Mathematics - including geometry, which was the dominant type of maths in the ancient world; and for that matter the philosophical discipline of Logic; are a type of *abstract model*, and as such utterly de-contextualized and without-referents.

For mathematics to have real-world relevance entails that it is legitimate to attach particular classes or categories of objects to the mathematical symbols. Clearly, the qualitative reality of these classes/ categories must be assumed.

Furthermore, it must be assumed that mathematical procedures (as modelled by the maths functions etc) are valid and necessary real-world processes applicable to the the assumed classes/ categories.

Thus, mathematics as-such has zero intrinsic real-world relevance...

Unless, like Pythagoreans and Platonists (ancient, medieval and modern) one additionally makes the fundamental metaphysical assumption that the real-world relevance of mathematics is necessarily true; because *reality is ultimately mathematical*.

On this basis, the job of science, or any other empirical investigation, is to discover the real-world entities to which refer (perhaps approximately) the ultimate mathematical realities (e.g. Platonic "ideas").

In other words; for some Platonists (and those in this tradition), mathematics *just-is valid*; and the real-world is (merely) a temporary and perhaps partial approximation of these realities.

In sum: one *can *assume that maths/ geometry/ logic is the ultimate reality; and explain everything else on that basis - and, because the assumption is metaphysical, it cannot be refuted by any observations.

But - if one does assume this, then one *cannot be a Christian*.

At least not in the was that Jesus (especially in the Fourth Gospel) spoke and taught.

If maths/ geometry/ logic is the ultimate truth; then God cannot be a person, cannot be our Father, and does not love us.

## 25 comments:

Conveniently, empirical physics backed by relatively straightforward mathematics seems to have demonstrated that physics and mathematics are not the ultimate truth -- they can never predict the outcome of quantum measurements, even in principle!

Bell's Theorem experiments seem to show that if math and physics somehow could predict quantum measurements, we would get diffwrent experimental results. Of course this bothers physicists to no end. Whatever *is* driving these measurements must transcend math and physics.

@RB - Well, as I mentioned, empirical investigations cannot (ether in theory, or usually in practice) disprove metaphysical assumptions; because the metaphysical assumptions frame what counts as evidence and how to interpret it.

Leaving aside advanced physics, which I know only second-hand...

This is why (as I've often written) no amount of "evidence" can ever disprove Neo-Darwinian natural selection when posited as the explanation for - say - the origins of life, or species. The assumptions are that natural selection IS the explanation for these, and everything after that is the linear process of science (which always contains contradictions and incompleteness).

The reason to abandon natural selection as an ultimate explanation is quite simply that there is no compelling reason (and never has been, and never could be) to assume and decide that it IS and MUST BE the ultimate explanation.

wrt Quantum theories; they seem Very Obviously to be tools for "saving the appearances" and not an explanation of reality - indeed, anything that includes randomness (and statistics) as an assumption isn't actually explaining.

MITTENS doesn’t attempt to explain the origins of life or deny selection occurs. It uses math to prove that TENS can not explain the species we observe as there is not enough time for the changes to occur.

@North - Maths doesn't *prove* anything in biology.

As I said above - "For mathematics to have real-world relevance entails that it is legitimate to attach particular classes or categories of objects to the mathematical symbols. Clearly, the qualitative reality of these classes/ categories must be assumed. Furthermore, it must be assumed that mathematical procedures (as modelled by the maths functions etc) are valid and necessary real-world processes applicable to the the assumed classes/ categories. Thus, mathematics as-such has zero intrinsic real-world relevance..."

And also: "the linear process of science (which always contains contradictions and incompleteness)."

That doesn't invalidate the idea, but it does mean that this is not a matter of proving anything in particular once for all. I was active in evolutionary theory for some 25 years, and genetic mathematical fixation etc. assumptions and arguments never crossed my path - it was a very peripheral (and somewhat) dubious corner of the subject.

But science is dead, as I have written repeatedly. All that remains (in any given field) is At Best communications between a few individuals who have the honesty, competence, and motivation to seek the truth.

Here I cannot agree. The Platonic view is that the divine manifests in the material. Mathematics is one way of understanding the underlying informational order. This does not mean that all human theoretical mathematics are correct; if anything, they are a series of approximations that we hope slowly converge on the most accurate model possible over time.

But when I build an antenna it works.

@North - If you don't want to discuss metaphysics, that's your decision; but that doesn't even begin to be an argument!

@Brett - Fair point, strictly considered; but (e.g.) Platonist mathematicians (such as Roger Penrose, among justly-eminent contemporaries, but many others over the centuries) do talk and act *as if* mathematics was - if not perfect - as close to the world of forms as humans can imagine within time.

I'm confused by your attitude toward basic assumptions.

On the one hand, your view is that these assumptions can never be rationally verified or falsified by evidence or reasons (since they determine what counts as evidence or a reason). On the other hand, you seem to be saying here that there's a reason for rejecting a basic assumption:

"The reason to abandon natural selection as an ultimate explanation is quite simply that there is no compelling reason (and never has been, and never could be) to assume and decide that it IS and MUST BE the ultimate explanation."

