Andreassen characterizes my previous discussions with him concerning eliminative materialism (the doctrine that nothing but matter exists) in this way:
I am happy to present the evidence and argument that convinced me, if only we could get past the jeer of “Meat robot!” that silences all serious discussion of the point.
Sir, if the only thing halting serious conversation on this topic is alleged untoward antics on my part, let me ask you ten questions on the topic. I make no statements and propose no arguments, and leave you free to answer however you will. They are questions, pure and straightforward.
Question One: Is there or is there not an Ultimate Prime number? That is to say, is there a prime number of which there is no higher number on the number line which is also a prime?
If there is no Ultimate Prime, is there an infinity of primes, such that given any prime number there is always another prime number higher than it?
Question Two: If you know the answer to question one, by what means do you know it?
Did you make an observation with your eyes at a particular time and place; or did you make a deduction from axiomatic first principles; or do you know the answer by some other means?
Question Three: If you made an observation at a particular time and place of the infinity of primes, please tell me where and when you stood, and what you looked at, so that I may look at this infinity of numbers with my own eyes for myself, and count them as you have done, and so confirm your observation.
If on the other hand, it is not an observation, is it something known by deduction from self evident first principles?
(For your reference, and in case you ask, I myself hold that the nonexistence of an Ultimate Prime is a formal truth which is deduced from self evident first principles. The argument can be found here: http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html If you came to this same conclusion by this same or a similar argument, you need not give it in full, merely refer to it.)
Question Four: If it is true that there is an infinity of primes, is this true in all times and all places and under all conditions? Or are there times and place and conditions where it is not true?
Question Five: If you answered that there are an infinity of primes under all conditions and in all times and places, does this include times and places and conditions which neither you nor I nor any human being nor any rational being whatsoever has observed or can possibly observe?
Question Six: Can a truth about a time or place or condition no observer has or can observe be confirmed by empirical observation?
Or, in other words, are there non-empirical truths?
Question Seven: If materialism is true, is it not the case that every fact is material fact?
In other words, is it true that if materialism is true, then there are no non-material facts, no non-material truths?
Question Eight: If it is true that all truths are material truths, and if empirical observation is the only means of gaining knowledge of material truths, then does it follow that all truths are empirical?
In other words, is it true that there are no truths known only through deduction from self evident first principles?
Question Nine: If the statement “there is an infinity of primes” is true and if no true statements can be made about nonexistent things, about what existing things is the statement true?
Does the subject of the statement (the infinity of primes) exist in the physical and material sense that the rocks underfoot and stars overhead exist?
I am including my question all prime numbers, including any unimagined prime numbers no human brain has thought nor contemplated as yet.
Does the infinity of primes have material existence, that is, do the prime numbers display mass, location, extension, duration, and other material properties?
Question Ten: Do you agree that if the infinity of primes has material extension, that is, if they occupy space, either brain space or outer space, then these primes, being endless in number, no matter how small their volume nor where located, would fill up all the space in the universe?
If so, does this describe the universe we see empirically around us?
If any questions are based on some unspoken axiom you do not grant, I am happy to discuss that axiom once you identify it.
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A word of explanation to Andreassen:
Perhaps you forget, sir, that the last time I tried to ask you about your beliefs using the Socratic method, your sole reply was to say it was insulting of me to ask you questions.
Your past behavior shows you lack the will to have a conversation on philosophical matters. You have voiced scathing contempt for philosophy, so your repeated attempts to discuss such topics is odd.
Your answers in previous conversations have been flippant and irrelevant, leading me to believe that you neither understand the issues, nor admit when you do not understand, nor are curious enough to ask.
Worse, when trapped by an awkward question, rather than admit anything damaging to your case, you make claims you simply know not to be true.
You claim to have measured the width of the line of demarcation of the horizon at sea; you claim to have measured the duration of the abstract and formal concept of checkmate; you claim to be able to see into my head and to know what I can and cannot visualize; you claim your thoughts fly around your desk, and have mass; you claim access to a sense impression unknown to the rest of mankind which allows you to sense the mass and position of atoms inside your skull.
None of these are honest mistakes. You cannot honestly think you performed a careful experiment last October to measure the width of the line of demarcation of the horizon with a spectrometer, when actually you were just staring at the ceiling and imagining what such an experiment might produce were it performed.
These are all your opinions of what empirical experiment would produce if metaphysical materialism were true, but not an honest report of a real empirical experiment.
Past experience argues that it is vain to engage you yet again on this wearisome topic. But out of an exaggerated and chivalrous respect for justice, merely because you allege not to have been given a full and fair chance to air your views, I will make the gesture of reopening the conversation.
What I will not do is answer any replies which resort to your usual tactics, so please stick to the topic and be straightforward. Anything less than sober answer to the actual questions asked, I reserve the right to ignore or delete.
Frankly, my time is short, so I would prefer you not to reply, but honor requires I make this gesture.
There is no largest prime.
But, however much it pains me, I’m going to have to quibble on, of all the embarrassing things, the meaning of the word ‘is’. Your question as written assumes that numbers exist. Now in the ordinary use of the English language we don’t pay much attention to this, but for purposes of going into axioms and fundaments I want to point out that it is not clear (at least to me) what it means to assert the existence of a number. I understand the sentence “There are two sheep”, but “Two exists” seems to me unclear. I understand “Given a prime I can construct a larger one”, but “This prime exists” does not have a meaning that is obvious to me.
Through being convinced by the argument which, if memory serves me, is due to Euclid: That given a prime, the product of that prime and all smaller primes, plus one, is itself prime.
It is known by deduction from axioms. The axioms, however, are learned by observation; they are not self-evident, but they surround us daily to the point where we forget that they are observations.
It seems that this is based on an unspoken axiom, namely some particular understanding of what it means for a prime to exist. I believe that all rational creatures, given the axioms of number theory and the definition of a prime, will agree that Euclid’s proof is valid, and therefore will know how to construct ever-larger primes. But in the absence of a rational creature to understand the axioms, I am not sure what it means to say that a prime exists; so I do not know how to answer your question.
Your questions five and six seem to depend on a particular answer to question four, which I did not give; so I shall pass them over for now.
I am not entirely certain what you mean by “material fact”. Do you mean “a fact which can be expressed using SI units, ie meters, amperes, grams, and so on”? If that is your meaning, then my answer is no; materialism does not imply that every fact can be reduced to the seven basic units. It allows for the future discovery of new basic units. Thus before the discovery of electricity there were facts which required expression in terms of a unit that wasn’t then known, but which are certainly material in the sense above. However, I do believe that such a fact as “This man has a strong sense of honour” is reducible to some set of facts which do not involve the concept of honour. Honour is too complex to be part of the fundamental laws; materialism is the statement that all such complex concepts are reducible to smaller ones which are in some sense mathematically simple, even if right now we don’t know how to do the reduction. (And yes, quantum mechanics is mathematically simple; the difficulty is all conceptual.)
The logic is valid, but the minor premise is flawed: Empirical observation is not the only means of gaining knowledge of material truths. In particular, we may deduce material truths from empirical truths; that is, we can gain knowledge of axioms by observation, and then deduce other truths from the axioms.
There are truths known only by deduction. But I object to the “self-evident”. In geometry, you would no doubt consider it “self-evident” that given a line and a point, there is exactly one line through the point that is parallel to the first line. But the obviousness of this axiom arises from your intuition about flat space, which is born of observation: You have been observing flat space all your life, and have never seen any other kind. A hydrogen-breathing squid from the accretion plane around the black hole at the center of the galaxy would not consider it self-evident at all, for he has never seen a point behave that way. Unless he had the geometric sophistication of Riemann or Einstein, or at least was familiar with the work of such geniuses, he would hoot you out of the classroom the moment you introduced that axiom in a proof. And even if he did have that sophistication, and was willing to accept the axiom for the sake of argument, he would treat it as a mathematical curio: A statement accepted for the sake of seeing what follows, much as we treat the two negations of Euclid’s fifth. It would not be “self-evidently” true of the actual world around him.
Your question nine again runs into the difficulty of what it means for a prime to exist. I’m happy to acknowledge that all rational creatures must reach a particular conclusion given certain axioms. That does not say anything about how the phrase “this number exists” should be understood.
Well, no. That doesn’t follow at all. It assumes that two infinities are the same size. If space is infinite, it may contain infinitely many things without being filled up by them; and indeed the distance between them may be arbitrarily large. Likewise the number line contains infinitely many even numbers, but the even numbers do not fill it up. (If you object that a number, being a point, doesn’t take up any space on the line, observe that the set “even numbers plus or minus 0.1″, which does take a definite space and is infinite in extent, doesn’t fill up the number line either.)
Addtionally, supposing the universe has eleven dimensions as some theorists think, the prime numbers might have extension in the seven invisible spatial dimensions and not in the three large ones. Which would account for our inability to observe those seven: They’re filled up by prime numbers and that’s why we cannot move around in them! (That’s a joke; don’t take it seriously.)
Time does not permit I answer in full now, but allow me to say this:
As soon as you overcome your reluctance to discuss profound philosophical matters, you will be worthy of discussing philosophy. Your is not a quibble, it is the very center and crux of the question and the reason why you and I cannot see eye to eye.
Your question is profound and profoundly interesting. If we say the prime number “two” exists, we are talking about “existence” in a difference sense of the word that the way we use the word when we say “two sheep exist” or “two moons of Mars exist” or “two moons of Barsoom exist” or “two unicorns exist in the story by Peter S Beagle” or (more confusingly) “two possible outcomes exist of this coin toss.”
