“God of the surprises”

I guess we are all familiar with the god of the gapsconcept. The common theological tendency to explain gaps in our scientific knowledge with the claim “god did it!” It’s an easy, if very lazy, strategy because there will always be gaps in scientific knowledge. As longs as one has a short memory and moves on to new gaps when the old ones get filled.

Well, I have come across a new term for a related phenomenon – “god of the surprises.” John Shook uses the phrase in his new book God Debates: A 21st Century Guide for Atheists and Believers (And Everyone in Between).

“In addition to the god of the gaps strategy pointing out what science doesn’t know, theologians have another strategy, a “god in the surprises” strategy, pointing to new scientific knowledge. Science is good at coming up with surprises, since the scientific method always seeks new evidence. The “god of the surprises” strategy tries to make naturalism appear inconsistent with cutting-edge science, as if religion does a better job of keeping up with science than naturalism. The trick behind this diverting illusion is to first display to the audience a shabby naturalism, crude and outdated, and then to draw attention to some surprising scientific discovery. News from biology: life has self-organizing abilities! Naturalism wasn’t expecting that, what with its outdated notion that life was just the aggregate sum of its mechanical chemical reactions. For life to have such amazing powers, something supernatural must be involved somewhere. News from physics: quantum entanglement is spooky! That’s a nasty shock for naturalism’s premise that every physical particle always has its own intrinsic properties. For particles to have such deep connections, while so widely separated from each other, something supernatural must be at work. Cutting-edge science can be co-opted by this strategy into humbling naturalism and supporting supernaturalism.”

Of course this strategy doesn’t fool anyone familiar with scientific discovery. Real science is always full of surprise and counter-intuitive explanations. it’s part of what makes it so exciting.

However,  I think some of the more theologically faithful do get fooled. Perhaps they even feel a bit smug with a delusion that science is “proving them right.”

But it is annoying to see the authority of science being use in such a cheap way.

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28 responses to ““God of the surprises”

  1. An interesting twist here is that while science has continual improvement and re-evaluation of its theories as a corner-stone, the opposite is the case with (at least) Christianity—making this particular approach hypocritical.Christianity has re-evaluated much of its take on the world over the years, but usually in a grudging and belated manner, and often making a literal reading of the Bible entirely absurd in the progress.

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  2. Do atheists feel the need to bolster their self esteem by engaging strawmen? Science isn’t about proving naturalism or otherwise, despite your strange attitude.

    You comment an awful lot on theology but you rarely venture to argue with actual theologians. Wise move Ken, I’ve seen them run rings around your solipsism

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  3. Arguing with theologians reminds me of that wrestling with a pig joke.

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  4. Richard Feynman:

    What is it about nature that lets this happen, that it is possible to guess from one part what the rest is going to do? That is an unscientific question: I do not know how to answer it, and therefore I am going to give an unscientific answer. I think it is because nature has a simplicity and therefore a great beauty. Richard Feynman, “Seeking New Laws,” pp. 143-167, in Richard Feynman, The Character of Physical Law, New York: Modern Library, 1994. Quote is from p. 167.

    At the risk of quote-mining, this appears to be Feynman’s version of Wigner’s famous Unreasonable Effectiveness of Mathematics argument. Wigner wrote:

    The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

    Both Feynmann and Wigner, in my reading, conclude that science can never answer the question as to why science and mathematics work as well as they do. No other observation from the world of science or mathematics has ever struck me as a more powerful apologetic than Feynman’s and Wigner’s point.

    The world is not only governed by orderly laws, but those laws are expressible in simple enough terms that we can make sense out of them and use them to make astonishingly accurate predictions. As Feynman suggested, if I read him correctly, science can never explain why this is so. It is, in fact, unreasonable that this happens.

    Are these two Nobel Laureates using science ‘in a cheap way’?

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  5. Ropata, where have you been?

    My debates with theologians have have hardly resulted in their running rings anywhere.

