I do want to say more regarding your response.

I'd have to say, "Of course mathematics is in the world.", in the sense you communicated so well. Do you have any thoughts, on whether that sense of mathematics being in the world is a perspective that is commonly held by those who ask, "Is maths embedded in the universe ?"

Most often I've encountered the question from people motivated to use the fact that there is math in the world, as evidence for the necessity of a God.

I'd have to say, "Of course mathematics is in the world — wonderer1

Mathematics is the world to the same extent that French or German is in the world, as a peculiar grammar by which we organize it for our purposes.

•Science is rigor, or the body of knowledge rigorously obtained.

•Logic is relationships which always replicate; a subset of science.

•Math is relationships of quantity; a subset of logic.

•Quantity is recursive boundary conditions - the extent to which you can divide something into equivalent parts.

•Logic is relationships which always replicate; a subset of science — Kaiser Basileus

Do relationships which always replicate exist in nature?

Mathematics is the world to the same extent that French or German is in the world, as a peculiar grammar by which we organize it for our purposes. — Joshs

Yes, I would agree with that.

No, there are no a priori things. Or did you mean the replication occurs in the context of nature? Rephrase?

An interesting article. Animal calls can be concrete signs, but that is not the same as the abstract signification of a symbol. Mathematics, an abstract elaboration of the basic concrete activity of counting is not possible without symbolic language; that was the point I made. Are you disagreeing with that, and taking this article to be evidence against it?

By that he meant the evidence we receive from the world is a response to the way we formulate our inquiries toward it. It can respond very precisely to different formulations, but always in different ways, with different facts. — Joshs

The way we formulate our enquiries towards the world is in response to the way the world appears to us. We have no control over how the world appears to us.

Redundant

The way we formulate our enquiries towards the world is in response to the way the world appears to us. We have no control over how the world appears to us. — Janus

What would you consider conscious control? Remember those magic eye puzzles with the embedded 3-d object? Or what about optical illusions where you can switch between tow images within the same picture? Isn’t that analogous to how well science can reconfigure the way that world appears to us though a gestalt shift?

Mathematics is the world to the same extent that French or German is in the world, as a peculiar grammar by which we organize it for our purposes.
— Joshs — wonderer1

So do you think ordinary languages, like French and German, would have facilitated equal progress in physics and cosmology since the 17th C, in the absence of mathematics?

I will add that the expression that mathematics is 'in the world' is meaningless, just as it would be to say that a carton of eggs contains the number 12. Mathematics gives us a common symbolic means to describe, quantify and understand the world in a way that is not just based on individual perception but is grounded in a shared understanding and inherited knowledge.

Isn’t that analogous to how well science can reconfigure the way that world appears to us though a gestalt shift? — Joshs

No, I don't think so. Science observes, and then attempts to explain what is observed. I see fire, for example, and I explain it in terms of phlogiston, then later I explain it in terms of oxidative combustion. I continue to see the fire the same way; its appearance does not change regardless of the theory about its cause.

So do you think ordinary languages, like French and German, would have facilitated equal progress in physics and cosmology since the 17th C, in the absence of mathematics? — Wayfarer

No. However, I don't see what that has to do with the sense in which mathematics can be said to be in the world.

Science observes, and then attempts to explain what is observed. I see fire, for example, and I explain it in terms of phlogiston, then later I explain it in terms of agitated molecules. I continue to see the fire the same way; its appearance does not change regardless of the theory about its cause. — Janus

Do you think you would see a group of lines the same way if you recognized them as just a pile of sticks compared with seeing them as forming a familiar Chinese character? Would your eye follow the shapes in the pile the same way? If you had never seen a computer before would you recognize the tower, mouse and screen as belonging to a single object? If you didnt know what a bus was for would you interact with it in the same way?

Seeing the same things and conceiving of them in different ways are two different things altogether. I haven't denied that we might come, and historically speaking have come, to conceive of things in novel ways.

↪Joshs Seeing the same things and conceiving of them in different ways are two different things altogether. I haven't denied that we might come, and historically speaking have come, to conceive of things in novel ways — Janus

I think I sent this to you before, from Francisco Varela, but I’ve always found it provoking.

One of the most seductive forms of subjectivism in contemporary thought is the use made of the concepts of interpretation, whether by pragmatists or hermeneuticists. To its credit, interpretationism provides a penetrating critique of objectivism that is worth pursuing in some detail. To be objective, the interpretationist points out, one would have to have some set of mind-independent objects to be designated by language or known by science. But can we find any such objects? Let us look at an extended example from the philosopher Nelson Goodman.