The discipline studying the question of existence, and what precisely we mean by it, is called ontology. I am asking you the central ontological question about materialism when I ask the ten questions above, namely, that if prime numbers ‘exist’ and are not material, what do we mean when we say ‘only material things exist’? Or if they do not ‘exist’ how is it that they have properties which (at least) seem to be objective and unchangible? For I cannot by any act of will or cleverness make there to be an Ultimate Prime.
I take your point. I was thinking of the phrase “It depends on what the meaning of ‘is’, is”. The context is not very philosophical.
“Honour is too complex to be part of the fundamental laws; materialism is the statement that all such complex concepts are reducible to smaller ones which are in some sense mathematically simple, even if right now we don’t know how to do the reduction. ”
Well, let’s not confuse materialism and reductionism. They often are found together, but neither strictly requires the other. One can embrace materialism (or physicalism) and still believe in material things behaving in ways that are not reducible to constituent part behaviors.
I don’t see how you can; either the matter moves along paths that are in-principle predictable from measurements, or you believe in something that’s no longer matter. But in any case, it’s true that ‘reductionism’ may be a better name for my position than ‘materialism’.
So, for instance, 13x11x7x3x2 + 1 = 30,031 is a prime.
But 30,031 = 59×509.
Well, that’s annoying.
So the universe must be infinite in volume to accommodate the primes. Can you really rule out finite cosmologies (e.g. spherical Friedmann) a priori like this?
The Bekenstein bound suggests that there is a limit on the amount of information in a finite region of space. So, if each prime has some physical representation, then it fills up space, and the larger primes take up more space. This is quite unlike your example of numbers on the real number line, which can scrunch together quite comfortably.
One concludes that the number line does not exist as a physical object. I look forward to your explanation of how materialists do physics without using numbers.
Pardon me, I remembered the proof wrong. The conclusion should have been “is prime, or has prime factors larger than the prime we started with, which was alleged to be the largest prime”. You’ve found an example of the second case.
I accepted the premise of question ten, that primes had extension, only for the purpose of answering question ten; it was not my intention to give the impression that I think primes are material objects. However, even in a finite universe I think we can accommodate an infinite number of primes with extension, provided they have extension in only one or two dimensions: That is, they are either lines or planes. You can do amazing things with fractals, as you no doubt know.
Additionally, extension is not their only possible physical quantity: They might have mass and charge, but no extension, like electrons. (To the best of our knowledge, of course.) And to avoid the problem of infinite mass, we might hypothesize that the mass of each prime p is proportional to 1/p; this series converges to some finite limit, I believe. The point being that there are lots of ways to accommodate an infinite number of material objects, even in a finite universe. I don’t subscribe to any of them in particular as a hypothesis of how things really are, I’m just saying that the argument “An infinite number of material primes would fill up all of space” is not in fact true.
It is not obvious that a larger prime contains more information than a small one. The generating algorithm can be described pretty compactly. In any case the function may grow asymptotically towards some limit, so that the number-line analogy would become (even number plus or minus (0.5 – 2^-n)) where n is the number in question; thus each successive even number takes up more space than the preceding one but they still don’t fill the number line. By fiddling with the constants you can get arbitrary amounts of unfilled space.
This is an area where logic and mathematics have made huge strides in the past few centuries, and medieval and Greek logic is no longer precise enough to be useful. As you say, infinities do not imply divergent sums, which is not obvious and may not have been understood by the old school logicians whom our host seems to favor.
I should point out that in your example of primes, using 1/p as the measure would result in adding an infinity of constants, which diverges. However, by the theory of the Prime Zeta Function, which is the sum of inverse powers of primes as a function of the exponent, for any exponent greater than one the series diverges, which implies that you need a measure proportional to p^-(2+d), where d>0. None of which changes your basic point, of course.
Now, if you want my opinion on this matter (or even if you don’t), there is undoubtedly an immaterial, acausal realm of some sort in which prime numbers dwell, which I believe to be part of the larger multiverse of mind (similar perhaps to the Mathematical Universe hypothesized by Max Tegmark). However, I would go further than Tegmark and posit a philosophy I call “Multiversalism”, according to which everything imaginable of any sort, be it mathematical, mythological, magical, or what have you, exists in the infinite multiversal mind.
So my advice to you and your kind, Mr. Andreesen, is to not be so caught up in the causal material web of this particular ‘verse, when there is an uncountable infinity of ‘verses in which exist imaginable things which are causally disconnected from us, and are, for all practical purposes, in the realm of the divine. And my advice to John and his kind is to not be so caught up in your monotheistic web of (non-)logic that you fail to see the truth of every other god or divine entity whom men have ever imagined into being from the acausal realms which exist in infinite diversity and combination beyond this world.
“…acausal realms…”
In my monotheistic web of (non-)logic if there is anything acausal, there can be only one, the cause of all the rest, multiverses and all.
As brilliant as usual, Darth. May I just expand a bit on your point about the zeta function? One writes it in product form and takes the logarithm, turning it into a sum. Expand each summand as a power series, gather the leading terms and your conclusion is then obvious.
But is Dr Andreassen ready to confront the acausal realm of quantum field theory, “that amorphous blight of nethermost confusion which blasphemes and bubbles at the center of all infinity—the boundless daemon sultan Azathoth, whose name no lips dare speak aloud, and who gnaws hungrily in inconceivable, unlighted chambers beyond time and space amidst the muffled, maddening beating of vile drums and the thin monotonous whine of accursed flutes”?
Dr Andreassen did ask a very interesting question that never got addressed.
Suppose, knowing the initial condition of atoms that consitute Shakespeare, is it possible to predict the tracing his pen makes?
I do think that the Thomists have no very good answer to the puzzles posed by Free Will. It is still a mystery. Sometimes, they say that the physical process is efficient causation and the mental process is final causation so the mental and physical are aspects of a single process.
But as CS Lewis says in Miracles, Rational thinking is supernatural. Real physical atoms or electrons are supernaturally displaced as a consequence of rational thought.
So what is it– is rational thought descriable in terms of a Thomist physics or is irreducibly supernatural?
Dr Andreassen was answered very thoroughly, but the answer depended on a technical distinction he did not understand.
My answer was that even if the mechanical motions of the men could be predicted from mechanical causes, that this would tell you only the mechanical causal information, not the final cause.
In other words, the description would leave out the meaning of the words and the poet’s intention and so, no, the prediction would be incomplete, or, even if somehow complete, would be meaningless.
I cannot speak for how a Thomist would answer. I am not well educated enough to speak for them.
And I answered this by pointing out that I didn’t give a damn about the final cause; I just wanted to know what the words of the poem were going to be, so I could publish it as my own work before Shakespeare could get it to his printer. Your assertion, at least at one point in that old discussion, was that this was not possible, because poetry could not be reduced to an algorithm. If what you meant was that I could produce the same words as Shakespeare but I still wouldn’t know why he chose them, then we clearly had very different understandings of what “poetry” we were speaking of. I was referring to a sequence of words evoking a meaning or impression in a reader.
Because you do not understand what we were talking about. ‘Final Cause’ is a technical term that means something. Whenever I try to explain what it meant, it bounces off your mental armor.
Which you cannot know without knowing the meaning of the words, or, in other words, knowing the final cause. In effect, you just said you don’t give a damn about knowing the final cause because all you wanted to know was the final cause.
And what, praytell, do you mean by such things as “sequence” and “word” and “evoke” and “meaning” and “impression” and “reader”?
Define just the word “reader” without making reference to any final cause, that is to say, without making reference to any mental as opposed to physical act, any purpose, any goal, any deliberate behavior, or any thoughts, symbols, references, and so on?
As to whether mechashakespeare could produce the same words as Shakespeare, my answer is the same whether you can or not, so I regard the question as irrelevant. Whether there is a strict one to one relationship between thought and the physical medium that symbolizes thought, or a flexible relation, or no relation, it does not matter: thoughts cannot be express or explained by references to the physical properties of symbols, only to their symbolic properties.
In order to show me wrong, all anyone need do it do it once: show a single example of a symbols whose properties are entirely physical and not symbolic, and you win the argument.
This is the point where the conversation foundered over two years ago. The next step is to examine what you think “being” is (which is a question of ontology) and what you think the way men can know being (which is a question of epistemology). So far you have not been willing to discuss these two questions. If that has changed, the discussion can continue. If you and I cannot identify the unspoken axioms where we differ, the discussion will remain at an impasse.
In this particular case, my question would be: why in your hypothetical do you even think it possible that a mechanical version of the brain atom motions of Shakespeare as you describe can exist, and would behave as you say? What are you assuming is true that has to be true in order to make your question meaningful?
When Shakespeare is done writing his poem, there will be a pattern of ink on his paper. I want to know the shape the ink describes. Can we agree that this is a question of physics, describable in terms of number and distance?
There are two parts to your question. First, why do I think I can set up a program, that is a pattern of electrons in a computer, so that I can interpret the patterns as corresponding to atomic motions; and so that the patterns interact according to my understanding of the rules that govern real atoms? Well, I’ve seen it done, on a small scale. Of course nobody has tried to model macroscopic objects on an atom-by-atom scale, but simulations of detectors and of the particles that interact with them are a daily tool of particle physics. The simulations have results that agree well with what we see in the real detectors.
I’m not sure if what I’m saying is really clear; this is a point that is to me utterly obvious, but then I’ve been working with this sort of thing for ten years. So, pardon me if I belabour the trivial. I can create a pattern in computer memory that is to be interpreted as the location, velocity, mass and charge of a particle. (I am trying to be careful to express the idea in terms of interpretations of patterns rather than in the way we usually speak of this, which is to go straight for the interpretation and say “I create an object which has location, velocity, mass and charge”; this makes my sentences a bit circumlocuitous.) Having created one, I can make others; let’s say I make ten in total. Then I make the computer calculate as follows: Suppose we had these charges in these locations; what would be the electric force on particle number 1 due to the charges of the others? Then, given that force, how much does its velocity change? And given its new velocity, how much does its location change? Repeat this calculation for each of the other particles. Now update each of the patterns in memory with the new locations and velocities (and masses and charges, if those should change), and repeat.
