The following two letters were sent to me in response to the article Existence and Cosmology: Part I; I assume that they were intended as public comments. If anyone sending me comments about essays I release publicly does not want them attributed, please say so in the letter. Comments can be sent to djls@gate.net.
The letters appear in typewriter type and my responses appear in normal type. Text from Existence and Cosmology: Part I appear in indented paragraphs.
From David S. Ross Ross@kodak.com
What about matter as infinite? An existent infinity of extended matter is not meaningful in precisely the same manner as infinite space is not.
I apologize if I have missed something, but I didn't glean from your posting the explanation of why infinite space is not meaningful.
I don't understand the basis of the claim that matter is finite. To make my confusion clear; are you claiming that there is some definite number of protons in the universe? If so, what is the argument for this?
For something to exist it must possess a definite identity. An `infinite' number of protons does not have a definite identity and hence cannot be said to exist. An `infinite' spatial extension similarly has no identity.
To view it another way, how could one establish the existence of an infinite number of anythings? No finite observation or set of observations could suffice. And that which is not provable even in principle cannot be true. As I, and others, have stated many times, the true is the proven, the potentially true is the potentially provable.
A `concept' claiming infinite content for a physical existent or set of existents is literally devoid of meaning. Each proton is a definite entity. Whatever definite number of such entities exist at any moment exist. What can it mean for more than that definite number to exist, if you disallow every other definite number. To `exist', by definition, means to have precise limits, to be something specific.
To quote Peikoff, ``The actual is always finite.''
Something very fundamental is involved here: You ask ``...What is the argument for [some finite number of fundamental particles]?'' The answer is very simple: There is no alternative.
To ask for a proof that existence has a finite content is to ask for a proof that existence has a definite identity. There is no proof. The proposition is axiomatic, as Objectivism correctly asserts. Finite content is part of the meaning of existence and identity.
To ask for an existent infinity is to ask for a contradiction in reality. It is to accept that an entity have content and in the next breath declare that whatever its specific content, it is not yet the complete actual entity.
The supposed alternative of an existent actual infinity of particles is non-conceptual -- literally meaningless. I submit that to take such an alternative seriously, one must break with Objectivism at its most fundamental level, the level of identity, of `A is A'. It is the principle of identity, that existence have a specific content, that proscribes the actually infinite. There is both literally and figuratively no room in reality for an existent infinity. Such an `entity' would have to always be something more than whatever it is -- we never reach the `is'.
You may remember that in earlier essays, despite challenges, I insisted upon calling myself an Objectivist; this was precisely because its core principles are absolute for me. The priciple of identity, which disallows existent infinities, is part of that core. I follow it wherever it leads.
I feel somewhat uncomfortable answering you by restating classic Objectivist principles as I am sure that you know them very well. I must, however, ask how you could reconcile the assumptions behind your question with Objectivist fundamentals. I personally do not know how one could remain an Objectivist when one accepts an existent infinity as conceptually valid and requires a proof for finitude.
I suppose one might still accept the totality of Objectivism's intertwined superstructure -- man as a being of volitional consciousness with reason as his primary tool of survival, man's life qua man as the foundation for ethics and his standard of value, the non-coercive functioning of man's mind with Laissez Faire capitalism as its only economic embodiment, the proscription against the initiation of force and the use of fraud as government's only valid function, etc.
You would, however, no longer have a coherent, fully-encompassing philosophic system. You would have undercut its base in objective reality. You would retain no right to call the system 'Objectivism'. It's very name asserts its base in objective reality. You would have accepted that existence can be other than what it is -- that it need not have a definite (meaning a finite or limiting) content.
You could then have no reply to any mystic or theologian who says that to be something an existent need not be something specific. You have no refutation for the non-conceptual if you accept it yourself. You have no way of rejecting the `concept' of god, much less any of his infinite attributes. Why need one give them content? The `concept' of the existent actual infinite is precisely what has already been granted.
Concepts, then, need no longer build upon other concepts into a coherent conceptual net founded upon reality. The entire Objectivist theory of concepts becomes inapplicable -- it has lost its base in objective reality. Objectivism is all of a piece -- tamper with its core and you no longer have Objectivism.
The intuitionist school places meaning first. No contradictions have ever appeared or can ever appear in intuitionist mathematics--for the very same reason that there are no contradictions in reality. Meaning, appeal to reality, is retained every step of the way.