If the assumption that natural selection is an ultimate explanation is a basic metaphysical assumption, doesn't that mean that there can't be any reason for accepting or rejecting it? Or, if the lack of any compelling reason for the assumption is a reason for rejecting it, wouldn't that be true for all basic assumptions including Christian or theistic ones?

Maybe I don't understand what you meant in the quoted sentence.

@ Jasper - There is a lot written on this blog relevant to your question - e.g. https://charltonteaching.blogspot.com/search?q=METAPHYSICS+INTUITION

But I shall try and say something here.

When you ask your questions, they seem to come from an assumption that assumptions *can* be verified or falsified by evidence or reasons. You then need to ask how this actually works, in a very specific instance, and why this is valid - and keep asking until you get a clear and valid answer...

(An answer that presumably isn't just "because I read in the mass media that this was what "scientists" have proved" or something like "because somebody {a teacher, maybe; or a bloke in the pub?] once told me this - at least I think so; but I can't exactly recall who or when"- which is how most modern people apparently decide the fundamentals of reality!)

You will soon discover that there is no remotely compelling theory as to why and how evidence could or does prove or disprove fundamental assumptions.

Or, when you discuss whether there is *no reason* for accepting or rejecting assumptions, you are (I am pretty sure) asking for an answer that applies to all people, and is compelling for everybody. Maybe you want a "truth machine", that does without individual human judgment - some kind of impersonal mechanism that tells you what counts as evidence, into which evidence is fed, and coughs-up "the right answer" as to what is true.

And then, how could we tell whether such a truth-machine was indeed always and necessarily telling the truth, after we have decided that it Must tell the truth?

But why do you assume that there is an argument acceptable to everybody that tells everybody what fundamental assumptions they must adopt? If there was such an argument, then That would be the fundamental assumption. And then we could ask why That is necessarily valid.

If I said (which I believe) that the fundamental assumptions must be coherent; then I have just introduced another assumption - and then I need to discuss how coherence is identified - whether it is a matter for each individual person to decide, or maybe something that is decided by the vote of a panel of accredited experts. (But then who accredits the experts, and on what basis? And who says that voting leads to the right answer?)

At bottom, we can only operate on the basis of "sets" of fundamental assumptions. Some of these sets mutually support each other, while others contradict each other.

And ultimately these fundamental assumptions are not stated in words or symbols, but in that underlying judgment and insight which words and symbols "represent" or "model".

Which ever way this is tackled, in the end we reach what could be called "intuition" - which is the single individual's awareness; and choice, for his own reasons.

@Jasper - continued:

Even if the bottom line choice is the mainstream metaphysical assumption that "I will believe whatever the majority of powerful people are currently telling me" - this handing-over of responsibility is rooted in the individual's choice to adopt this rule.

The big problem is that most (nearly-all) people live by basic assumptions (such as the above) which they then deny; and instead assert that their assumptions are based on "evidence", or even that they do not have any basic assumptions but just live by common sense or something. They wont even acknowledge that there is anything to discuss; and reject all such discussion as irrelevant, airy-fairy nonsense!

But once somebody has begun to ask the questions that you ask, and has started to become aware and honest about assumptions; I think all answers converge on an existential awareness of our-individual-selves in "the world" and our intuitive choices as to how we desire to live in this world -- what we personally believe and choose to be the way that this reality is structured, and proceeds.

Ultimately we cannot argue that somebody else ought to believe as we do - because other people want different things from life; but we Can ask them to become aware of their assumptions, and the implications of the assumptions; and aware that they have In Fact *already* made fundamental decisions about the nature of reality, the purpose of their own life, and what they want for the future.

But becoming aware of these already-made decisions, and that we have indeed made them yet could have chosen otherwise, may lead to recognizing that we (fundamentally) do Not want our assumptions, and *do-not want* the life we have already-chosen.

Then, we may even find something that we Do want.

As happens more than occasionally, Bruce, you have written a comment better than your original post. I suggest you promote it to be a full post!

But could you please add a paragraph to flesh out your assumptions about where the best intuition comes from? Direct knowing? The Holy Spirit?

@ Jonathan - Thanks.

Beyond a certain point it is important that we each think and discover for ourselves; and being "told" (what is actually a personally-derived, personally-applicable, intuition) can be counter-productive to the necessary attitude.

>Well, as I mentioned, empirical investigations cannot (ether in theory, or usually in practice) disprove metaphysical assumptions; because the metaphysical assumptions frame what counts as evidence and how to interpret it.

Right, but this is exactly the point here: if we start with (honest) empiricism and mathematics as metaphysical assumptions, and *apply them consistently*, we end up discovering hard limits to their explanatory power.

The "scientists" who do not accept these limits can only do so by rejecting internal consistency, honest empiricism, or accepted mathematics. (and of course they do)

For our purposes, true "randomness" means "incapable of being modeled by a finite algorithm", meaning we cannot scientifically explain it, even in principle! Scientists need to be more honest about this too, of course.