    Your mate Glenn permanently excludes my comments on his blog now after I revealed the shallowness if his attacks on science. He really can’t handle normal vigorous but well meant debate. He ended up running rings around himself in the end. His preventing of my comments now indicates avoidance of true human enquiry.

    Your mate Matt seems to run away from discussion when he finds difficulties. MandM seem to also have deleted or prevented my last comment. Hardly running rings.

    And you yourself, Ropata, seem to enjoy making wild but irrelevant comments. You don’t even seem to read the posts, let alone run rings around them.

    Ah well, I guess that’s the nature if theology.

    But, as I have told you before. I have absolutely no interest in theology. It’s not an honest subject so I keep away from it.

    However, I will defend science against the religiously motivated straw mannery that theologians seem to specialize in. I guess it pissed them off that I refuse to play their game and they are forced to justify themselves more sensibly.

    Now, as you have got those feelings off your chest have you got a sensible comment to make on my post.

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  6. @ropata, Its a bit ironic to be throwing out accusations of straw mannery looking at your last post.

    Surely questions about how we can understand things lie in the fields of human consciousness, or when it comes to why induction works, perhaps probability. I don’t know whether or not we can formulate or answer scientific questions in these areas, but if not, I am happy enough to accept that fact with grace and be bloody thankful about what we can know. As far as I can tell, this is what Wigner is talking about in your mined quote above.

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  7. What about sharing that joke, Nick. I don’t think I have come across it.

    Mind you I think of arguing with theologians as jelly wrestling. I think their obtuseness, dishonest arguments, and avoidance of any testing against reality is part of their training.

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  8. I like it.

    Should also impress Ropata. After all GBS was also a Nobel laureate.

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  9. Ken’s straw man was this :
    The common theological tendency to explain gaps in our scientific knowledge with the claim “god did it!” It’s an easy, if very lazy, strategy because there will always be gaps in scientific knowledge.

    I don’t know which theologians Ken is talking about, they certainly wouldn’t be respected academically. I suspect Ken is still (rightly) annoyed by his namesake Ken (Ham).

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  10. Having had a quick look at the blogs of the afore mentioned Glenn and Matt, it looks like they enjoy wrestling so much that they are looking for sponsorship to go pro.

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  11. Richard Christie

    I think Wigner makes a mistake to externalise mathematics as if it is some sort of entity or truth of itself.
    It is merely a language that paraphrases certain human thinking patterns and concepts such as rate of change for example.
    Thus the question as to why it works to explain the physical world is to my mind irrelevant. It’s like asking why thinking works.

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  12. Ropata
    Mathematics is entirely a human product or invention/ development.

    It is a thinking tool.

    Confounding argument to include Mathematics in natural phenomena is a bit revealing.

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  13. Richard Christie

    Heh heh, couldn’t have said it better myself Woody.

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  14. Richard/Woody. That’s a bizarrely incurious attitude for freethinkers. I don’t think you really grasp the force of Wigner’s argument. It requires some appreciation of the outrageously abstract conjectures of mathematics to understand how crazy it is that they proved useful to science often decades or centuries after they were conceived.

    In “The Problems of Philosophy“, Bertrand Russell writes:

    The general principles of science, such as the belief in the reign of law, and the belief that every event must have a cause, are as completely dependent upon the inductive principle as are the beliefs of daily life All such general principles are believed because mankind have found innumerable instances of their truth and no instances of their falsehood. But this affords no evidence for their truth in the future, unless the inductive principle is assumed.
    Thus all knowledge which, on a basis of experience tells us something about what is not experienced, is based upon a belief which experience can neither confirm nor confute, yet which, at least in its more concrete applications, appears to be as firmly rooted in us as many of the facts of experience. The existence and justification of such beliefs — for the inductive principle, as we shall see, is not the only example — raises some of the most difficult and most debated problems of philosophy.

