Bad Science, Worse Philosophy: the Quackery and Logic-Chopping of David Foster’s The Philosophical Scientists (2000)
10. Foster’s Biggest Blunder
I have refuted Foster’s first argument, his claim that life is too improbable to have evolved through natural selection. But about half of Foster’s book is concerned with establishing or drawing conclusions from another idea: that, as he himself puts it on page 16, “the universe can be best pictured…as consisting of pure thought.” Essentially, he claims to be taking up an idea of Sir Arthur Eddington’s that “the stuff of the world is mind-stuff.” He uses this to develop his central argument that the only real things in the universe are mental things, this entails a mind that shapes the universe, and this mind is God. If you are starting to recall a certain Bishop Berkeley, you know more about philosophy than Foster seems to. He makes no mention of this obvious corollary, nor the very-abundant criticisms that apply as well to Foster’s arguments as to Berkeley’s.
As for this Eddington fellow, I had not heard of his name before (though I now say I should have), and he gets no mention in the Cambridge Dictionary of Philosophy, but he was a man of some fame in the field of mathematics and science (a kind reader provided me with a useful URL on Eddington: . He is a largely neglected figure in the history of philosophy, as are many of the people Foster quotes as authorities. But Eddington is certainly famous for one particular oft-quoted line about the Second Law of Thermodynamics (Foster quotes it twice, on pages 34 and 123; in fact, throughout the book Foster quotes various books and scientists, though there is no index or bibliography, and although I am suspicious if some are quoted out of context, I have not gone through the expense of checking his sources; he gives no page references, anyway, which makes quote-hunting a difficult task).
I will not concern myself with whether Foster’s quotations accurately reflect the original authors’ intentions or beliefs, but only the extent to which his quotations, as given, are relevant to his arguments. This may involve me in criticism of the quotes themselves, but this should not be construed as criticisms of the authors whom Foster quotes. If they have been quoted out of context, the fault is Foster’s, not mine. As but one example, Foster employs some elements of the work of Bertrand Russell in developing his argument that the universe is mental, as if to gain the prestige of at least one renowned and respected philosopher. But when one considers Russell’s own position on the matter, which Foster never mentions, using his name in such an argument seems a bit duplicitous. On page 142 of Russell’s An Outline of Philosophy (1927) he writes quite directly that “The stuff of the world may be called physical or mental or both or neither, as we please; in fact, the words serve no purpose. There is only one definition of the words that is unobjectionable: ‘physical’ is what is dealt with by physics, and ‘mental’ is what is dealt with by psychology. When, accordingly, I speak of ‘physical’ space, I mean the space that occurs in physics.” Foster might have benefited from reading this. Indeed, his book would have improved in honesty and merit had he cited it and addressed it. But Foster never mentions any criticisms, much less this one.
At any rate, Foster relies on two threads of reasoning to build up his basic premises, from which he will attempt to wring out the conclusion that ‘the universe consists of pure thought.’ First, he tries to show that there is no such thing as ‘substance’—-that science has explained matter away to the extent that nothing is left but pure mathematics attached to no substantial thing at all. Then, he tries to show that since pure math is all that remains, and since pure math is entirely mental, then therefore all that remains, i.e. the entire universe, is mental. Q.E.D. But his premises as well as his argument are flawed.
His first premise is based on arguments like the one he paraphrases on page 20, retelling what he claims to be A. N. Whitehead’s attempt to explain-away matter. Foster writes that “there is no known way of describing…or analysing the wood” of a table leg “down the ladder of cellulose, molecules, atoms, and electrons where one can state ‘This is matter.'” This is an odd statement. By definition electrons are matter, as are the quarks which comprise the protons and neutrons around which the electrons reside. Any half-educated physicist will tell you that matter is simple to define: matter is whatever possesses mass. The smallest division of matter is that where, when you cut further, you end up with massless energy instead—-in other words, electromagnetic radiation, what we call ‘light.’ Foster seems unaware of the simplicity of this. Instead, he claims that Whitehead, a literal guru of logical analysis, rejected or attempted to argue away a clearly defined scientific term.
And so, he takes this already-bogus idea that we no longer have anything that we can call ‘matter,’ and joins it with the correct and hardly-disputable observation that scientific explanations are becoming more and more mathematical. With this, on page viii, he concludes of the history of science that “a world of substance was being replaced by a world of mathematics as the basic reality” and “these ideas were very suggestive that reality was of an abstract and even ‘mental’ character,” and this conclusion, Foster claims, is ‘proven’ by the discovery of the DNA code, which has a specificity that “transcends chemical science.” In other words, he says this shows “we now have to admit supernatural science” whose “supernaturality” is capable of “numerical proofs.” The only proof he offers, though, is that the “specificity” of biochemical molecules is “supernatural,” i.e. far too unlikely to have arisen naturally. His examples are hemoglobin, with a chance of spontaneous arrangement of:
1 in 10650
And the genome of the T4 bacteriophage, with a chance of spontaneous arrangement of:
1 in 1078,000
I have already refuted these so-called ‘proofs’ in the previous section.