I think that the intuitionists have many good ideas in mathematics, but I think that it is not quite right to say that they appeal to reality to ground mathematics. Brouwer and his followers often speak of mathematics as an `essentially languageless activity of the mind', or some such. The explicit philosophical premises behind intuitionist mathematics are sometimes vague, but they have a generally Kantian feeling - one becomes aware of mathematical concepts by introspecting, not by attending to reality. The intuitions that the intuitionists place at the base of mathematics often are Kant's synthetic a priori truths, aspects of our experience of reality that are necessary because they are contributed by consciousness, not by reality.
For a discussion of this, I recommend Stephan Korner's essay `The Philosophy of Mathematics'.
What I mean by ``intuitionism'' is not necessarily what all mathematical intuitionists mean when they use the term; they do not ordinarily proceed from a conscious, Objectivist base. I agonized a bit over the use of the term -- it does have some unfortunate Kantian connotations -- but finally decided that nothing else would quite do. The word is part of mathematical history. ``Constructivism'' is a possible alternative; it does emphasize the limitation of mathematical reasoning to constructive processes and constructible entities, but does not address the status of the core concepts.
Many are misled by a false dichotomy between reality `out there' and `non-reality' (I suppose) inside one's head. When one introspects, everything that one finds is part of reality (that subset of reality that is one's mind) and all the subject matter in that mind is derived from reality; there being, of course, no other source. Some intuitionists may not realize this when they state that mathematical concepts appeal to the intellect directly. They do, but only because of their consonance with reality both external and introspective. However, one must look at internal reality with the same care one exercises with external reality.
To quote Peikoff (OPAR p35) ``Even if, someday, consciousness were to be explained scientifically as a product of physical conditions, this would not alter any observed fact. It would not alter the fact that, given those conditions, the attributes and functions of consciousness are what they are. Nor would it alter the fact that in many respects these attributes are unique; they are different from anything observed in unconscious entities. Nor would it alter the fact that one can discover the conditions of consciousness, as of anything else one seeks to know, only through the exercise of consciousness.'' [emphasis added]
With this quotation I agree 100%. I think Peikoff does not seriously entertain the possibility that science could 'explain' consciousness competely by reference to physical conditions. Causal correlation with specific states of matter is not an explanation of content or identity of mind.
Consciousness is something other than the physical conditions which accompany it. The three Objectivist fundamental axioms (not to be explained or proven, but simply pointed to) are existence, identity, and consciousness. Identity is just another way of saying what it means to be an existent; this applies equally to physical reality and to consciousness. This leaves two fundamental realities, one physical (matter), one conscious (mind), each axiomatic and neither `explainable' in terms of the other. This too is part of Objectivism's core.
Note that Euclidean geometry, with its undefined and undefinable `concepts' of `point' and (straight) `line', were part of Kant's package of synthetic a priori truths. Yet, in Euclidean geometry, as axiom system, point and line are whatever satisfy the place-holders `point' and `line'. The terms contain no intrinsic meaning, no genuine parallelism to reality.
That is what separates Kant's synthetic a priori truths from mathematical intuitionism, and historically, that is what makes Euclideanism just one formalism among many. Each geometric axiom system is instantiated by whatever model assigns some consistent content to the inherently meaningless terms `point' and `line'.
Kant had no real idea of what was fundamental and what was not. He rarely paid attention to meaning, and understandably so. Meaning is not to be had when a knowable reality is denied. He swallows uncritically the infinite and the infinitesimal when he accepts points and lines as meaningful fundamental entities. Intrinsic meaning, paralleling existence and identity, is not his starting point.
Acceptance of the infinite is rejection of existence and a longing for another unknowable 'deeper' reality. Kant's ideas could not have exerted the historical influence that they did without tapping into this psychologic mind-set.
An Objectivist grounding of mathematics would begin by noting that basic mathematical concepts such as 'oneness' and 'moreness' derive from reality, both internal and external, and would insist that this parallel to reality be maintained in all further reasoning. The most fundamental mathematical concept of all, 'oneness', a unit, is the direct parallel to and abstraction from `existent entity' in reality.