    There is no proof for the scientific method. There is overwhelming evidence that it works, so we use it.
    If you claim that the only path to knowledge is science, then the burden of proof is on you. Or you could try and claim that you do have true knowledge apart from science. Or you can engage in special pleading — science of the gaps.

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  15. A few remarks to various comments:

    o That mathematics is a good description of physics is not at all surprising—if we assume that the universe follows the kind of development it appears to follow. This development is basically (in an over-simplified statement) a set of very basic (currently unknown) rules applied upon an initial set of conditions, then applied upon the result, and so on. A good analogy would be Conway’s Game of Life.

    (Incidentally, the great applicability of mathematics could be seen as at least circumstantial evidence for a non-Created world.)

    o Mathematics in the sense of the school subject or academic discipline may be a human creation, but what is underneath is very real (if abstract), making the claim that mathematics is a human creation similar to the claim that biology is a human creation.

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  16. Ropata – “There is no proof for the scientific method. There is overwhelming evidence that it works, so we use it.” Do you not realise how silly that statement is? Have you not heard of the proof of the pudding?

    Perhaps we could also say:

    “There are plenty of “proofs” for the theological method and conclusions (which are the same as the assumptions). There is no evidence they work. But theologians still go ahead and use them. After all, if you don’t test against reality anything goes.”

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  17. I was using the formal mathematical meaning of the word ‘proof’ not your colloquial version. This sort of semantic error is the reason theologians get tired of arguing with you.

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  18. Of course you are not using a proper proof – that is one that checks against reality. The point is that theologians love logical proofs because they can manipulate them to produce the results they desire. Hardly honest but very convenient if you want to prove the existence of something which doesn’t exist.

    That is why their conclusion never test well against reality. And that is the real way to prove things in the end. In science reality keeps us honest.

    This is not a semantic error at all.

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  19. Ropata – is that true? Do theologians get tired of arguing with me? I thought they were running rings around me.

    So Glenn excludes my comments becuase they make him tired! Sure it’s not that he is just annoyed because I point out that reality is different to how he claims it is – and produce the evidence?

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  20. Ropata,

    I have repeatedly observed your habit of quoting well-known people in order to support a point you are trying to make. However, in most of the cases I have the distinct impression that you either do not understand the wider context of these cited passages or you wilfully leave it out in order to put a certain “spin” on them.

    A case in point is your quotation from Bertrand Russell’s “The Problems of Philosophy”. Said quote is part of a much larger epistemological discussion, which touches on such diverse areas as different forms of belief and their respective justification, the question of a priori knowledge of universals, a workable definition of “truth” and “knowledge” etc.

    Now, what you apparently want to get out of his essay is the notion that since science frequently employs inductive principles, and since induction can not be proven with mathematical certainty to be reliable, that this somehow renders all scientific knowledge suspect and simultaneously opens the door to alternative ways of knowledge acquisition.

    However, without going into a discussion of the problem of induction or epistemology in general, the above conclusion is not even supported by Russell himself, which is why it is misleading to cite him in support of your position. To say it in Russell’s own words, from the chapter “The value of philosophy”:

    “Philosophical knowledge, if what has been said above is true, does not differ essentially from scientific knowledge; there is no special source of wisdom which is open to philosophy but not to science, and the results obtained by philosophy are not radically different from those obtained by science. […] If, as many philosophers have believed, the principles underlying the sciences were capable, when disengaged from irrelevant detail, of giving us knowledge concerning the universe as a whole, such knowledge would have the same claim on our belief as scientific knowledge has; but our inquiry has not revealed any such knowledge, and therefore, as regards the special doctrines of the bolder metaphysicians, has had a mainly negative result.” [emphasis mine]

    Thus, Russell clearly repudiates the „different ways of knowing“ idea that you seem to adhere to. Insinuating otherwise is contradicting his clearly stated position.

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  21. Welcome back Iapetus. It’s good to see your posts clearing the air on the philosophical issues.