Again, I’m sorry to belabour the obvious, but I trust it’s clear that, at any rate, I can make such a program as I describe; and although I wrote with ten atoms in my example, only minor practical limitations prevent me from doing the same with the many moles of atoms in Shakespeare’s brain. Is this clear?
Then we come to your second question, which is whether such a simulation has anything to do with reality. When I’m done interpreting the patterns in computer memory as locations of atoms, do my interpretations in fact go anywhere near what Shakespeare actually did? My reason for thinking that they would is twofold. First, I’ve seen it done (indeed I’ve done it myself) on a small scale, with particle accelerators and detectors. Second, if the simulation does not correctly predict Shakespeare, then Shakespeare violates the second law of thermodynamics. Now, strictly speaking it is at least possible that human brains are, in fact, an exception to this law of physics. To the best of my knowledge nobody has checked; it would be a very difficult experiment to do. Nevertheless, I am reasonably confident in my prediction that thermodynamics does describe human brains, since it applies everywhere else that anyone has tested it.
No. And I am not sure why you would think that was possible.
Is it not the case that the description in terms of number and distance is meaningless without presupposing a knowledge of the purpose (or final cause) of the symbols?
Your question is that if the ink marks produced by a nonliving and unintelligent mechanical process were measured but not understood, would that be the same as reading the thoughts of the greatest poet in the English language?
The Greek letter omicron and the Arabic number zero have the same shape and can be drawn in the same ink. In all physical respects whatsoever they are the same. So whatever is different about them, namely, the symbol they represent, the final cause for which they stand, is not physical.
As for the rest of your comment, in your description of computer modeling of molecular motions, you seem to overlook that Shakespeare was not a molecule. He was alive. He thought. He acted, and his actions cannot be understood without understanding his motives and purposes and ends, that is, his final causes which prompted his thought.
So your argument, as it was two years ago, is still the same circular argument: Yes, if we assume that the physical description of the physical parts of a physical system describes all there is which can be described about the system, then it follows that there is nothing else to be described. In that case a perfect copy of just the physical aspects of the physical system without anything else would be a copy of the physical aspects and that would be all that there is by definition. But you cannot even ask the question without references to terms and concepts which presuppose nonphysical aspects or dimensions to the question.
A copy of Shakespeare, if it were indeed a perfect copy, might indeed copy all his mechanical hand-motions as he wrote poems, but in that case the copy could not be described, nor would his actions be understood by an observer, without reference to what the copy was thinking and what the copy was trying to do.
You impatiently dismiss the nonphysical description of the nonphysical dimension or aspect of the system. But a copy of the physical parts without the nonphysical parts is just a pile of atoms which neither move (except as they are moved) nor think. They have no purposes and take no actions. They are dead. Hence, in effect, you are asking whether a perfect copy of Shakespeare which was dead and unable to move or think could move and think like Shakespeare. The answer is no.
I say again, that we cannot move past this impasse unless you answer on what grounds you base your philosophy. I mean questions of ontology and epistemology.
By ‘epistemology’ in this case, I mean that you claim you know something about the nature of all reality, namely, that it is physical and nothing but. Something persuaded you of this counter-intuitive conclusion.
Is your conclusion based on an argument from first principles, like geometry? Or was it based on an observation or experiment, like physics?
If it is based on an argument, what is the argument?
If it is based on experiment, what was it? What experiment did you perform and when did you perform it? What did you actually see with your actual eye?
What kind of knowledge are you claiming the statement ‘all reality is matter’ is? It is deductive knowledge or empirical knowledge?
I am not dismissing it. I am asking you, in order that we may confine the discussion to one thing at a time, to temporarily put that part of it in abeyance. At the moment we are not even agreed on the part that ought to be trivial, namely how physical systems behave. We cannot discuss interpretations until we know what we are interpreting, and right now you don’t seem willing to draw any conclusions about how the simulated ink atoms will behave.
Yes, fine, but he consisted of molecules, and a molecule doesn’t know whether it’s part of Shakespeare or a rock, it just follows the same laws of physics. Or, if it doesn’t, the computer model will give wrong predictions. Are you willing to straightforwardly assert that this is the case? I have been trying for two years to get you to answer this simple question; in fact that is the whole purpose of the Mechaspeare thought experiment.
If I want to say the poem out loud, I have to be able to read the English language, yes. That is irrelevant to the point I was making, which was about whether the atoms of Shakespeare’s body are correctly described by the same rules that describe the atoms of my desk.
Additionally, if I say that the keyboard on my desk is roughly 40 cm below my eyes and 20 cm in front of me, I do not see how that is meaningless, even if you do not know my purpose in having a keyboard. Suppose I cared nothing for poetry, for Shakespeare, for communication, or for writing; suppose I were a Martian and I just wanted a moderately difficult test case for my computer that calculates future molecular positions. Regarding the Earth with my vast, cool and unfriendly intellect, I decide that Shakespeare, scribbling frantically away in his London apartment, is sufficiently large to make a reasonable test case. I therefore load in the information about his atoms at some particular time, run my simulation, and check the simulated ink-blots against the real ones in London. If my simulation works, the real and simulated marks are identical in terms of number and distance; if not, they differ. Do you dispute that I, a Martian knowing nothing of Shakespeare’s thoughts, can make such a comparison?
No, that is only what the physical parts of his body was made of.
No. The laws of physics describe the physical aspects (mass, length, duration, candlepower, current, etc) of the physical system (atoms, etc.) and only result in a physical description. You cannot use a physical description to describe a nonphysical thing.
Telling me the weight of a guillotine will not tell me whether it is just or unjust to cut the head off an aristocrat. Telling me the number of moles of ink in a drawing will not tell me if the drawing if beautiful or ugly.
Obviously, the thoughts in Shakespeare’s mind are described by entirely different rules than the rules that describe the Newtonian motions of the molecules in Shakespeare’s brain, or, for that matter, Shakespeare’s chair.
You are correct that the same mechanical rules of mechanical motions describe the mechanics of the molecular motions. You are incorrect in thinking that these mechanical brain atom motions are one and the same as the meaning Shakespeare’s consciousness directly makes of the substance of his thoughts and memories, feelings and thoughts and inspirations, or which, through the medium of symbols (written or spoken or otherwise) other men become conscience of Shakespeare’s thoughts. The reason why we know you are incorrect is that the one cannot describe the other, the one does not model the other, and the one cannot be used to deduce the other.
It is true that there is some link between gross mental states and gross physical reactions. A man who drinks wine may become drunk. And angry man or a lusty one may grow red in the face, or a fearful man start to sweat. This is insufficient basis to say that the sweat IS the fear or that the brain electron motions ARE the thought.
You have not yet established in your argument that mind and body are one substance, nor that one is real and the other is unreal. In fact, you have not talked about substance and reality at all.
Your argument cannot prevail unless you prove that matter and only matter is a substance. YYour argument cannot prevail unless you explain away the common sense appearance that minds exist and that we think thoughts. In effect, you are trying to proof that only empirically verifiable statements are meaningful.
Because the location of the keyboard is the same whether you write a logical syllogism or an illogical one; unless you move the keyboard between syllogisms, in which case it is irrelevant. The physical properties of the keyboard are meaningless in that this information does not tell us anything about the topic under discussion. That is what the word meaningless means: it does not mean anything.
This conversation, for two years and counting, has consisted, in effect, of you asserting that one could in theory deduce whether a statement were valid or invalid by examining the distance between the keyboard and the typist. Each time I point out that the information about the validity of the sentence is irrelevant to the information about the keyboard position, because the two are not the same, you say that they must be the same.
When questioned, you offer neither evidence nor rational argument to say why they are the same.
And you simply ignore certain question which are central to the discussion. So I will ask again: And what, praytell, do you mean by such things as “sequence” and “word” and “evoke” and “meaning” and “impression” and “reader”? Describe these things using only physical measurements of their physical properties: mass, length, duration, candlepower, current, moles of substance, temperature?
Yes, and I am trying to discuss the physical parts of his body.
Quite so, and I am asking you a question about the physical aspects of the ink.
We do have a disagreement that could be described in these terms. But it has nothing to do with Shakespeare; there I am making a separate point.
Now, I answered your questions on prime numbers to the best of my ability. You have not yet found the time to respond in depth to that thread of discussion. I must confess to a slight reluctance to answer a different series of questions before the previous ones are done with. Instead, I wonder if you might answer some of mine?
First, can I, or can I not, make a program to predict all the molecular movements in Shakespeare’s body?
Second, if I made such a program, would it, or would it not, make some prediction, expressed in terms of number and distance, for the shape of the ink blots on Shakespeare’s notepad?
Third, if it made such a prediction, would it be right or wrong?
Fourth, if it were wrong, would that indicate that the laws of physics were not correctly describing the movements of the atoms within Shakespeare’s body?
We are in disagreement on much more basic issues. Before we attack these advanced concepts, can we please get to a mutual understanding of our respective positions on the much more fundamental question of how atoms move, and whether their movements may be predicted? I am not asking you to agree with me, I’m asking you to tell me what your position is. In two years I’ve been unable to get anything out of you on this subject except vague mumblings about life and immaterial parts. If you would straightforwardly say that the molecular model of Shakespeare would not allow me to predict the physical shape of the ink blots – never mind their meaning or symbolism or final cause – then that would be a great step forward.