Your points deserve an entire essay of their own addressing them. In fact, that was the essay I said was needed in the original essay. I guess it is probably time for me to write another paper for JW's list (in my copious free time). A more detailed paper on ''Mathematics, Meaning, and Reality'' is now on my to-do list.
I also expect to post an essay on Kantian philsophy. In almost every respect -- metaphysical, epistemological, ethical -- Kantianism and Objectivism are polar opposites. In a nutshell (a most appropriate metaphor) Kant undercuts our perceptual faculty by positing an unknowable reality, negates our conceptual reasoning capability by declaring only tautologies provable, and undermines our humanity by generating an ethic of self- sacrifice and divorcing morality both from the achievment of values and from reality.
This concept of sequential states is very solidly grounded. It is a fusion of the very same concepts, derived from reality, that are at the foundation of intuitionist mathematics--oneness, twoness, nextness, betweenness, moreness. These cardinal/ordinal concepts are immediately given -- immediately intuited from reality -- and carry genuine meaning at the most fundamental level.
Objectivism does not recognize any concepts as immediately given. Percepts are given, but a directed process of consciousness is needed to form concepts.
What I mean by ``immediately given -- immediately intuited from reality'' is that these concepts are immediately available from reality for all to construct and internalize. It is, of course, early percepts that serve as the raw material from which these first concepts are intuited by a directed consciousness.
Objectivism insists that existence, objective reality, is implied in an infant's very first discriminated perceptions. Once `existent entities' is conceptualized, we have the core intuitionist foundation for mathematics.
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From Steve Rogers (srogers@mcc.com):
Some comments:
For example, George Smith in Atheism: The Case Against God, arguing from Objectivist fundamentals, is critical of those who ask why the numerical constants of nature have the values they do -- mass of a proton, charge or spin of an electron, velocity of light, the gravitational constant, and so on. The entities display these constants because they have the intrinsic properties they have; they exist with that identity and that's that.
Yet, within the past several months, there has appeared a new formulation of basic physical principles which predicts accurately, that is, derives from more fundamental properties, several of the fundamental constants of physics. Similarly, there are theories to relate the origin of the big bang to `prior' quantum vacuum states. The big bang was previously regarded as an unexplainable starting point that had to be accepted as the way nature is -- the way existence exists.
The point of such discussions is not that one should not attempt to further explore or explain physical properties (if this is a common misconception, I have had the uncommon luck of not encountering it). The point is to prohibit explanation of physical phenomena in terms of something more fundamental than reality. Smith's example is in the context of people asking why constants have a particular value to insinuate that some external agent must be acting to give them that value (hint hint starts with G). It is not his purpose to say that we should not try to explain such constants in more fundamental terms, or to express them in terms of properties of more fundamental entities.
I think you are foisting a position on Smith, and others by implication, that they just don't have. I'm not convinced Smith is making the case you are refuting, though he would be wrong if he did.
My comments are based on pp230-231 of Atheism: The Case Against God where Smith favorably quotes Corliss Lamont's The Philosophy of Humanism to strengthen his case against the explanatory value of god. The quotation is:
``In specific scientific explanations as well as in ultimate philosophical questions a stage frequently ensues where it is profitless to keep on asking "Why?" At such a juncture we have to say: "Things are simply constructed this way or behave this way." The speed of light is what it is; the law of gravitation operates as it does; and the number of protons and electrons in each type of atom is what it is. In none of these instances can an intelligible answer be given as to why...In science as well as philosophy, then, we eventually hit rock-bottom in the pursuit of certain inquiries.''
Definitely we do hit rock-bottom, but how do we know when? -- That is my whole point.
When is it profitless to keep on asking ``Why?''. When do we answer, as Corliss Lamont and George Smith require, ``Things are simply constructed this way or behave this way.'' When do we say things are the way they are because that's the way they are?
My answer, in effect, is never -- even though finite existence, finite causality, and axiomatic existence tell us there must come a time. As I worded it, in this matter ``we don't know how to know.''
In other words, if ``existence exists'' means things are the way they are with no further explanation possible, it is a truth without an application -- a truth by default and perhaps, in any specific context, a non-truth to be swept away by the advance of science.