    Coincidentally, I have recently read “The Problems of Philosophy”, but that was during an overnight ferry trip between Danzig and Stockholm, so I went quite fast through.

    I have to say, that seeing your clarifying posts in the past on philosophical issues (as opposed to the attempts to use Philosophy for obfuscation or concept smuggling) inspired me to read some of the original texts. I really enjoyed Hume’s “An enquiry concerning Human Understanding”, but have got a bit bogged down in Kant’s “The critique of Pure Reason”, even after swapping to the English translation. On the other hand, the inspiration to read these could be coming from the intersection of a nice shiny new iPad and free downloads from project Gutenberg 😉

    Anyway, the question I wanted to ask is related to the nature of mathematics (also raised earlier by Ropata’s quote mining from Russel). I must say that I found Hume’s (as far as I understood it to be be) reasoning on the source of all knowledge being tied up with experience resonated with my own gut feelings about this.

    I found it a little bit less clear and cut and dried with relation to a priori knowledge (or in particular, logical or mathematical deduction), but got a bit of an impression that he was also suggesting an ultimate human experience background to this also.

    I am not sure on this issue myself, but I am currently leaning towards logic and wider mathematics being a definitional exercise performed by human reasoning that is ultimately triggered (but not proved) from an experiential background. I.e The idea of 1+1=2 comes from actual physical experience with rocks of whatever, but then we define some general rules or axioms using our own mental symbology that fit in with this which we then use as building blocks to build edifices of increasing complexity.

    In this sense, I would consider mathematics to be a human creation. That brings us however to the next point (I think the Ropata’s mined quote from Feynman touches this), which is the question of the surprising (or not) capability of mathematics to describe and make predictions about reality (ala physics). In my current thinking, I am wondering about how surprising this is.

    My thinking goes like this. Some of mathematics when correctly applied to facts has allowed scientists to make predictions about reality which are then confirmed to various levels of confidence by empirical observation/testing. This however does not apply to all mathematical concepts or ideas applied in all ways.

    However, if you accept my earlier paragraph about mathematics as being defined by humans, based on experiential triggers, then perhaps it is not surprising that there are some tie ups to reality.

    I suspect that the question of how surprising the effectiveness of mathematics in science is, could be tied up with the nature of probability itself (as so many things are). In this case though, the experiences as the triggering inspirations behind the defined mathematical axioms/rules could well tilt the probabilities to a sufficient extent that the level of success of mathematics to describe/predict (or in some cases not predict) reality is actually not surprising, but about what you would expect given the range covered by the mathematical concepts.

    I will stop there before I boor everyone to tears, but I would be interested in any of your thoughts on these issues.

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  22. PS. I hope that in post above I don’t sound like somebody who thinks that they have worked out the secrets of the universe all on my own. I hate those people. Please take my post in the spirit intended, me attempting to develop a (not at all earth shattering) point of view based on any sources of info I can get my hands on.

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  23. Hi Nick,

    Glad to hear that you have been encouraged to take up philosophical studies. Additional kudos for directly going to the original authors.

    I can understand why Hume as a thoroughgoing empiricist appeals to you. He did to me, as well, and although I believe that some of his positions are untenable, he got many things spot on.

    Regarding Kant, I can empathize with your difficulties (especially if you started with the German original without being a native speaker). He was a university professor trying to address an academic audience, which is why many people consider his style to be rather impenetrable, dry and boring. Maybe it might be a good idea to first read a commentary on his work in order to get an overview of his philosophy before tackling the man himself.

    Regarding the philosophy of mathematics:

    First of all I have to admit that I have not read and thought about this particular field as much as, say, about epistemology. Thus, my apologies if the following may seem a bit unstructured and stream-of-consciousness-style.