But Foster does not rely entirely on this pseudo-scientific ‘proof’ of the supernatural. He tries to shore up his argument with more philosophical tricks that are just as invalid. Relying on the example of Whitehead’s ‘table,’ Foster develops the opinion, repeated on page 169, that “when physics is explored to its depths, one comes across a world of mathematics rather than a world of ‘things.'” Of course, what Foster really is observing is not a change of opinion as to what the stuff of the universe is. Rather, he is merely observing a decreased ambiguity of description. Using the example of Whitehead’s table, the word ‘table’ is only distinct from a mathematically-precise breakdown of its structure in that the latter description is more precise, whereas the former is more ambiguous. For ‘table’ may refer to anything of remotely similar shape or function, made of any possible material, or even to just the image or memory of a table, or to something else entirely, like a time-table. But a mathematically-precise breakdown of an entity’s shape, location, and composition leaves absolutely no ambiguity left—-you will then know precisely what table is meant, and what its exact shape and composition is. But nothing has changed about that table’s composition. All that has changed is the precision of our description.
Thus, Foster is making a most embarrassing blunder. Contrary to what he seems to take for granted, the world is not innately mental simply because it is mathematical. In fact, math, more than any other kind of abstraction, is distinctly not mental. Mental properties are things like love and purpose and evil—-the sorts of things that require a mind in order to exist. But numbers and equations do not require a mind to exist. That two objects are the same in quantity to any two other objects is true by definition whether anyone ever observes the fact or not. Certainly, a mind must exist to appreciate this, but when the minds are gone, the mathematical facts will nevertheless remain.
On page 71 Foster shows another example of how he has this all backwards. There, he asserts that “in the absence of some ‘life spirit,’ bodily growth and structure are determined by the cells” and thus the DNA. This is a casual remark, but it betrays the underlying inversion of the case at hand: for it would actually be an argument for ‘mind-stuff’ if there were no DNA, if there was instead an ambiguous ‘life spirit,’ as he puts it, which acts intelligently. Instead, we find a causal-computational chemistry-set that acts without need for intelligence. That is actually evidence against his argument. Yet he plays it up as if it were evidence for his argument! In other words, Foster seems to assume that the less like mind-stuff everything actually appears, the more like mind-stuff the universe must be. Welcome to logic-chopping 101.
Foster need to learn what math is. The only thing about math which makes it at all mental is that we employ it as a specialized language for describing things without ambiguity. By categorizing the properties of quantity and relation, we create mathematical words and sentences in order to describe what we see more exactly. But the things described with mathematics do not require a mind to exist. It is the other way around: mathematics requires things to exist. Otherwise, there would be nothing to describe, mathematically or otherwise. Since math is nothing more than a language lacking all ambiguity, it differs from English only in that English relies on ambiguity for the purpose of assisting the rapid communication of ideas between two brains who carry around their own code-books of life experience and linguistic education.
English, like all everyday languages, is only useful if the point to be communicated does not have to be very exact, and if both parties can get along despite a great abundance of errors in reading the real intended meaning of the messages sent between them. If I say, “get that ball,” my audience can understand me only if they are smart guessers: they rely on contextual clues like the fact that there is only one ball-like thing that we have been referring to, or there is only one ball-like thing in the room, or they may even read my body language for clues, etc. But if we wanted to leave no room for guessing, if we wanted to be precise and unambiguous, we would use mathematics: we would describe the floor with a grid and give the exact mathematical coordinates of the ball, we would give the exact mathematical details of the ball’s shape and composition, we would delineate the exact mathematical description of just what we mean by ‘get,’ perhaps detailing the exact body motions involved using the grid and other details already established. Needless to say, if we had to talk that way all the time, we would never get anywhere. It would take a lifetime just explaining, and another just decoding, the simple instruction “get that ball.” This is why computer programmers go mad trying to build smart computers—-because to talk to a computer, you ultimately have to speak in mathematics. Thus, what is unique to a mind is not math—-any machine can be made to understand math. Rather, what is uniquely ‘mental’ is the ability to understand ambiguity—-i.e. non-mathematical descriptions of the universe.