I recognize two exceptions. [1] Existence (meaning the physical world, existents other than mind) and consciousness are indeed axiomatic as Objectivism asserts. Neither is explainable in terms of or reducible to the other. This is a deep and complex issue; there will be at least one essay on mind and matter. (There is now.) [2] An application arising in the back-analysis of states of existence already traversed, for which see the forthcoming part II of Existence and Cosmology.
These two matters aside, my point is that we can never say with any conviction -- as Corliss Lamont and, by implication, George Smith feel they can -- ``In none of these instances can an intelligable answer be given as to why...''
In fairness to Smith, I don't know if he still considers these specific items to be among the ones that limit science; his book was published some time ago. If he doesn't, he demonstrates my point: Don't be too quick to set philosophic limits to what science can explain -- that is the role of religion.
We discussed previously Peikoff's rejection of Quantum Mechanical explanations of physical reality because they `contradict' the law of the excluded middle. An object may be here or there, but surely not in both places at once. The previous Zeno's Arrow analysis even uses this very dichotomy in the analysis of particle motion qua particle.
But what happens when particles at the sub-atomic level also display wave characteristics? What happens when suddenly, between observations, not only can we not say where the particle is, but its very existence as particle, with specific position and momentum, becomes physically unsupportable?
We are in the presence of a new physical paradigm at the micro level having no counterpart in previously observed macroscopic reality. What would Peikoff have -- mathematical continuity in motion with absolute position at every instant? Then we would indeed have an existent infinity irreconcilable with Objectivist premises, irreconcilable with reality!
Peikoff cannot arbitrarily extract `position' or `particle' from their macrophysical conceptual net and expect them to apply unchanged in new realms.
Once again, I think you are foisting a position on Peikoff which he is not making. Your statement ``What would Peikoff have . . '' implies that you think he must logically make some of the claims you attribute to him. I don't think this is the case.
The only logical alternative to a quantized explanation of motion (to my understanding) is continuous motion. If the latter is the case then my walking across the room requires me to perform an infinite number of individual motions. Does he wish to allow the infinite to be said to exist?
I foist no position on Peikoff, but his positions do have consequences, whether or not he chooses to acknowledge them. He alone boxes himself into a corner. If he is indeed committed to a non-quantized physics of exact particle position at every mathematical instant in time, he thereby commits to an existent infinity of points. He commits to mathematical continuity as physical reality. Do you see any alternative?
In all fairness, I must state that I address Peikoff's views on Quantum Mechanics as posted on Objectivist forums and as communicated to me by Objectivists whose accuracy I have no reason to question. If I have mis-stated Peikoff's views in any particular, please let me know. To me, it seems his views on Quantum Mechanics require an existent infinity of point positions, with all that that implies regarding the violation of the axiom of identity.
He needs positional continuity if he wishes never to consider an electron as anything other than a precisely positioned particulate entity and never wishes to consider what positional observations imply about its identity between such observations.
Yes, but he has misapplied the law of identity. There is no reason why an electron's identity cannot be such that it is capable of manifesting itself in more than one place at a time. It would only be contradictory if a person asserted both that an electron was and was not at a given place at a given time. A contradiction only arises if we consider the statement ``An electron is at point A'' to mean `The electron is not at point B''
He simply asserts that the law of identity precludes the actual existence of the contradictory -- the particle cannot be in two places at once.
Your contention ``But what happens when particles at the sub-atomic level also display wave characteristics?'' is really irrelevant to Peikoff's point. As a philosopher, his position would be: I don't know or give a dang what happens, but whatever it is, it is NOT a single entity with two locations.
Why? Why can't it be that a single entity (such as an electron) properly understood, can `have' many locations simultaneously? What in Objectivism conflicts with this hypothesis? The answer is, nothing, with the exception of the macroscopically derived naive concepts of `location' and `particle' which may well be invalid on a micro scale. How can Peikoff know they will remain valid? What does Objectivism know of electrons? (See the Binswanger excerpt below regarding `location' and my next comment regarding `entity')
What conceptually prevents particulate entities from having manifestations at multiple locations? Remember, Quantum Mechanics never actually talks of detecting the same particle at two locations simultaneously as Peikoff seems to imply. We always detect one particle at one location. It is only the evolving pattern of multiple sequential particle detections, as in the two-slit experiment, that leads us to conclude that particles have additional properties encompassing multi-positional wave characteristics when not manifesting themselves as localized particles.