    Generally, I agree with many of the points you raise. I think there is strong evidence that our ability to conceptualize and understand universal entities (which I take here to be identical to abstract entities, since a discussion of whether there is a difference and what it consists of fills volumes) like numbers has a strong empirical component. For instance, in order to understand for the first time what is meant by the number “2”, we need to be given a concrete example like a pair of shoes. Or consider the way children learn to count the numbers 1-10 by using their fingers.
    In this context, I read about studies which show evidence for little children and certain primates being apparently born with a rudimentary sense of arithmetic, i.e. they realize when things are added or removed from a collection. This would indicate a form of genetic/neuronal hard-wiring of (at least some) mathematical abilities.

    Now, the interesting thing is what happens after we have grasped the universal entity by way of a concrete example. It is obvious that once this understanding has occurred, we never need to think about particular embodiments again, but can completely think in the realm of the universal. Moreover, we seem to be able to understand and explore relationships between universals which we have never experienced in a particular embodiment (Russell gives a good example in his essay regarding a proposition whose truth we immediately recognize, despite the fact that by its nature it can never be instantiated).

    I think here is the point where a completely empirical account of our understanding of mathematics (and of universals in general) suffers tremendous problems which Hume and empiricists following after him have not satisfactorily addressed. If all our knowledge comes from experience, how is it possible for us to generate knowledge about universals, which by their very nature are not amenable to experience?

    So how to get out of this awkward situation?

    As an answer, you could deny that anything like universals are real and see them as arbitrary, meaningless categories of our mind that we dream up and imprint on the world of sense-data to make it intelligible for us, which lack, however, any correspondence to reality. The only “real” things are the particulars that we know through experience. The philosophical term for this stance is “nominalism”.
    I am not really convinced by this. When I comprehend a mathematical equation, there seems to be such a necessity and inevitability about it that I find hard to reconcile with the idea that I am merely following an arbitrary convention that might as well be different and that mathematical statements can not be “true” or “false”. Or consider that we talk about “the orbit of a planet”. However, the term “orbit” is a universal and would thus be an illusion. I find that hard to accept. While an orbit may not “exist” in the sense of a tree or car existing, I feel that we nonetheless say something meaningful about reality when we talk about an “orbit”.

    So what is the alternative?

    Currently, my thinking (a better word would be: bold speculation) goes along the following lines:

    The foundations of mathematics clearly lie in experience. We have observed the world around us and tried to codify some of its properties in symbolic, abstract language. Since we are creatures shaped by a continuous, constant interaction with our environment, our thinking patterns have evolved in a specific way that was best suited to our survival. And it is certainly beneficial to a creature’s survival if its sensory apparatus as well as its cognitive architecture provides an accurate reflection (however imperfect) of the reality it finds itself in.

    What I am trying to say with this is that a case can be made for universals somehow being part of our reality and that we have evolved a way of dealing with them, not through direct apprehension by the senses, but by an innate knowledge that was later codified and formalized through the development of logic/mathematics. On this view, mathematics “works” because it is based on foundations that evolved in response to something our ancestors learned to recognize.

    Anyway, these are my thoughts at present, Naturally, I reserve the right to alter my stance completely in the future…(-;

    If you want delve into the philosophy of mathematics a bit further, here is a good place to start:

    http://plato.stanford.edu/entries/fictionalism-mathematics/

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  24. Thanks for the advice about Kant, I think I will try that, as I have been feeling quite negative about what I was reading, but at the same time aware that I was probably not catching on to a lot of the subtlety of what he was saying.

    Now to mathematics. I will attempt to adopt your terminology in what I say (at least as far as I have understood it to mean), as I do not have the background/confidence to speak shorthand in these subject areas. Correct me if I use something wrong.

    Firstly, when it comes to ‘grasping the universal’, I would suggest that the neuronal/genetic basis of this is a generalisation or abstraction capability. There seems to be a bit of evidence coming through from the neuroscience side of things that generalisation is behind a lot of capabilities, whereby brain structures form automatic capabilities for dealing with the physical world formed by generalizing from repetition and experiment. I suspect that these capabilities were developed and extended into the social/cultural sphere as an evolutionary advantage, and now also lie behind the intellectual rationalizing/instinctual cognition also.