One should be able to encounter situations where grinding forward with a set of metaphysical assumptions allows you to disprove them. For example, if we start with "empiricism and math can explain everything" and "non-contradiction" as metaphysical assumptions, everything can seem okay ... until math and empiricism themselves tell us that there are specific things they will never be able to explain (this has, in fact, happened).

Now we are stuck -- we *know* our metaphysical assumption set is broken. We may not know *how* it is broken -- which assumptions need to be altered, added, or removed -- but we know it *is* broken.

Hi Dr. Charlton,

If you don't mind I'll try my question again. I think we're talking past each other. You ask me, "why do you assume that there is an argument acceptable to everybody that tells everybody what fundamental assumptions they must adopt?" But I don't assume this. I'm convinced by the kind of argument about the nature of assumptions that you make in your comments above, and I agree with your views about fundamental assumptions.

But given your view that fundamental assumptions can't be verified by arguments (or evidence or reasons) I was puzzled by the sentence I quoted:

"The reason to abandon natural selection as an ultimate explanation is quite simply that there is no compelling reason (and never has been, and never could be) to assume and decide that it IS and MUST BE the ultimate explanation."

In this sentence, it sounds like you're saying that we have a reason to abandon a certain fundamental assumption: the assumption that natural selection is an ultimate explanation. You seem to be saying that the lack of any compelling reason for that assumption is "the reason" for abandoning that assumption.

But that claim would then contradict your view (which I accept) that fundamental assumptions can't be verified or falsified by arguments (or evidence or "reasons"). If we have a reason to give up this particular assumption about natural selection, then either the assumption in question is not a truly fundamental one or there can be reasons for and against a certain fundamental assumption.

Do you see what I mean? Again, the problem might be that I misunderstood what you were saying in the quoted sentence.

@Robert - Yes indeed. This line of argument was very rigorously made (wrt physics especially) nearly 70 years ago by Owen Barfield in Saving the Appearances. I first encountered something similar in Zen and the Art of Motorcycle Maintenance - fifty years ago.

Then there was Godel, for an earlier, and higher status, version of this (wrt mathematics) - but which I discovered only about 30 years ago.

Yet, when I began to do my own research (for the doctorate) I had a similar crisis wrt how many replicate measurements I ought to be doing in lab measurements, how many was "enough" - and why - and how should I deal with their variations (and why)?

So the stark contradictions of mathematics (or science) when regarded as fundamental metaphysics, is pretty undeniable - and can be reached by anyone capable of honest enquiry.

And yet... Somehow this makes no substantive difference at a cultural level - except to lead to the dishonest pseudo-nihilism of "post-modernism".

For myself, I needed to be able clearly to distinguish the level of metaphysics, of primary assumptions - from lower level activities such as maths, science, or indeed history. This only happened - eventually - in 2008 - as part of me becoming a Christian.

@Jasper - I am just pointing out that the argument was never even made. e.g. The basic idea that Natural Selection was the explanation for the Origin of Species was that because animal breeders could produce striking quantitative change in traits, then "nature" could do the same as breeders - and Then it was simply assumed (and has never yet been demonstrated!) that many and extreme such quantitative changes would be able to lead to the extreme and great qualitative diversity of living things.

And then the conviction gradually crept in that this Must Be the only such cause of qualitative diversity.

Such an assumption has nothing to do with science, and seems instead (judging by the rhetoric and strategies of its advocates) that Natural Selection, then later genetics, then later still the Modern Synthesis of natural selection and genetics - was in fact driven by the covert desire to eliminate purpose (teleology) from biology.

Probably because purpose sooner or later implies deity.

I go into this in more detail here.

https://www.authorea.com/doi/full/10.15200/winn.145830.07350

The other problem with the model of natural selection is that although it proposes a mechanism by which some variations become common while others become rare / extinct, it does not tell us *which* variations will be created to enter the selection pool in the first place. The variations supposedly come from "random" mutations, apparently caused by DNA copying errors and ionizing radiation -- which gets us back to the fundamentally inscrutible QM processes I mentioned earlier.

This means there's a huge hole by which an outside deity in control of the "random" elements could control the direction of evolution. Almost nobody talks about this.

@RBII - Plus "randomness" is not a reality - it is an assumption of mathematical models - originally just a tool for calculating probabilities in gambling!

https://charltonteaching.blogspot.com/2015/11/probability-doesnt-really-exist.html

Reality self-selects from the possible future states, this is why quantum effects are probable. It does not disprove math in any way

Math is an instrument, more fundamental than physics, but not the ultimate reality. Math is static, it cannot be solely responsible for our dynamic world

Interesting

@Ap - Three short comments in five minutes? Maybe your lithium levels are a bit low? ;-p

Right, the word "randomness" is shoved in when scientists mean "we can't figure out the pattern." Maybe for large N there is some clustering, but as for The Next Coin Flip, science's answer is "we've got nothing."

As my best friend says when something "improbable" happens: "What was the 'probability' of that happening? Well, it happened, so the probability was clearly ONE HUNDRED PERCENT."

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