Remember, the particle is never physically multi-locational, in the Peikoffian sense; the `waves' are probability waves that tell us the likelihood of detecting an entity qua particle at a particular location. The question of some deeper underlying physical structure remains open.
A fundamental particle is a rather complex entity -- but Objectivists already knew this. To my knowledge, Peikoff never blinked at the apparent dualism of matter/energy interconversion and questioned how a minute particulate entity could manifest at another time as a vast fireball of energy; it is `somehow' transformed. Why does he balk now when it is suggested that this very same minute particulate entity can at other times (between detections as particle) manifest as a multi-location wave?
The answer is simply that he wields the weapons of logic as clubs rather than scalpels. He needs to better understand what Quantum Physics is actually saying before declaring a law of logic violation! Quantum wierdness phenomena are not fantasies of ornery, unreasonable physicists. They are ways reality manifests itself. It does not take too great a knowledge of Quantum Physics to appreciate that the weirdness is in the facts, the experiments, long before it is in the theory.
Even though we may be ``in the presence of a new physical paradigm at the micro level having no counterpart in previously observed macroscopic reality'' the philosophical axioms still hold. It is not incumbent upon Peikoff (or philosophy as a discipline) to provide a counter-explanation of the phenomena in order to deny the validity of an explanation proposed by a physicist. Your ``Peikoff cannot arbitrarily extract ...'' comment is way off base because it ignores the proper division between philosophy and science. As a philosopher, its his job to stay out of such explanations, and that's what he does. He wouldn't know a momentum from a hole in the ground - the point is, he (and philosophers in general) don't need to, in order to determine a model of reality that contains contradictions is invalid.
But what is the contradiction? That an electron simply ``can't be'' in two places at once? Again, what does philosophy know about electrons? Must we call them non-entities if they, at times, show wave characteristics? I thought ``as a philosopher it is his job to stay out of such explanations.''
The fact is, he crossed over into science's realm, and he did so invalidly, when he denied the possibility that an `entity' could be in two `places' at `once'. What in philosophy contradicts that? The law of non-contradiction does not; it only says that an electron can't both be in a place and not be in that same place at the same time and in the same respect. The requirement that every existent have a definite identity does not; if it is alleged to be in two or more places at the same time, and that has precise meaning (as it does in a specific detailed quantum model) then that is part of its specific identity and no excluded-middle violation exists. What is left?
Again, as I have emphasized repeatedly and in detail and with examples, in earlier essays, meaning -- consonance with reality -- take priority over formal logic. Without a prior analysis of meaning apparent contradictories may not truly be forced alternatives.
Philosophy won't explain the phenomena, that's the job of science. Philosophy doesn't tell you not to look for explanations in reality, it tells you not to look for explanations outside reality. I don't think you understand what's in the discipline of philosophy and what's in science, or why (perhaps a harsh comment, but there it is). I think this is the crux of the problem you perceive - not that people are using the law of existence to justify refusal to fully examine or explore physical phenomena.
Let's look a little more closely at ``[W]hat's in the discipline of philsophy and what's in science [and] why.'' You make a virtue of sticking to one's turf, but it is no virtue if a philosopher criticizes science without appreciating exactly what is being said.
I certainly agree that a major philosophic contribution to science is to haul scientists up short if they frame hypotheses that intrinsically violate reality and reason. I use this precise methodology, as you have seen, in dealing with `explanations' of physical phenomena that violate identity/non-existent infinity requirements in reality. Peikoff does the same with the law of the excluded middle.
The issue is not whether we understand what is in science and what is in philosophy -- reality is in both. Some issues can be addressed effectively by both disciplines; the mind-body `problem' is one. The issue is whether we apply philosophic considerations with retention of meaning and with adequate understanding of what science is actually saying. In sum, do we deal with genuine meaning or with bare formalism?
One must understand clearly what physics is actually saying and observing before one asserts law of logic violations. I have spent much time, in many contexts, in previous essays explaining why meaning is primary. We must know the intrinsic independent meaning of each logical `alternative'. Only meaning, not mis-applied formalisms such as the law of excluded middle (see my digits of pi discussion, for example) or even the law of non- contradiction (see my discussion of the parallel postulate) guarantees parallelism of concept with reality and non-violation of the principle of identity. Only meaning keeps concepts within their conceptual net.