    I agree with you about a key point being the generation of knowledge about universals. However, I don’t necessarily see this as a big problem. In fact, I see this as perhaps a different form of the previously mentioned generalization capabilities. In this case, we are using a similar process of thinking about things in different ways until a new level of abstraction becomes clear. The fact that this abstraction could be a completely new branch or mathematics is not important, the important bit is that this new universal is at this point still just structures and symbols in our brain and does not have an external reality (apart from the neural correlates of the symbols). I think that this idea is what you have identified as nominalism.

    I find your proposed alternative to nominalism interesting, but for me there seems to be something missing there. And that is an explanation (or even a convincing story) for how we could develop an innate capability for dealing with universals outside of an experiential base. This of course does not mean that we don’t have it, it just means that I can’t think of any way for that to work.

    My alternative to your objections to nominalism go as follows.

    The true or falseness of mathematical statements is not arbitrary, rather they are part of the whole definitional framework of mathematics and an artifact of our evolved abstraction capability. I suspect where the arbitrary feeling comes from is actually a hidden comparison with reality giving the universals a feeling of being greater than just symbols in our brains.

    In terms of an orbit, there is an equation that describes an orbit, and then there is an orbit that a planet has. At some level or our perception, the equation seems to perfectly describe the orbit that see in physical reality, so that makes us think that there is something super special about that equation. And there is, but there are also a hell of a lot of equations that don’t describe the orbit.

    Further, as we take a deeper or more comprehensive look, typically we have found that our equation doesn’t describe the actual orbit, but is just an approximation, cue the refinement of Newtonian gravity with Einstein’s general relativity. Note here also, that the mathematics for general relativity are quite different than that for Newtonian including completely new concepts of geometry.

    Rereading the above, I see that I have still not addressed directly the exact crux of your objection, but this post is already too long. I will post and think further.

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  25. I will now attempt to tease out a more comprehensive explanation for the unsurprising effectiveness of mathematics to describe reality, building on my last post.

    If, as I have suggested, mathematics is a consequence of our evolved cognitive abilities for generalization and abstraction and exists purely as symbols and abstractions in our brains, then how come we can use mathematics with surprising success to describe and predict actual reality?

    I would firstly say, that as it is based on our evolved abilities, then mathematics will be naturally constrained by those abilities, but as those abilities have been formed by massive scale interactions with reality (at least localized reality) over long time scales, it is perhaps not so surprising that there is some intersection between the range (or perhaps landscape) of possible concepts we could explore with mathematics and the reality that we can observe directly or indirectly with our senses.

    Also, there seems to be some evidence that mathematics is incomplete. In particular Gödel’s incompleteness theorem (which I have yet to fully understand), but also certain areas where our mathematics (at least currently) do not seem to have much purchase, cue Quantum woo example at the low end with possible questions about low level logic like the the laws of identity and contradiction, and emergent or chaotic behavior of complex systems at the top end where we don’t seem to have achieved much descriptive or predictive power at all.

    Along with this comes the fact that our mathematics as yet seems to be giving us “approximate” descriptions of reality, not perfect descriptions. I can see the temptation here to start elevating the mathematics to a higher level of a priori specialness as providing ideal/perfect or hyper real models, but the flip side of this is that we must then downgrade reality to the role of the approximation. I see no basis for making this jump and suspect that this actually comes from our own feelings of specialness and self satisfaction at what we have managed to cook up in our heads than a cold assessment. In my opinion, reality is always going to trump us.

    Then there is the fact that we have created/found/explored whole areas of the possible mathematical landscape that do not necessarily describe or predict anything about reality.

    And conversely, we have managed to describe the same aspects of reality using completely different types of mathematics, cue Max Borns matrix approach to quantum mechanics which delivers the same descriptions/predictions as Schrödingers more conventional (at that time) partial differential equation wavefunction. Although, I think that you can also translate one to the other, so maybe these are actually functionally equivalent. Perhaps a better example is the afore mentioned refinement of our understanding of gravity by moving to some exotic mathematical ideas such as alternative geometries.

