of “theoretically”.) To address that question, we have to address at least a little of the question “What is knowledge?” That’s rather a big question for an amateur philosopher, but I’ll see what I can do.

First of all, whatever we mean by “knowledge”, it seems clear that it is not synonymous with “representation”. If we were to imagine an infinitely “true” mirror that perfectly reflected the incident light, or a computer disk copier that made perfect copies of one disk onto another, we would not say that the mirror, or the second disk had “knowledge”. What we call “knowledge” involves, I believe, a process of abstraction and interpretation. Abstraction involves making a representation of part of the world – the part we think relevant for our analysis. Interpretation is adding meaning. (I will not, at the moment, try to give a meaning for “meaning” – it is just whatever we add to a representation in order to possess knowledge. For that matter, I won’t discuss the nature of “representation”, either.) If I know a fox is in my chicken coop, I do not know exactly how many kilograms the fox weighs, or exactly where each chicken is relative to the position of the fox, but I know if I don’t get out there, fast, I am going to lose some chickens. Knowledge therefore involves both subtraction and addition. We subtract data that we believe irrelevant to our analysis (abstraction), and we add meaning by a process of interpretation.

So what is “exact” knowledge – that is knowledge that could “comprehend all the forces by which nature is animated and the respective situation of the beings who compose it”? It would seem to require a complete representation, leaving nothing out – i.e., perfect representation plus meaning, instead of abstraction plus meaning. It is therefore a purely additive process. But, as I discussed in “Creating the world” (11/5/09), a representation must be represented somewhere. Whatever mind or computing device is doing the knowing must have at least as many data storage locations as there are data to be represented – and in fact, must have more, since exact knowledge is additive. But if exact knowledge is to leave nothing out – if it is to incorporate every possible thing that could have any influence whatsoever, on the thing known, then it seems the knower must also know itself, and this leads to an infinite regress.

Maybe we could try a different formulation of “exact” knowledge. Thinking of the way “infinity” is usually represented in mathematics, we might try to define exact knowledge by some “limit” formulation, saying that, however much data we have already represented about the thing to be known, we can always if necessary represent more, so that, without ever claiming to have represented everything, we can always represent “as much as we please”. This theory seems to require that the thing to be known is in some sense “small” with respect to the knower, but it stops short of requiring infinite regress. But is it good enough for Laplace’s demon? It seems that with this definition of “exact knowledge” all we are saying is that we can make the probability that we have missed some important piece of information arbitrarily small. There always remains some non-zero probability that some important fact we haven’t considered can come crashing in and invalidate our model. It seems that Laplace’s demon is qualitatively in the same relation to determinism vs. uncertainty as the rest of us – it just has a really big brain, so it can know a lot more.

Another approach is to assume two separate universes – this approach might appeal to someone who still clings to some form of Cartesian dualism. The knower exists in a universe that is not part of the universe in which the known resides. But in order for this to escape the problem of regress, it must be impossible for the knowing universe to affect the known – the knower must be an pure observer, only – otherwise, the knower must still know itself, in order to know all possible influences. We must also posit some form of one-way communication in which information can pass from our universe into the other without even the information-bearing entities themselves being in anyway touched or affected.

It seems that even if such a knower-in-a-separate-universe were to exist, this could be of absolutely no interest to beings in our universe. This separate universe theory is of the same sort as the theory of pure, philosophical solipsism – the theory that only I exist, and everything else that seems to exist is merely a phantasm in my own mind. Each theory is completely untestable, as is inescapable implied by its own hypotheses. Beyond stating such a theory, and noting its inherent untestability, not much of interest can be said.

The above questions seem to render the thought experiment of Laplace’s demon useless as an argument for the determinacy of the universe. Does this imply that the universe is not determinate (i.e. that it is inherently stochastic)? Or could it be that it is determinate, but that this determinacy is unknowable? Personally, I find it hard to render the concept of “unknowably determinate” coherent, but perhaps some philosopher cleverer than I can do so.

Note that I’m not even discussing the possible implications of quantum mechanics. Quantum mechanics holds, of course, that there is inherent uncertainty at the level of the most fundamental constituents of the universe. (Quantum mechanics, by the way, although cast in the most abstruse mathematics – math well beyond my feeble capabilities – is at root an empirically based theory, developed not from abstract philosophical considerations, but in an attempt to explain some otherwise extremely intractable experimental data.) Quantum mechanics is sometimes – although not necessarily – held to imply that some “built-in” level of uncertainty exists at the macroscopic level, also.

Note that the above discussion is not about human limitations, or whether “exact knowledge” is possible to a human mind. The infinite regress problem does not say “no human brain can hold all this information”, it asks “how could the universe contain complete knowledge of itself?” Similarly, the “knowledge as a limit” idea is not about capabilities of human intelligence – in fact, I would argue that no human mind could even come close to getting “as close as we please” (in this quasi-mathematical sense) to exact knowledge about any real world problem. Rather, this is an argument about “theoretical” possibility, as I say above. I admit, I’m not really sure exactly what such a “theoretical” possibility means, except that if something is not “theoretically” possible, than it darn tootin’ is not a practical possibility, either.

Postscript: After writing this essay, I happened to look up the Wikipedia article on Laplace’s demon (http://en.wikipedia.org/wiki/Laplace's_demon). Some of the objections I make in this essay were covered therein (if somewhat more tersely), and physical arguments, including quantum mechanical, were gone into more deeply. The Wikipedia article did not mention the “knowledge as a limit” idea, nor the fact that if the demon were in an alternate universe, some form of one-way (and only one-way) communication between universes would be necessary.