I cannot answer the question as phrased because it contains an ambiguity. When you speak of a molecular model of Shakespeare, does this model include his mind and his intentions, in short, the final causes which cause the hand motions?
If so, the answer is “yes” — you can predict what shapes Mecha-Shakespeare will write on the page by asking him, and, if he answers honestly, he will tell you what he is thinking and what he intends to write before he writes the words. That is, assuming, of course, he does not change his mind between the moment he answers you and the moment he writes.
If not, the answer is “no” — there is no way, merely by looking at the Newtonian mechanics of the muscles and bones in the arm and hand, and the motions of molecules in the brain, to anticipate how those molecules will move. Only the Newtonian motions, as if, for example, we throw Shakespeare out the window, or the medical facts, as if, for example, haggard Shakespeare takes a stiff drink to get his mind focused on his poetry, would we be able to guess beforehand.
The reason is because the motions being discussed are deliberate, not the reactions of external forces.
To prove me wrong, all you need do is write a single example of a description of an intention using only Newtonian terminology of mass, impulse, time, acceleration, and so on. Can you do it? Can you tell me why you cannot do it?
Ah. Vague mumblings, is it? The deaf man complains that my speech is unclear.
So we are back to sneers and jeers rather than honest discussion. As I predicted. Please excuse me from further conversation on this topic.
I see I need to ask you simpler questions.
And what, praytell, do you mean by such things as “sequence” and “word” and “evoke” and “meaning” and “impression” and “reader”?
Please define the word “reader” without using the passive voice and without using any abstract nouns and without reference to concepts related to final cause, thought, or symbols.
Dr Andreassen’s point is simple enough and I, though holding diametrically opposite view redarding theism and naturalism and not agreeing with him, understand him to mean that Can thinking cause supernatural movements of atoms.
CS Lewis boldly answered Yes in his Miracles.
You are avoiding the plain question.
It is immaterial what the ink marks that Shakespeare’s hand mean. All we want to know is Can we predict them knowing the initial configuration of Shakespearean body?
It is to laugh. Avoiding? I have spent two years discussing the issue with him, and written countless pages on the topic. I am doing the opposite of avoiding the issue: I talk about it far too much.
I am afraid I do not understand the relation of your comment to any topic we were discussion. Your thought is too incoherent for me to venture more of an answer. A simple denial must suffice: no, I am not avoiding anything.
It would be very useful to critique CS Lewis’s argument if you do not believe that the Rational Thought supernaturally moves atoms.
He proceeds by distinguishing physical cause and effect chains with logical ground and consequent chains.
Then, he suggests that these chains are exclusive–if we suspect a physical cause and effect relation between two given events, we depreciate the logical relation between those events to the same extent.
Thus the rational thought, that proceeds by logical chains, is exclusive of the physical cause-effect chains and thus is immaterial. But, it is common sense that the rational thought produces effects in the physical world i.e. making sounds or making ink marks on a sheet of paper. Thus, rational thinking is supernatural and moves atoms.
He does not bring in Final Causes.
I am afraid I do not understand the relation of your comment to any topic we were discussion. Your thought is too incoherent for me to venture an answer.
I do not believe what you are asserting I believe. In fact, I have often said the opposite. Nor, as far as I can tell, is your rebuttal a rebuttal of anything being discussed here.
And you have grossly, grossly misread C.S. Lewis if you think he is not talking about final causation when he is talking about the supernatural nature of rational thought. That is, in fact, the point of his talk.
Splendid! I am glad to have finally gotten a firm answer on this point.
In that case, will you agree that we now have an experimentum crucis that, at least in principle, distinguishes between our positions? To wit, fire up the Shakespeare simulator, or a simulator of anything that has intention, and see if it gives the right answers. If it does, you are mistaken. If it does not, I am mistaken.
Further, if you will, there’s a point I’d like clarified. If I fire up the Shakespeare simulator, then, since you claim it cannot give the right answer, at some point it must make a mistake. It must say, in effect, “Newton predicts that this molecule will swerve left”, but in reality the molecule goes right. Is this not so? Then how do you distinguish between this, and “the rational thought moves molecules”, as Gian put it? You seem to see some distinction, because you heap scorn on such formulations every time they come up. I don’t understand the difference.
Ah, no, you did not get a firm answer. You got an if-then statement.
I said that if a certain impossible thing were the case, one could build a nonliving and nonintelligent emulation of an living intelligent organism, then the nonintelligent emulation would not make the same motions as an intelligent organism. You have yet to clarify the ambiguity as to how one builds a nonliving and nonintelligent emulation whci also somehow and for no reason does the same things a living and intelligent organism does, such as, you know, live and think thoughts, but without being alive and thinking.
In other words, I said that if the axiomatic metaphysical statement of materialism were true, such that all mental motion was physical motion, then it would be true that mental motions were physical motions.
If you built a model of Shakespeare and did not put a brain in it, all that would happen is that it would all over dead. The ink blot in such a case would be meaningless stains. If you did put a brain in it, the model would act as the brain directed, and write whatever he wanted to write. What you are asking is a paradox and an ambiguity, whether or not a model could have a brain that was not a brain, one that reacted without acting, one that was not self aware, and so on.
You keep telling me, and have for two years, that if the model’s brain atoms are in the exact same configuration as the originals, and if the original is self aware, then the model will be self aware, and I keep saying that this is true if and only if self awareness is described by brain atom positions, a fact not yet in evidence, and an assumption for which you have not put forth argument one.
Which was exactly where we were two years ago, the first time I said the conversation cannot proceed a single further step without you being willing to examine your ontological and epistemological axioms.
Against my better judgment, then, and out of a sense of fairness:
1. Do thoughts exist?
2. Do they exist in the same sense of the word ‘exist’ as atoms exist?
3. How does any man know any truth?
4. How do you know the answer, whatever it is, to the questions above? If you say thoughts exist, how do you know they exist? If you say they do not, how do you know?
If you don’t wish to answer, I am content not to cover old ground again.
At least one of us is being unclear; perhaps it is me. I have told you what my molecular simulation contains: It has terms for the position, velocity, charge, and mass of each atom, and a rule for applying Newton and Maxwell to calculate new positions and velocities. Only that, and nothing more.
I do not understand what impossibility you are referring to. Is it impossible to build a molecular simulator such as I have described? Surely not; it is plain repetitive math, and computers are good at that. If you are saying that it is impossible that the simulated Shakespeare would act like the real one, fine, but that is a firm answer to the question I asked.
I’m asking a very simple question. I’m going to make a computer program with the exact terms I outlined above, no more and no less. I will look only at Newtonian mechanics. (Plus Maxwell for electricity.) I will not put in any term describing Shakespeare’s thoughts or intentions. It may be the case that his thoughts and intentions are emergent properties of his atoms; but if I understand you correctly, you do not hold this to be the case. Thus, are you not giving a firm answer? To wit, you say that the simulated Shakespeare will fall over in a slump, lacking (so to speak) the elan vital that animates the real one; and any simulated ink that reaches the simulated page will do so in meaningless spatters.
This is unclear. Of course the model must include the atoms which comprise the brain. But I suspect that this is not what you mean by “put a brain in it”; for I intend to look only at the location, velocity, mass, and charge of those atoms. I suggest that, if you were speaking of anything not included in those quantities, you use the term ‘mind’ rather than ‘brain’, to make the distinction easy to observe.
Today I am not making that assertion. I have in fact changed my mind on the point in the two years we’ve been arguing, and come to the conclusion that the model is not necessarily self aware; but that is not relevant to the extremely limited and simple question I’m asking you, which is about its physical behaviour.
Yes.
Not precisely the same. They exist in the sense that desks or chairs exist: That is, one may arrange atoms so as to form a desk, a chair, or a conscious brain thinking a particular thought.
Either by observation, or by deduction from observations. (Or by being told of observations or deductions made by others, but the principle is the same.)
I know that thoughts exist because I experience them: Direct observation.
If I may ask one more question. On what observation, since all knowledge is observation, do you come to the conclusion that thoughts exist in the sense that desks or chairs exist: That is, one may arrange atoms so as to form a desk, a chair, or a conscious brain thinking a particular thought?
My own experience is not an observation properly so called.
I am aware of my thoughts to such a degree that without paradox I can claim I am my thoughts, or the origin of my thoughts. When one thought leads to another thought in my awareness, this is done by either logical formalism or by emotional association, but in any case not by the rules concerning mass, position, and location of thoughts. Objects like chairs and physical organs like brains I observe through the senses and I sense have the properties of mass and position and location. Their motions in extension, the field of my view, can be described in terms of changes in mass and position and other properties.
By way of contrast, my thoughts have no extension of which I am aware. I do not sense them with a sense impression through a medium. Thoughts emit neither color nor sound. I am aware of them by direct introspection, by self-awareness. They are not driven by any mechanical means I can detect, but they are pulled or attracted by final causes, that is, by purposes, and they are bound, not by laws of nature, but by laws of logic.
Even there, my experience is that I can think illogical thoughts even though I ought not, where a chair obeys the law of gravity not because it ought but because it cannot do otherwise.
I have no observation whatsoever to tell me thoughts exist, if by ‘observation’ we mean external reality received through sense impressions. What I have is an immediate experience.
Now, my immediate experience tell me that your observation, that thought can be constructed like chairs, is not only false, but is categorically false. You not talking about two different things, but about two opposite things.
My experience makes both a practical and a philosophical distinction between subject and object, external and internal, self and other, mind and body, physical and spiritual. Thoughts are not things, do not act like things, cannot be described as things, do not follow the laws of things. That is my experience and my observation.