There is another fact Foster needs to grasp. Mathematical truth is not the same thing as empirical truth. The latter involves predictions, such that an empirical statement is true if and only if the experiences that it predicts come to pass. But mathematical statements, being a subset of ‘analytical statements,’ are true if and only if they agree with other predesignated statements. In essence, math is merely the analysis of descriptions. It is a procedure where nothing more is said than A = A. This means that mathematical calculations are simply an attempt to find out if two entities, functions, quantities or relations are the same. If they turn out to be the same, we call that equation “true,” meaning the two things are the same thing. If they turn out to be different, then we call that equation “false,” meaning the two things are not the same thing. All of mathematics comes down to this art of answering the one simple question “are these two things the same?” in all those instances where the two things concerned can be described with zero ambiguity. If they cannot be so described, the problem cannot be addressed mathematically, unless the ambiguity itself is unambiguous, in which case we can only use statistics to do the figuring. Failing that, all that remains is ordinary language, and the inevitable errors of ambiguity inherent in it.
In light of the above facts, Foster makes some very mistaken statements. On page 14 he avows that “what is extraordinary” is that the operations of the universe, including those operations which generate what we call matter, are entirely “mathematical.” Yet, in truth, what would really be extraordinary is if they were not mathematical. Likewise, to him, “it is a mystery” that the operation of the universe can be described using numbers. But to any sensible person, this is not a mystery at all. Both observations are nothing more than the simple and inevitable consequence of the universe being consistent and predictable. After all, any consistent, predictable universe can be described mathematically. This follows necessarily from the simple logical fact that anything which functions without ambiguity can be described with an unambiguous language, and mathematics is nothing more than an unambiguous language. After all, if quantities and relations did not remain fixed, if they were ambiguous, then their behavior would be unpredictable. In fact, we cannot predict behavior at the sub-atomic level precisely when that behavior becomes ambiguous. Of course, QM demonstrates that even sub-atomic ambiguity is unambiguous, so that sub-atomic behavior can still be described statistically. Nevertheless, since the possibility of mathematical description is automatically entailed by any consistent and predictable universe, there can never be any extraordinary mystery in such a universe being so described.
This has apparently escaped Foster, for he employs this pseudo-mystery, using quoted authorities, to ‘prove’ his thesis that the universe is mental and perhaps even divinely created. For example, he quotes Eddington on page 15 as saying that “the universe appears to have been designed by a pure mathematician.” Of course, as I have already shown, any consistent and predictable system will appear that way. But even without the logical necessity of this, one can see how the conclusion being drawn here is already invalid. The game of chess can be described to the last detail in purely mathematical terms, yet we can be quite certain its inventor had no notion of its mathematics, and it was certainly not necessary nor even probable that he should have been a mathematician. A knowledge of math is not needed to invent or even play chess.
Nevertheless, Foster pursues this theme with abundant redundancy. Sir James Jeans is quoted on page 14 as saying that “Nature seems very conversant with the rules of pure mathematics.” Yet if there are two distinct entities, it does not follow that they are very conversant with the number 2. ‘Number’ is simply a description of one of their properties. Jeans may as well say that a game of craps is very conversant with the laws of probability. Then, on page 15, Sir James Jeans is again quoted as saying that “our efforts to interpret nature in terms of the concepts of pure mathematics have, so far, proved brilliantly successful” and that therefore “the Great Architect of the Universe now begins to appear as a pure mathematician.” This is the same fallacious reasoning refuted above: the reason, and the only reason, mathematical descriptions are so successful is that the universe is so consistent and predictable. Nothing more can be inferred. Jeans is doing nothing more than noting the fact that precision improves prediction, and yet he concludes from this that God knows math. This is yet another non sequitur. It should be obvious that any improvement in the precision of our description of a system will improve our ability to predict the outcome of that system. The only thing that would prevent this from being true is if that system were not at all predictable, if it instead followed the personal whims of God.
Foster misses these obvious flaws in his premises and continues to finalize his conclusion that the universe is mental. To this effect, he analyses the argument of Sir James Jeans on page 27 as follows: “1. The reality of science is mathematical” and therefore “2. Mathematics must be admitted as the real ‘things in themselves.'” Herein lies yet another instance of logic-chopping: the reality of science is not mathematical. The description of the reality of science is mathematical. Foster does not seem aware of this error. On page 14 he stated on his own that “mathematics might be more fundamental than ‘the thing in itself.'” Did it not occur to him that the description of a thing cannot possibly be more fundamental than the thing being described? Foster is simply repeating the blunders of Plato. Simply because a mind can categorize things does not entail anything about the things being categorized, except their ability to be categorized.
Another instance of this kind of logic-chopping is given at the conclusion of page 31, where Foster offers his own crude syllogistic argument. He states “1. Reality is organism,” i.e. it is defined by the way its parts are organized, which is true. Then he adds the step “2. The model for organism is combination mathematics” and “3. Combination mathematics is equally the model for literacy and meanings,” and then he draws on these premises to conclude that “Reality is organized mind stuff.” Can you see the mistake? He dropped a key word: model. It exists in his two minor premises, yet when he combines these with his major premise to arrive at a conclusion, he drops it.