    Then we should take into consideration that a lot of mathematical concepts have actually been developed by scientists (perhaps primarily physicists), precisely for explaining empirical reality. In this case, they will be intuitively or conciously discarding (or choosing not to investigate) possible concepts because they do not seem to be relevant to what is being explored. This would then be skewing the perceived ratio of how much of our mathematics has/can be practically applied to reality description/prediction.

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  26. Nick,

    Reading your two posts, I have the impression that we share a lot of assumptions about the origin of our mathematical abilities (and ability to comprehend abstracta/universals generally) being necessarily interwoven with experience. Where we seem to differ are the questions of

    a) whether experience alone is sufficient to explain them and

    b) what the exact ontological status of said universals/abstracta is.

    Concerning question a), your answer seems to be “yes”. Concerning question b), I am not really sure about your answer. Some passages of what you wrote seem to indicate that you hold universals to be merely in our heads, while other passages seem to contradict this view.

    Here is an example. You wrote:

    “The fact that this abstraction could be a completely new branch or mathematics is not important, the important bit is that this new universal is at this point still just structures and symbols in our brain and does not have an external reality (apart from the neural correlates of the symbols).”

    So the universal is merely a concept in our minds with no independent reality. But you qualified this statement with the phrase “at this time”. Does that mean at some later point in the future we might discover that the universal in question actually exists independently of human minds? But that would mean that you have discarded nominalism in so far as you do admit the existence of universals. The only issue would be finding out which universals that exist in our heads have a counterpart in reality and which ones do not.

    Or here:

    “In terms of an orbit, there is an equation that describes an orbit, and then there is an orbit that a planet has. At some level or our perception, the equation seems to perfectly describe the orbit that see in physical reality, so that makes us think that there is something super special about that equation. And there is, but there are also a hell of a lot of equations that don’t describe the orbit. “ [emphasis mine]

    But a nominalist would dispute that there really is anything like an “orbit”. What you see are particulars, i.e. you look at the position of a planet at different times and see his position changing. Abstracting away from these different positions to arrive at an imaginary path the planet travels along is, according to the nominalist, a mental exercise with no equivalent in reality. And this is a view I find intuitively unsatisfying. Which, of course, does not mean that it is false.

    The ambiguity in your position elaborated on above is also apparent in your discussion of why “mathematics works”. If I understand you correctly, you are saying that we are born with an ability to concoct generalized concepts from particular experiences. Since said experiences are based on our interaction with reality, it is not really surprising that there is an overlap between some of our concepts and empirical reality.

    However, this view faces some serious problems that need explaining:

    1.) If you hold that all of our knowledge comes from experience, why can we understand universals and propositions containing them at all? Merely saying “We are born with this ability.” is not really explaining anything. Take Russell’s example from his essay: the proposition “All products of two integers, which never have been and never will be thought of by any human being, are over 100.” is not only understandable, but we see its truth as clearly as anything, despite the fact that there can never be a concrete instantiation of it. Thus, it qualifies as “knowledge”. However, we acquired this knowledge without any experiential input. How can this be?

    2.) You pointed out some of the problems with mathematics, i.e. that it does not give a 100% accurate description, might not be applicable in all cases, suffers as an axiomatic system from necessary incompleteness etc. Nonetheless, there are cases where a mathematical description seems to be our best and most accurate form of characterization. What does that indicate for the ontological status of the mathematical entities involved? Do they refer/relate to anything outside of our minds? If yes, it would be a repudiation of nominalism. If not, why does it seem that we can explain something? Pure luck? An illusion?

    In response to my attempt at an account of our mathematical abilities, you wrote:

    ”I find your proposed alternative to nominalism interesting, but for me there seems to be something missing there. And that is an explanation (or even a convincing story) for how we could develop an innate capability for dealing with universals outside of an experiential base. This of course does not mean that we don’t have it, it just means that I can’t think of any way for that to work.”