My observation is that I observe object and my experience is that I experience thoughts, and there there is no object, not one, I have both observed and experiences. There is nothing, nothing, I have seen with my senses which I have also known through my self awareness.
So, then, on what observation is your conclusion based? What did you see which informed you that thoughts are like the atoms in a chair? Tell me, so that I can go look at it, whereupon I will see what you saw and therefore believe what you believe.
If, on the other hand, I can see what you saw without being convinced, then there is something other than observation involved, some form of reasoning or some source of knowledge for which you answers do not yet account.
On what observation, since all knowledge is observation, do you come to the conclusion that thoughts exist in the sense that desks or chairs exist?
“By observation, or by deduction from observations”. The conclusion that thoughts are patterns of atoms lies at the end of a chain of reasoning. The beginning of that chain is that all objects that anyone has ever looked at obey the mechanistic laws of physics. But I make a deduction, or rather induction, from this which I suspect you will not allow: That the atoms of Shakespeare’s brain, or anyone’s brain, also follow the same mechanistic laws. It appears to me, although as noted I’m having some trouble nailing you down on the subject, that you disagree with that statement. That is the purpose of the Mechaspeare thought-experiment: I’m trying to understand whether this is in fact the source of our disagreement. But you seem unable or unwilling to take the question I asked as an honest one. Moreover, I have seen you answer it both ways: First claiming that Shakespeare’s physical motions cannot be predicted in this way, and then claiming that, nevertheless, all the atoms of his body are following the laws of physics. Can you please pick one of these positions, or else explain how they are reconciled?
Is a thought an ‘object’ that can be looked at with the senses? Or are we dealing with at least two kinds of object, objects of the senses, material objects, and objects of thought, non-material objects?
You look at the beginning of a chain of reasoning, and attack the end. Brains and bodies are objects that can be looked at with the senses. I assert that they are fully described, down to their individual quarks, by the laws of physics. From this beginning it will eventually follow that thoughts are patterns of atoms, or – to please Nostreculsus – of field amplitudes over quantised Hilbert spaces. Of course this may be wrong; I may have made an error either of reasoning or of observation. But you cannot break the chain of reasoning by attacking its last link with a question suitable for discussing the first. I’m trying to discuss the basics; you persist in jumping to the end.
Not at all. I am asking you to define your terms like a scientist should. I am also asking you to state your axioms, like a mathematician should.
I will ask you again: Is a thought an ‘object’ that can be looked at with the senses? Or are we dealing with at least two kinds of object, objects of the senses, material objects, and objects of thought, non-material objects?
If you like, I can reword the questions, using the technically precise terminology of my field of expertise:
1. Define ‘substance’?
2. When we speak of the mind-body question, are we dealing with one kind of substance, or two?
If you would like my expert help, your argument requires you at this point to say that there is only one kind of object, that is, a material object which can be apprehended by the senses.
Your argument then should make the case that the subjective experience of the thinker in his thoughts is a material phenomenon or a by product of a material phenomenon.
Or, if you prefer a more subtle argument, you could argue that the subjective experience of a thinker in his thoughts cannot be known except for the material phenomena accompanying the experience, and that therefore the subjective experience is not within the realm of legitimate knowledge, and that therefore the question of its substance is unanswerable.
But whether you want my tactical advice or not, in this case your response that my question is unfair or illegitimate because I am asking you to clarify the central point of the debate is an illogical and insincere response. It neither answers the question nor says on what grounds the question cannot be answered. It is just a dodge.
I would be very happy never to debate this matter again with you. If you wish not to answer my questions, go in peace.
Your question is fair, and I will answer it: There is one kind of substance, and the apparent division between the two kinds you mention is only apparent. I will add, however, that this one substance has, or can have, the properties you ascribe only to mental substances, such as meaning, validity, about-ness; and it is almost always convenient to mentally make the division you insist is ontological.
However, you are still not answering my question, nor giving the grounds on which it cannot be answered, or saying why it is irrelevant. Instead you accuse me of dodging questions when I say that they are not directly related to the basics I’m trying to establish. It is very hard to argue with a man who won’t tell me what his position is in terms I can understand. I have answered all your questions to the best of my ability, while you still avoid mine. I suggest that mere courtesy now requires that we take turn about, and you do your best to answer my questions about Mechaspeare in a straightforward manner. For your convenience I will try to restate them one more time:
Given that the Mechaspeare simulation contains only physical terms, that is mass, charge, location, velocity; do the simulated atoms end up in the same (simulated) positions as the real ones?
Alternative question: Is the question itself somehow illegitimate or impossible? Is there anything that prevents me making such a program as I have described, and just comparing its output to the real Shakespeare? I am not making any deep philosophical points about meaning, I just want to compare lists of atomic positions. Is this somehow impossible? If so, why?
Supposing you do not find the question impossible, and you do answer that the simulated atoms behave differently from the real ones: Do you agree that this shows that Shakespeare is not described by the laws of physics? Does this imply that, somewhere within Shakespeare’s brain, the laws of physics predict that an atom would go left, but in fact the atom goes right?
Normally I would rejoice that I finally got from you a clear answer of your position.
I am afraid that, after all this time, the accusation that I am dodging your questions is insufferable. Out of a spirit of amity, however, I will swallow the insult.
Yes.
Yes. The question establishes only that a material model of Shakespeare will have the same material properties as Shakespeare. No mental or immaterial qualities, what you call ‘output’ are part of the question.
Yes. You may compare MechaShakespeare’s mechanical reactions to Shakespeares mechanical reactions, such as, for example, throwing them both off the Leaning Tower of Pisa (one real, one simulated) and calculating their rate of fall; or such as injecting both with poison (one real, one simulated) and tracking the change in blood pressure, temperature, and time of death; or such as smothering both with chloroform (one real, one simulated) and measuring the changes in the EEG readings of the brain, or the temperature of the brain stem.
You are making a philosophical point about meaning, but, since you are untrained in the discipline of philosophy, you do not admit it, nor recognize it when it is pointed out to you.
Comparing lists of atomic positions is not impossible.
Whoa! Not so fast. The simulated atoms behave as the real ones only to the degree and in the ways that the hypothetical has so far defined. We are talking about physical, mechanical, and medical reactions to the body of Shakespeare and sim-body Mechashakespeare.
We are talking about what happens if the real Shakespeare is doused with oil and lit on fire, and then measuring the ignition temperature of his hair and bone marrow and comparing that with sim-dousing Mechashakespeare with sim oil and lighting it on sim fire. Your question is, assuming the simulation accounts for all mechanical and material motions of only the material parts of the model, will the two models come to the same result?
The answer is yes, if and only if we limit the question to mechanical actions. Mechashakespeare and Shakespeare are both dead bodied on the pyre. The ignition point of the simulated bone marrow should indeed match the real ignition point of the real Shakespeare if the simulation is accurate.
The answer is no, if MechaShakespeare is alive and can think and take actions. In the that second case, MechaShakespeare might be braver or more cowardly than the real Shakespeare, and might decide to run around the Globe Theatre screaming or might decide to plunge into the Thames and extinguish the flames.
While it may be the case that MechaShakespeare has the same thoughts and passions, the same courage and quick-wittednes and the same desire to live and knowledge of swimming as the real Shakespeare, this is a question, if I understand you, you have specifically ruled out of consideration.
Obviously, Mecha-Shakespeare and real Shakespeare may indeed have the exact same reactions as each other, running twelve long strides, stumbling, batting at the flames with the left hand for two minutes, etc. Just as obviously, Mecha-Shakespeare and Shakespeare, if their thoughts and attitudes and passions and inspirations are different, might have a different reaction. One is overcome by grief by bad reviews and lets himself burn, while the other jumps into the Thames and is eaten alive by a swan. Only if their thoughts were exactly the same would the outcome of their thought be exactly the same, this is, if they had the same purpose and used the same reasoning or same instinct to attempt the same means of achieving their goals.
In your hypothetical, you ruled out any discussion of their thoughts and actions. Then you ask if their actions would be the same. The answer is, given the information and assumptions in the hypothetical, the hypothetical is unanswerable.
I neither agree nor disagree. The question is incoherent. You are asking if physics can describe something physics is not only not designed to describe, but which physics cannot describe.
I don’t understand what the question is asking. If Mechashakespeare jumps into the Thames because he wants to live and Shakespeare lets himself burn because he wants to die, the laws of physics will be exactly modeled down to the last atom and electron in the simulation. The simulated burning will match the real burning, up until the point when the waters cover him, and at that point the simulation will differ from the real world, but the laws of physics are the same in both.
That is assuming, of course, that MechaShakespeare and Shakespeare act differently. If they act the same, the laws of physics will still be the same. So in either case, the simulation will be functioning correctly.
I get the impression you are trying to ask a different question that you don’t know how to ask.
It may imply it, or it may not.
The act of the atom going to the left or right, or the actor drowning rather than burning, is part and parcel of the act of thinking. Physics does not predict thinking nor does it try to. It predicts mechanical reactions to mechanical impulses. If there is a one-to-one relation between thoughts and brain atom motions, that has not been established in your hypothetical.
While it may be the case that one and only one configuration of brain atoms represents or reflects one and only one subjective state of mind, it may not be the case.
And, in either case, predicting the brain atom motions cannot predict the content of thought because the prediction does not take into account the relevant factors, such as intention and passion and appetite and goals. Neither does predicting the thoughts allow one to predict brain atom motions, even assuming a one to one relation.
So I myself do not see the implication the question asks about, unless there is some further assumption in the hypothetical.