What his three-premise syllogism actually entails is not ‘Reality is organised mind-stuff’ but ‘The model for reality is organised mind-stuff.’ In other words, we think about the world by thinking about the world. This tells us nothing. All he has really done here is define ‘model’ as ‘organized mind-stuff’ or, in simpler terms, ‘organised thought.’ But should we be surprised at finding that a model, which is by definition an organised thought process, happens to be an organised thought process? Foster thus turns an innocuous conclusion that is of no real consequence into a profound metaphysical conclusion, by merely choosing to disregard the rules of logic. He sweeps under the rug the most important words in both his minor premises—-the subject of premise 2 and the object of premise 3! This is a representation of what he has done:
- Reality is Organization = A is B
- The Model of Organization is Math = C(B) is D
- Math is the Model of Language/Meaning = D is C(E)
- Ergo: Reality is Language/Meaning, which he rewrites as ‘organised mind-stuff’ = A is E
It should be apparent that 4 is an invalid conclusion from 1, 2, and 3. He needs to show that “B is E” or in other words, that “Organization is Language/Meaning” which he cannot, because it is false—-not all forms of organization comprise a ‘language.’ But even if he could establish this premise, his major premise is already false: reality is not ‘organization,’ reality is organised. Why is reality not equivalent to organization? Because not all real things are organized, and not all forms of organization correspond with reality. Thus, Foster blunders twice in his most pivotal argument! And his blunders are shocking.
Foster tries again on page 164, arguing as follows: “the idea that thought is form in space is very ancient…the logic is very simple: 1. Thought is form. 2. Space, whether real or imaginary, is the medium for form. 3. Therefore, thought is the shaping of space.” The flaws in this argument are again numerous. First, he has invalidly introduced a verb in his conclusion: the word ‘shaping’ appears nowhere in his premises, so placing it in the conclusion is a plain case of logical invalidity. Second, he treats real and imaginary space as if they were the same thing, but they are not. He has left out that key word: model. Imaginary space is actually a model of real space, and so where real space is the medium for form, imaginary space is only the medium for models of form. Here is his argument:
- A = B (thought = form)
- If B, then C (if form, then space)
- A = D (thought = shaping space)
Premise 3 nowhere follows from 1 and 2. The only valid conclusion, given these premises, is ‘if A, then C,’ or ‘if thought, then space,’ or in other words, space is the medium of thought. But neurophysicists will not be surprised at that—-thought (mind) is form (brain and brain function), and form is an expression in the medium of space. In other words, thought is a physical process. This is exactly the opposite of what Foster wants us to conclude—-he wants thought to be super-physical. So how could someone arrive at his conclusion? One must have the premise ‘B = D’ or ‘form is the shaping of space,’ which is a distortion of reality: form is the shape of space, but form is a thing, not an action, so it cannot be the shaping of space. That would have to be action, not form. But action is nowhere mentioned by Foster. This is not surprising, since doing so would expose the reason that he cannot use this argument, even when properly formulated.
Here is why. To reach his conclusion that ‘thought is the shaping of space’ he must begin with the premise ‘thought is action’ and add ‘action is the shaping of space.’ But his sense of ‘shaping space’ is ‘creat[ing] matter’ (p. 163) and as an example of this, he cites the creation of the universe as a possibility (p. 164). But if that is the case, then the premise ‘action is the shaping of space’ is false, since all forms of action we know of are the moving around of matter and energy, not the creating of energy. What is lurking behind Foster’s logic, unbeknownst to him, is the fact that thought does move things physically: we can think about picking up a stone, then extend our hand and pick it up. But there must be a chain of physical causation, a manipulation of already-existing energy through channels where such manipulation has already been made possible: the electrical connection between the computational brain and the hand and arm, the physical proximity of the stone and the hand, the sufficiently weak resistance of the medium between the two which allows the hand to move to and grab the stone, the sufficient amount of chemical energy available in the body, and the ability to convert that energy into the kinetic energy, which is afforded by the body and its muscles and organs, etc. Foster wants to skip all of this and argue that thought can shape space directly, just by thinking, and that this must be how god works. His argument crashes in ruins the moment you ask him how thought can shape space directly. With no answer to that, he has no theory, and thus no argument worth our time.
 See my critique of Mark Steiner’s more sophisticated deployment of the same argument as Foster’s in Fundamental Flaws in Mark Steiner’s Challenge to Naturalism in The Applicability of Mathematics as a Philosophical Problem.