    This criticism is entirely warranted. And I currently have no plausible answer. But note that the same criticism applies to your model, unless you wholeheartedly embrace nominalism. Presently, it seems you want to retain universals in some form.

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  27. Interesting points.

    Firstly, I would like clarify one of my previous statements:

    My usage of “at this point/time” wasn’t meant to imply that we could discover that the universal had independent existence from human minds at some point in the future. I think that on this point I am probably a strict nominalist. What I meant was that the universal would always just be in our minds, but we could discover at some point in the future that we can use this new universal to actually describe/predict some aspect of reality (most likely in an approximate way). A possible example of this would be Riemannian geometry. As far as I know, this existed in peoples minds for a time without being used to describe empirical reality, until such time as Einstein applied this to describe and predict gravity.

    Your point about the planetary orbit however, does make me think that I am not a strict nominalist, but let me try out an argument for a modified form of nominalism. I will coin it relativistic nominalism. It goes like this:

    A planet is a macroscopic object that occupies a region in space. That is an intrinsic aspect of the objects existence. However, a key lesson from special relativity is that space and time are unified as space-time and that therefore we cannot consider space alone. The implication of this, is that the planet is not just defined by the volume of space it occupies, but also by the volume of time that it occupies. Using this refinement, the actual object in reality includes it’s orbit as an intrinsic part of the objects presence in space-time, so the mathematical equation that describes the orbit, is just describing an aspect of the real object. (Of course, point like elementary particles don’t fit this model as they occupy no volume of space, but then again at this level we have entered the realm of quantum mechanics so all bets are off anyway 😉

    Perhaps this adjustment to nominalism is more intuitively satisfying to you, but I suspect it might not be to an actual nominalist as I suspect that they would then just challenge the actual reality of space-time. There seems to be adequate precedent for this too. Correct me if I am wrong, but I seem to remember Kant considering space and time separately as something other than aspects of reality. For me though, in an attempt to base my arguments on a solid as possible base, and as a strong empiricist, I have no choice really but to integrate the current scientific understanding of reality as much as possible on the philosophical side, and as far as I can tell, it is a pretty orthodox modern approach to consider space-time as an actual aspect of reality.

    Next, in relation to your numbered points.

    I think your comment at 1) is predicated on your assessment that I am not a true nominalist. I think/hope that my two points above have perhaps shifted me enough back into the nominalist (albeit the neighboring relativistic nominalist) camp to sidestep your point here, as then my definition of universal is again as something entirely in the mind, in which case it is plausible that our knowledge of universals can be gained from experience.

    As far as the ontological status of mathematics is concerned, I think I have argued myself into clearly stating that mathematical entities exist entirely in our minds and have no basis in reality outside of our minds. I don’t however think that the fact that we can describe/explain/predict aspects of reality using these mathematical concepts in our minds is an illusion or pure luck. Instead, I am proposing that there are match ups between some of the mathematical concepts and actual reality due to probability. In other words, due to the wide range of concepts that we are capable of exploring with mathematics and the fact that the whole edifice rests upon our experience of reality, that it is highly probable (or even inevitable) that there is some overlap with reality. Don’t ask me to try and prove this though, this sounds a bit too much like string theorists trying to test string theory with the anthropic landscape concept.

    I will concede however, that my argument that all mathematical reasoning can be ultimately based purely on an experiential grounding is not really as clearcut as I am trying to make out. This feels right to me, but I don’t think I could describe how this would work in a convincing fashion.

    So I agree here with your conclusion that my argument suffers from the same or similar criticism that I made of yours. Given this, I am grateful that I will almost certainly never have to decide between them. I am quite accepting of the fact that there are things that I don’t know and also things that I will never know, but it is fun chewing over the various arguments, and who knows, perhaps I will think differently tomorrow, I certainly did several days ago.

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