Your thought experiment does not identify the difference between us. If materialism were true, then MechaShakespeare and Shakespeare might or might not have the same outputs given the same inputs, and if materialism were not true, MechaShakespeare and Shakespeare might or might not have the same outputs given the same inputs. The question of how accurate the predictions of material behaviors would be in either case has nothing to do with the question of whether matter is the only reality.
I recall answering these questions in these words or something close to them two years ago, and repeating myself countless times. Obviously, I have done the opposite of dodging the question: I have answered them too much and too readily, over and over and over, neglecting more important duties and happier company, to a point beyond weariness, only to be insulted for my pains.
Mr. Wright, is there some experiment (a thought experiment would be fine!), the results of which would distinguish between your position and Mr. Andreassen’s?
If yes, could you explain it?
If no, then no amount of debate will do, I’d think.
No, by definition.
No, but I can explain why his hypothetical of MechaShakespeare is meaningless, even at best.
Obviously, if there were a difference that could be determined by an experiment, he and I would be discussing physics, not metaphysics. The reason why the conversation has proved so frustrating for me, is that he does not have a category in his mind for metaphysical discussions, that is, no knowledge of the rules, the epistemological rules, for how such a conversation would take place.
I have asked him repeated for the last two years to address this issues, and perhaps my questions were not clear enough or pointed enough to draw the conversation into a fruitful area.
The Metaphysical difference between us is whether thought exists as a substance. He is not able to put his position into technical philosophical terms, and so he might not phrase it this way, and might not have thought of it this way, but the only logically defensible position for a reductionist materialists is to say that all substances are material, including thoughts and abstractions and ideas and spirits.
This logically implies two things: first, that only mechanical cause is meaningful. The other types of causation, particularly formal cause, do not actually cause the things they seem to cause. Second, that if only mechanical cause are meaningful, the content of thought is not determined by the content of thought, but by the material medium of thought, in this case, by brain atom shape and position and movement. This seems to imply a lack of free will and an inability for any thoughts to have truth value: but I personally have my doubts if that implication is logically inevitable.
Be that as it may, upon making the claim that all thought is made of material substance, the theory has to fit the observations and experience of real life, that is, the materialist has to reconcile the appearances. Since it appears that thoughts obey rules of formal causation and final causation (namely, that I think about X for the sake of goal Y, or because of mood or emotion Z, or because of the rules of logic and a desire to avoid illogic) the materialist has to explain away the appearances. Generally there are two ways of doing so, one by saying final cause is an epiphenomenon or illusion, the other by saying final cause and mechanical cause exist in a pre-established harmony.
I myself believe all this theory is based on a category error: I believe that physics is only meant to describe the physical motions of physical particles, and to the degree that it describes the physics of brain chemistry, it can make some limited statements about brain capacity and health, or say whether whether a man is asleep or sane or not, and perhaps even one day find a close relation between mental states and physical brain-changes, but so far not even a theoretical way of stating the problem exists. Physics deals with mass, duration, length, temperature, current, candlepower, moles of substance, and other physical measurements of units in extension. Mental states deal with true and false, fair and foul, efficient and futile, and other qualities that cannot be quantified and cannot be expressed in terms of extension.
Anyone who thinks that physics is merely glorified ballistics would not even begin to imagine that everything in reality, physical and mental, can be reduced to it.
In sum, the reason why the Mecha Shakespeare hypothetical is meaningless is that it does not control the variable the discussion is about. It is not an example of, one the one hand, a model that takes both physics and metaphysics into account, my model, and, on the other hand, a model that takes only physics into account, his model.
In the Mecha Shakespeare hypothetical, all that keeps happening, and has been happening for two years, is that his hypothetical question serve to establish one and only one tautological idea: namely, that a sufficiently accurate model of physical motions can model physical motions.
What he should be trying to establish to forward his argument is that a sufficiently accurate model of physical motions can model everything both physical and mental. If he established that, or got me to agree to that proposition, then it would be easy for him to prove that everything both physical and mental is ultimately reducible to physical motions.
Instead he asks me what Mecha Shakespeare would do, and he leaves it ambiguous as to whether Mecha Shakespeare is alive or dead, thinking or not thinking, capable of acting on his own like an organism or only reacting to external pressure like a clockwork. He cannot resolve the ambiguity because he does not see the ambiguity.
He starts from the premise that all things are physics, and reaches the conclusion that all things are physics, and when I say physics does not predict or even if it did predict, cannot describe or give the reasons for human action, he changes the subject.
That is why no experiment, not even a thought experiment, cannot settle the issue. The topic under discussion is one where experimental knowledge has no bearing whatsoever.
Is this clear? If not, ask me a follow up question.
I can’t figure out what game you are playing here. You cannot simulate a droplet of water according to the scheme you outline above. You cannot even simulate one molecule of water; not without electron orbitals, the exclusion principle and much more that would be inexplicable by the laws of Newton and Maxwell.
What’s more, any scientifically literate person must know this. The last time the simulation you propose was even vaguely plausible might have been in the age of LaMettrie.
So you are not proposing a scientific experiment, nor even a Gedankenexperiment. You are simply proposing a counterfactual. “What if there were a machine which could predict a man’s choices, before his actual decision.”
So, what if. Can we finally move on to Newcomb’s paradox then?
For purposes of this discussion, Mr Wright and I have agreed to let atoms and Newtonian mechanics stand in for all of physics. The complications of quantum field theory, the strong force, and so on are not relevant to the argument. If this really bothers you, please feel free to mentally substitute whatever lattice-QCD simulation you like. I hear they’re up to calculating the mass of the proton from first principles, these days.
We haven’t been having a two-year argument over the details of the physics in the simulation.
Really? Then why do you repeatedly use the word “Newton”, when you actually mean “physics”? Why does your rhetoric repeatedly refer to this particular type of physics?
That’s quite a heap of words, if all you mean is “physics”.
I am going to advance a very unconventional hypothesis. I claim that Shakespeare had the power of creation. I claim that Shakespeare was the “onlie begetter” of his sonnets. And he did this by selecting words. The sonnets did not exist, until Shakespeare made these choices.
The poet writes, “Mine eye and heart are at unceasing war”. Then he considers, “a mortal war”. Ah, perhaps “unyielding war”. Sense wars with sound. Shakespeare makes his choice and a work is created which did not exist before. You assert that these nuances of meaning and the aesthetics of assonance are material configurations, but, so far, you have given no evidence for this. And that is the crucial issue.
Certainly, the materials of the poem are already latent in Shakespeare’s brain. I’m sure that a Marlowe, familiar with Shakespeare’s prior work, might make some predictions as to what his next line might be. A great many absurd continuations may be assigned zero probability. But that is the best possible prediction of unknown information; a judgement of likelihood.
You are welcome to assert that your very notional programme could also give such a list of possibilities. Programmes that predict shopping behaviour already exist, models of voting patterns exist – all without any extraordinary philosophical consequences.
So, if my wild hypothesis is true, if Shakespeare can truly create something that did not exist before, then the poem is a message. It is information that did not exist before. New information is information undetermined by prior knowledge. It is uncertain, and so the best possible prediction will be probabilistic.
There is no paradox here. Shakespeare’s brain is not violating any law of physics. But, the laws of physics require boundary conditions, conditions that are just given, somehow. For instance, the big bang specifies the initial conditions of the universe. Let us agree, “for purposes of this discussion”, that God set up these initial conditions at creation.
Shakespeare seems also to have had some small power of creation.
The second part of your comment is brilliant and right to the point. Bravo.
The first part is not on the mark, because Dr Andreassen and I have been discussing this for two years, and we have both been using Newtonian mechanics as a shorthand for physics. One of the few, very few, points we agree upon is that modern quantum mechanics or the modern theory that ‘causality is probability’ has no bearing on the issue he and I are discussing. I am not arguing, indeed I loathe the argument, that the will is free because causality is probability.
For that reason we both use the metaphor ‘Newtonian’ to refer to the mechanics of physics. It is an agreed-upon abbreviation between the two of us for the sake of clarity.
Consider the following three descriptions of the poet.
(a) The Midsummer Night Theory. The poet throws his head back, his eye in a fine phrenzy rolling, and the Muse speaks to him. He faithfully transcribes the revelation to the best of his ability.
(b) The Oscar Wilde Theory. The poet is a craftsman and an artist of words. In the morning, he takes out a comma, and in the afternoon, he puts it back again. He wanders in a branching labyrinth selecting the choicest pattern.
(c) The Andreassen Theory. A construct of atoms moves under mechanical and electromagnetic forces and generates a certain determinate pattern of ink on foolscap.
Now, theory (a) and (b) are certainly more akin to each other than either is to (c). In both, there is an act of creation. In both there is a message. But the Oscar Wilde theory differs from both the others in that it is describes a branching process, while in the other two, the poet follows a linear chain of causation.
You rule that the sort of physics that permits branching is inadmissible evidence. This may be sufficient for the contrast between the meaning and creation present in both theories (a) and (b) and their absence in the materialistic model (c). But this ruling of yours only confuses those who favour the Oscar Wilde model.
You are a writer. Would you care to comment on the validity of these three models of your activity?
I would like to withdraw the request for comment. You undoubtedly have enough demands on your writing time, already.
The Phrenzy theory is how I write and the Oscar Wilde Theory is how I rewrite.
The Andreassen Theory is logically incoherent to the point where I cannot see or imagine how it is even on the same topic as the others. It is not describing what a poet does, nor is it describing any human actions. I am not saying it is an incomplete description; I am saying it is not a description AT ALL.
The ONLY thing he is describing is the only part of the process that has NOTHING TO DO with the creation of a poem.
What I make as a poet is not shapes of ink. The material part of the book is the only part no one care about. It is not an unimportant part; it is nothing at all.