You are very correct in asserting that ''philosophy tells you not to look for [scientific] explanations outside reality.'' To follow your prescription, one had better first know exactly what science has found reality to be -- and in Quantum Physics specifically, what is quantum fact and what is quantum interpretation (of which there are many). I see Peikoff railing against quantum fact. He could, if he wished, embrace a parallel universe model and have no further problems with one entity in two places at once. Of course, he might have other problems. I tried in my discussions above to deal with quantum fact.
The quantum 'weirdness', as emphasized, is first in reality, then in the explanations. In certain situations, an electron, photon, or other fundamental particle behaves as if it had a 'road map' of the surrounding universe. That is a quantum fact. How we understand that ''as if'' is where the interpretation comes in.
You feel Peikoff's position would be ``whatever [a sub-atomic particle] is it is not a single entity with two locations.'' What you visualize is particle P at location A. Then when you hear ``it is also at B at the same time'' what you then visualize is something else at B and think ``how can P defined to be the particle at position A also be at B.''
You yourself (and Peikoff) not reality construct a formal contradiction. The physical reality, as we have seen, is always one particle detected at one position! The weirdness is in what the pattern of detection of succesive particles says (again many hypotheses) about what's going on between particle detections. The physical reality is not some mathematical diagram with points A and B where if P is A, it is not also B.
In sum, while I agree with Peikoff's emphasis that physical explanations must be restricted to what does not violate what we know about reality, I feel he misapplies this necessity when he attempts to use the law of excluded middle as the principle that is violated.
One further observation: Through the ages, philosophic thought has been molded by science's base in reality -- rarely the reverse -- except as poor philosophy has inhibited science and good philosophy encouraged it. Philosophic thought has been relatively incapable of contributing to scientific explanation. Working scientists generally ignore philosophy and conclude it irrelevant to their endeavors. For the most part, philosophy itself must bear the responsibility. Objectivism, however, with its intractable committment to reality, can be a shining exception. Objectivism is genuinely potent.
SR
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Some additional related material:
The following quotation is from Harry Binswanger, dealing (apparently) with the Arrow Paradox. It is excerpted from Q and A Department: Identity and Motion from The Objectivist Forum, quoted in The Ayn Rand Lexicon under ``motion.''
``The concept of "location" arises in the context of entities which are at rest relative to each other. A thing's location is the place where it is situated. But a moving object is not in any one place -- it is in motion. One can locate a moving object only in the sense of specifying the location of the larger fixed region through which it is moving during a given period of time. For instance: "Between 4:00 and 4:05 p.m., the car was moving through New York City." One can narrow down the time period and, correspondingly, the region; but one cannot narrow the time down to nothing in the contradictory attempt to locate the moving car at a single, fixed position. If it is moving, it is not at a fixed position.'' [emphasis added]
In the same essay he also said ``Reality does not contain either points or instants (in the mathematical sense).'' As I have emphasized, this is a philosophic necessity to avoid existent infinities.
Here we find Binswanger clearly endorsing a quantized model of motion as a resolution to the Arrow Paradox, just as I did. One can reduce the `spans of time' to a limit, but ``one cannot narrow the time down to nothing.'' Binswanger's ``reality does not consist of points or instants'' means that time and space are not infinitely divisible; that is, they can be divided to some limit and not to points of zero size or instants of zero duration.
A physicist would likely strengthen Binswanger's statements by adding that once one has narrowed the time unit to a `quantum time' the car is at a specific `location' or quantum position, but each particle in the car is not a mathematical point location and the time is not a mathematical instant, and hence no infinities are present in reality. He would also point out that the accuracy of quantum localization is related inversely to that of measurement of momentum. Binswanger (wisely) omits these inclusions because they are not inside the field of philosophy, but are, in fact, part of science. Binswanger is deliberately vague -- he sticks to what he knows and does so accurately. He does not deal with the scientific implications of reality not consisting of points or instants.
Nevertheless, here we see science remaining within constraints set by Objectivist philosophy! The specific constraint: no existent infinities -- they violate the law of identity.
To quote Peikoff from Objectivism: The Philosophy of Ayn Rand, (p31) ``For example, one can continually subdivide a line; but however many segments one has reached at a given point, there are only that many and no more. The actual is always finite.'' [Emphasis in original]
The actual is always finite!
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