The story qua story is the same written by hand on paper, by ink on parchment, by electrons in a computer, verbally spoken by a skilled bard. Indeed, if the poem is fine enough, it retains it greatness even in translation from Greek to English. Story is thought.
Imagine if some questioner were mistaking the wedding for the white silk substance of the wedding dress. You might tell the questioner that white dresses exist outside of wedding ceremonies, or that some weddings, even most, take place without a white wedding dress — and if the questioner continued to evade, ignore, or not respond to the comment, you would begin to have your doubts about how sincerely curious he was to discuss the legal, contractual, sexual, romantic, and most sacred sacrament of marriage.
“What I make as a poet is not shapes of ink”
You have not understood Dr Andreassen’s point yet.
No, I think I understand his comment perfectly well, thank you. I dare say I understand it better than he does, because I could certainly argue it better if given the task.
I believe Gian is correct: You either do not understand my point, or you are unable to articulate your understanding in such a way that I understand it. You persist in thinking that I’m arguing for a particular ontology. Now I do of course have an ontology, but right now I’m not trying to argue for it; I’m trying to establish the precise point at which our two ontologies diverge, in terms of what they say about Mechaspeare. (I like specific examples, they are easier to think about.) You refuse to answer my question, or you answer it in such a way that I cannot make out what you are saying. I laid it out again in my comment above (the one posted at 15:21), so perhaps you’ll have a look at that.
I would be interested to see the argument by Lewis which Gian refers to; is it online? Perhaps, if someone else states the thesis I disagree with, it will be easier to see if that is the thesis you agree with; and then at least we can proceed on the basis of knowing where we diverge.
I am afraid your characterization of the argument, or my position, is so far off the mark that I cannot make any comment about it without being rude to you.
Let me say merely that I do not have an opinion about your ontology; but I do believe that the conversation will be frozen at an impasse until such time as you put your ontological belief on stage, and allow us to examine and debate them. I have said this many, many, many times: so many times, in fact, that I am deeply offended that you now dare to claim that we have already been discussing it, and that I am at fault because I am misreading your stance on the topic of ontology. It will be a miracle if I can write this reply to you without descending into uncouth expletives or speculations about your psychology.
You cannot establish that point without making the distinction between mechanical cause and final cause, because that is the point where we apparently disagree.
Indeed, I thought that we two years ago came to a point where we both agreed that all the mechanical motions of atoms in Mecha-Shakespeare’s brain were governed entirely by Newtonian mechanics? On the mechanical level of things, I do not think we disagree at all.
We agree that Mecha Shakespeare can mimic Shakespeare’s reactions down to an atomic and electronic level. The two are as exactly the same as man and his image in a mirror.
We disagree that from this fact it is a legitimate conclusion to conclude that MechaShakespeare’s actions (which I assume will be the same as Shakespeare’s if and only if MechaShakespeare’s thoughts, memories, motivations, intuitions, emotional associations, appetites, passions, moods, and divine inspirations are the same — a point not yet addressed) can be defined and described by a description of the mass, duration, length, temperature, current, candlepower, moles of substance of the material part and only of the material parts of the MechaShakespeare model.
So the conversation goes around and around in a circle. You are assuming the material model being the same will make the mental model the same, but I do not make that assumption and do not even know how to imagine making that assumption.
Mechashakespeare’s body will be the same as Shakespeare’s body if and only if all the mechanical causes have the same material properties as the original; but Mechashakespeare’s mind will be the same as Shakespeare’s mind if and only if the mental (aka final) causes have the same immaterial causes as the original.
You keep assuming his thoughts must be the same because his brain is the same, and I keep saying his thoughts will be the same if his mind is the same, but that mind and brain are two different aspects or different dimensions of an underlying reality, and the one cannot map onto the other.
You keep saying thoughts are matter because mind is brain, and I keep saying that because thoughts cannot be expressed in terms of matter, brain is a description of the organ of thought, not the content of thought.
The problem is that my belief is based on a distinction I seem not to be able to make clear: I am someone who thinks that determinism and indeterminism are mutually compatible, not incompatible; and that one describes only the mechanics of the model, no more, and the other describes the mind and forms, purposes and idea of the model, no more. You ask how the mechanics materially description changes the non-mechanical nonmaterial description, and I keep saying it does not. The two descriptions describe, and are meant to describe, two entirely different aspects or viewpoints or dimensions of the model.
To me, the question you are posing is meaningless. I do not believe the axiomatic assumption of methodological monism on which it is based. And experience has shown no words of mine can draw you attention to that assumption, or get you to acknowledge it, or defend it.
So we are at an impasse. Until the assumption is open to discussion, the discussion cannot continue.
So far, you have not said one way or the other, and have expressed impatience with the question.
The argument is in the first few chapters of MIRACLES, and it says that since the actions of the brain cannot be described, without paradox, in mechanical, naturalistic terms (for if they could be, they mechanical actions would rob all thoughts of truth value) therefore thoughts are supernatural.
Gian’s interpretation of the meaning of the argument differs from mine. Personally, I think Gian is mistaken, but it has been years since I read it.
I do not believe CS Lewis is claiming that brain atoms routinely break the Newtonian Laws of motion due to spirits levitating by telekinesis atoms into correct positions in the brain gears for thoughts to be thought-through as the thinker directs but in defiance of what Newton’s Law predicts.
Shakespeare’s brain is violating the laws of physics if CS Lewis is right. Also Platinga.
Actually, the way they put it, the rational or creative mind changes the initial condtions following which the laws of physics take over.
As Platinga puts it, the universe is NOT casually closed at the moment the rational thought affects the physical world. As the laws of physics hold only for a casually closed universe, their is no violation of the laws of physics.
That is, the creative thought supernaturally moves the atoms in the brain. CS Lewis was explicit on this point.
All I wish to know is whether Mr Wright agrees with CS Lewis or not.
And if not, why not.
Because I wish to know whether his argument is essentially the same as that CS Lewis makes in Miracles or his argument is an independent one.
This interests me; where does Lewis make that argument?
Hey John, i’m reading a book that I have some clues about, but it’s very applicable to this whole debate- it’s called Incompleteness by Rebecca Goldstein, and I will attempt to try and sum it up here- the statement “This statement is unproveable” is not a pradox, or a contradiction- it is true, but *without being proveable*. This idea is contrary to all materialist/positivist/empiricist- whatever word you want to call it – and I would love to hear your take on it.
Thank you,
Braden
My take will be rather disappointing. As far as I know all reasonably well read men since the time of Goedel are aware of the incompleteness of formal systems. One cannot prove the axioms of geometry with geometry.
Indeed, a common trope of modern and postmodern philosophy is to apply this notion of Goedelian uncertainty and draw the conclusion that since all systems, formal and informal, rest on axioms not provable within their own system, that all human knowledge and learning is futile, all bets are off, and therefore eat, drink and be merry for tomorrow we die.
On the other hand, Christian theology since roughly the Eleventh Century has held that there are certain moral truths or axioms which are so obvious that no one can honestly deny them. No one can somehow “not know” that is it not wrong to kill and maim the innocent for gain or for sadistic pleasure. Indeed, part of the pleasure of sadism, perhaps the greater part, is the knowledge that one is defying a moral certainty. This teaching can been mocked without being answered and ignored without being identified, but for obvious reasons it cannot be denied.
So the state of moral learning in the modern age falls roughly into two camps:
The first is the nihilist camp who concludes that since moral teaching cannot be reduced to an observational science, it is unreal and arbitrary. Some members of this camp allow that whatever is harmful to others may be prohibited by he public magistrate for the pragmatic reason of maintaining the public peace, but not for any reason related to truth or virtue. Counter-intuitively, such questions as killing a baby in the womb is defined as non-harmful, as is sodomy and drug abuse and harlotry, whereas such questions as mocking the prophet of Islam by posting a YouTube video, or giving shelter to an orphan named Elian Gonzalez falls into the category of harmful behavior which must be met with lawful force, policemen in riot gear.
The second is the Christian camp, who concludes that moral teaching is based on objective truth. There are other camps which agree, but this is the major faction.
The first camp has a few sad intellectuals who like to talk about the incompleteness of Goedelian formal systems, but, even a passing familiarity with Goedel shows that his argument had to do with geometry and math, that is, formal syllogistic reasoning, which is not the only source of reason, nor even (these days) a major form, and not the only source of certainty.
Oh, no! I’m sorry, I don’t think i was very clear, my bad. What I think the incompleteness theorem states is that objective truth is there without being proveable, which I find to be a very Christian concept – that things are, in fact, True (big T truth) without being proveably so… also I’m still reading it, so I might not totally understand it. I think that what Goedel is saying – and the book seems to suggest it heavily – is that Goedel thought that this sort of proved a Platonic version of truth. I guess I would look at the incompleteness theorem as a way to get to the Christian camp of thinking, but I might be wrong. Thanks!
Braden
Goedel was saying something very specific and limited about the nature of systems of logic. Russel and Whitehead has spent many years attempting to reduce arithmetic to a set of formal logic propositions, and did not. Goedel in effect proved that they did not because they could not.
I find this confusion often obtains in folks who have not studied philosophy. They cannot make a distinction between (1) the apodictic certainty of a formal logical proposition (that twice two is four, or that tautologies are true, cannot in any non-frivolous way be contradicted or doubted) (2) certainty as it applies to metaphysical, physical, ethical, political, or aesthetic statements and judgements. If jurors were instructed that only the apodictic certainty of a mathematical statement would be admitted to convict the accused, or scientists held that only apodictic certainty would confirm the conclusions of their experiments, then, of course, not a single man could be found guilty nor a single experiment prove anything.
Most people seems not to understand that there are standards of proof according to the subject matter or the discipline involved. You do not use Euclid to prove a murderer is guilty, you use Blackstone. You do not read Aristotle’s Ethics to prove a point in the debate between the Steady State Theory or the Big Bang theory, you reproduce Hubble’s observations. And so on.
Everyone above the sophomore level of philosophy has always known that all propositions which can be proven rest on axioms which cannot be proven. The metaphysical conclusion of the Logical Positivists is that, because axioms are unproven, they are open to doubt, or, worse, utterly without meaning.
These men, if I may be blunt, merely want to sleep with whores or commit other acts of villain and self indulgence and are using the argument that since Goedel proved Russel cannot reduce arithmetic to syllogisms, therefore no one really knows for sure that whoring around and catching the clap is a bad thing. Since skeptical openminded doubt exists in the issue, it is therefore licit.
But just in case their motives are more honorable than I take them to be (http://www.amazon.com/Intellectuals-From-Tolstoy-Sartre-Chomsky/dp/0060916575) the intellectual argument that since perfect certainty of apodictic syllogism is unavailable in one specific discipline that uses apodictic styles of proof, therefore no one knows anything and everything is licit, is a not a logical conclusion under even the most favorable assumptions.
It merely denies that any other type of knowledge exists aside from knowledge of logical categories and mathematical abstractions. Our friends the reductionists materialists will no doubt be surprised to learn that all scientific and empirical learning is held to be worthless.
And, in any case, the argument refutes itself. If it is true that I would be telling a lie were I to say that perfect certainty exists in some few clear cases in moral reasoning, and if Goedel’s argument somehow did indeed prove it true that no perfect certainty in moral reasoning or any other field exists, then it would follow that such a lie is licit, for the selfsame reason: if no one knows anything for sure, no one knows lying is bad.
So, by that logic, if I say “perfect certainty exists in some few clear cases in moral reasoning” either I am telling the truth or I am lying. If I am lying, and no moral certainty exists, then lying is permitted; and if I am telling the truth, telling the truth is one of those clear cases where the moral reasoning is certain. So either way, the statement cannot be denounced.
It is the Pure in heart that shall see the Face of God.
That it, only the pure-hearted are able to see the moral axioms.
For the moral axioms require intellectual perception but one’s heart needs to be clean. Otherwise the moral axioms are not cleanly perceived.
This business of using the word “Newton” as shorthand for “all the laws of physics” (and chemistry, I presume), raises a question for Dr Andreassen.
Let’s suppose,Dr A, you have your computer all loaded with your simulator programme. Now I ask you to turn on all the laws of science, but please do not turn them all on at once. Add in dynamic laws one by one. I ask you, precisely which laws do you need to get the phenomenon we call “thinking” or “writing” or “creation” to emerge?
At first, nothing moves at all. I presume you say “No thinking there”. Now let’s just turn on a uniform gravitational field. So, the bodies fall and accelerate. “No thinking yet.” Lets add Newtonian gravity and three bodies (or more). Now the system might exhibit deterministic chaos. But does it exhibit “thinking”?
Still no? Let’s add rigid bars, axles, leverage and all such mechanics. You could make a Babbage universal difference engine. Is that enough for thinking? Let’s add chemistry. Just the old school approximation with valences, please, not quantum chemistry just yet. Now it looks more “biological”. Is our Frankenstein’s creature thinking yet? Or do we need the mysterious quantum to juice up the uncertainty?
A jolt of Maxwell? “It’s alive! IT’S ALIVE!!” But are we there yet?
You have written repeatedly and at length that Newtonian mechanics plus classical Maxwell electrodynamics is sufficient to generate “thinking”, in the rhetorical passages I quoted above. Then you admit that those rules would not actually work, and say, “It’s shorthand for many other laws”. Odd, that your “shorthand” is so much longer than the bare word “physics”. And we still don’t know whether you require deterministic chaos, or an uncertainty principle or a Turing machine or some other ingredient. We still don’t know what exactly is your hypothesis.
As some very precise scientist wrote
As I have said many times, Mechaspeare does not represent an assertion, but a question. I have an opinion on what will happen when you run it, but the purpose of setting up the thought experiment was to find what Mr Wright thought.
To answer your question, it depends on what you mean by thinking. If you want to run the Mechaspeare experiment and generate authentic Shakespearean sonnets for sale, then Newtonian gravity suffices, since you can run a Turing machine under it. If you want to make a conscious being that has subjective experience, then I don’t know what is required.
But I already told you that he and I discussed this two years ago. What you are saying has no bearing whatsoever on the discussion. We are speaking of Newtonian mechanics for the sake of simplicity, as a shorthand. He and I have agreed on the term. I do not want to discuss with him the nuances of difference between various models of physics, for the very strong reason that such nuanced discussions lead to an error I abhor, which is the belief that a non-causal physics allows for free will.
So please withdraw the question. You have no business criticizing a terminology on which he and I have agreed, if our terminology does not create a confusion or ambiguity.
Certainly. I am happy to withdraw any question about procedural imprecision in the Mechaspeare Challenge.
I am sorry to have caused offense. You are correct that you answered something like the above a while back, but I did not understand it, for it is deeply alien to my way of thinking. Moreover, I think your answer demonstrates a point where you don’t fully understand how a mathematical model works, and I assumed such understanding, which made your answer doubly incomprehensible. Specifically, you say:
That may be so, but nevertheless it is possible to apply a physical model to the brain, and it will give some definite answer. To analogise, if you want to calculate the travel time to Alpha Centauri with a constant acceleration at one gravity, and you apply Newton instead of Einstein, there is nothing in the equations that will tell you “Newton cannot model this regime”; you will get a numerical answer. It will just be wrong. Likewise, if you apply physics to a realm it cannot be used for, nothing in the laws of physics will tell you so; the computer will not print out “INVALID SUBJECT – DOES NOT COMPUTE”. On the contrary it will give you an exact answer according to the rules of physics you gave it. If thoughts have a physical effect, then that answer will be wrong, because I didn’t put the thought into the model. But you are asserting that the model is impossible; presumably you are using the word in some other sense than “you can’t do that”. Obviously you can do that.
No, sir. That is just not true. I don’t think you understand how much the laws of physics constrain atomic movements. Given particular initial conditions of velocity, mass, and so on, there is one and only one possible final state. If the model and the reality differ in outcome, then either the initial conditions differed, or something other than physics is at work. Each atom, at each time, has exactly one velocity, and exactly one change in its velocity, due to the force of the other atoms in the system; and if nothing else is causing the atoms to move, then they end up in exactly one place. Not two. If you have two outcomes then you have something other than physics, and the laws of physics were not “modeled down to the last atom”. They were broken.
Let me recap: Suppose we again take Shakespeare in his London garret, and measure the mass, blah, blah, blah, and ask “Where does this atom end up in one minute, assuming that the laws of physics fully describe the situation?” You say that the question is unanswerable, for we have not taken into account Shakespeare’s thoughts. But I say that the question has a definite answer, whether or not thoughts have physical effects. If knowing Shakespeare’s thoughts is necessary to make accurate predictions, then the answer will be wrong; fine. Nevertheless you will get some sort of prediction by applying only the laws of physics. And if that prediction is wrong, you know the laws of physics have been broken: They do not describe the situation.
If I neglect air resistance in a problem of ballistics, I will get the wrong answer. That doesn’t mean that “What do these equations predict, supposing no air resistance” is a meaningless or unanswerable question. Nor is it meaningful to say that a law is not broken when you apply it beyond its regime; if air resistance is important, then the laws of airless ballistics are broken for that problem. Likewise for physics.
Sir, I regret that your explanation is insufficient to ameliorate my offense. You could have chosen, instead of a base and patently false accusation, to say that you did not understand my many, many answers, and ask for clarification, or been honest and said that the two of us have a difference of axioms and approaches and therefore have a great deal of mutual misunderstanding to overcome.
Instead, you chose to blame me. Sir, you are the one who decided to discuss a technically difficult philosophical question with someone expert in the discipline of philosophy which you have neither studied, nor have an aptitude to practice, and for which you have no respect. Instead of approaching the fascinating topic with honest curiosity, you regard it as an opportunity to browbeat me as if I were some dim student and you some wise teacher. Instead, something nearly the exactly opposite is the case.
Even here again, you accuse me of not understanding how much the laws of physics constrain atomic movements.
No, to the contrary, I understand extremely well. Indeed, I regard atomic movements as more constrained than the modern model of quantum mechanics, at least in the Copenhagen interpretation, would tend to allow.
I regard atomic motions as determined, that is, as exactly defined to an infinite degree of precision, by the laws of physics, with nothing left over or left out of the explanation, and nothing else to explain.
There is no way a serious man reading what I have said could not know this is my belief. If you are not serious, or are not reading, having me repeat myself yet again will serve neither of us.
“One cannot prove the axioms of geometry with geometry. ”
This is NOT Goedel’s Theorem.
The theoram says that given a formal system, there exist true statements in it which can not be proved.
That is, there is a category of true but unprovable statements.
The axioms are trivally provable.
Let’s see you prove the fifth axiom, then.
Actually, Gian is quite right.
You cannot prove the parallel postulate from Euclid’s other axioms. Gian simply says any axiom is trivially provable from itself.
Ah! It has been many years since I read Goedel, and now that you remind me, I confess that I misspoke.
Of course you are correct. Goedel was not speaking of the axioms of a formal system, he was speaking of propositions within the system, and his argument showed that each must have at least one proposition which is both true and unprovable within the system.
I nominate Euclid’s proposition 1.4 (a proof of congruency of triangles) as the Goedelian unproved truth in Euclidean geometry.
I accept your correction with thanks.