A point in space seems to be perfectly objective. But how are we to define the points of our everyday world? Points can be taken either as primitive elements, as intersecting lines, as certain triples of intersecting planes, or as certain classes of nesting volumes. These definitions are equally adequate, and yet they are incompatible: what a point is will vary with each form of description. For example, only in the first "version," to use Goodman's term, will a point be a primitive element. The objectivist, however, demands, "What are points really?" Goodman's response to this demand is worth quoting at length:

If the composition of points out of lines or of lines out of points is conventional rather than factual, points and lines themselves are no less so. ... If we say that our sample space is a combination of points, or of lines, or of regions, or a combination of combinations of points, or lines, or regions, or a combination of all these together, or is a single lump, then since none is identical with any of the rest, we are giving one among countless alternative conflicting descriptions of what the space is. And so we may regard the disagreements as not about the facts but as due to differences in the conventions-adopted in organizing or describing the space. What, then, is the neutral fact or thing described in these different terms? Neither the space (a) as an undivided whole nor (b) as a combination of everything involved in the several accounts; for (a) and (b) are but two among the various ways of organizing it. But what is it that is so organized? When we strip off as layers of convention all differences among ways of describing it, what is left? The onion is peeled down to its empty core.

Thanks that's an interesting passage, and I find nothing to disagree with in it. I was thinking more of actual objects than of points and lines or spaces constructed form them. When I throw the ball for my dog, I know he sees it. I don't know whether it appears exactly the same to him, and given the differences between dog and human physiology, there are probably differences.

No. However, I don't see what that has to do with the sense in which mathematics can be said to be in the world. — wonderer1

I agree. It seems obvious to me that number is in the world, as least in the world as it appears to humans. It is hard to imagine any world without more than one thing in it, and our world obviously is replete with a vast multitude of things.

Math is a language and like all languages is as useful as it's ability to describe reality.

Most often I've encountered the question from people motivated to use the fact that there is math in the world, as evidence for the necessity of a God.

Not in my experience, but it might be selection bias. Certainly it is sometimes used to challenge the plausibility of "the universe is necessarily meaningless and valueless and anyone ascribing any sort of teleology to nature is necessarily deluding themselves." But this doesn't entail arguments in favor of any sort of explicit theism.

The best example of this view I can think of is Nagel's "Mind and Cosmos," which looks at significant problems in the "life is the result of many random coincidences and looking at them as anything other than random is simply to give in to fantasy," view. But Nagel is an avowed atheist. Likewise, Glattfelter's "Information, Conciousness, Reality," Winger's "Unreasonable Effectiveness," etc. don't seem particularly theistic to me.

They just seem to challenge some of the dogmas of a particular type of atheism popularized in the 20th century, which has made some pretty stark metaphysical claims about meaning, value, and cause. These claims are, IMO, more grounded in existentialism than many people acknowledge, and I think equating challenging them with "theism" has become a bit of a strawman in atheist infighting.

IMO, there is nothing particularly theistic at expressing awe at the regularities in the world. We appear to have a universe with a begining. So at one point, there was a state at which things had begun to exist before which nothing seems to have existed. This forces us to ask the question "if things can start existing at one moment, for no reason at all, why did only certain types of things start to exist and why don't we see things starting to exist all the time? Or if things began to exist for a reason, what was the reason?"

I don't see how this is essentially a theistic question though. It seems like a natural outgrowth of human curiosity, God(s) or no.

I think there is a parallel to this phenomena in history actually. Prior to the advent of the Big Bang Theory, popular opinion was that the universe must be eternal. Evidence for an origin point was itself considered to reek of a sort of corrosive theistic influence. But of course, that evidence piled up, and today I don't think most people think acceptance of the Big Bang Theory in anyway precludes atheism. I think it's possible you could see a similar thing with teleology, although I can't say for sure. Teleology doesn't seem to contradict atheism, just a particular brand of it.

IMO, there is nothing particularly theistic at expressing awe at the regularities in the world. We appear to have a universe with a begining. So at one point, there was a state at which things had begun to exist before which nothing seems to have existed. This forces us to ask the question "if things can start existing at one moment, for no reason at all, why did only certain types of things start to exist and why don't we see things starting to exist all the time? Or if things began to exist for a reason, what was the reason?"

I don't see how this is essentially a theistic question though. It seems like a natural outgrowth of human curiosity, God(s) or no. — Count Timothy von Icarus

One can trace a Platonism beginning in Greece, making its way through religious Christian thought and finally arriving at a humanism which retains the idea of the uncaused cause and the pure immanent identity of what presents itself to itself, but transfers these from God to mathematical idealities such as identity, pure quantitative magnitude and
extension.

One can trace a Platonism beginning in Greece, making its way through religious Christian thought and finally arriving at a humanism which retains the idea of the uncaused cause and the pure immanent identity of what presents itself to itself, but transfers these from God to mathematical idealities such as identity, pure quantitative magnitude and
extension. — Joshs

Mama say what? :yawn:

Not in my experience, but it might be selection bias. — Count Timothy von Icarus

Definitely selection bias on my part.

The best example of this view I can think of is Nagel's "Mind and Cosmos," which looks at significant problems in the "life is the result of many random coincidences and looking at them as anything other than random is simply to give in to fantasy," view. But Nagel is an avowed atheist. Likewise, Glattfelter's "Information, Conciousness, Reality," Winger's "Unreasonable Effectiveness," etc. don't seem particularly theistic to me. — Count Timothy von Icarus

As modern philosophers go, Nagel is a bit too far to the scientifically naive side, for my taste. Wigner's argument is what I've encountered the most, but it seems like puddle thinking to me. I'll have to look for Glattfelter.

IMO, there is nothing particularly theistic at expressing awe at the regularities in the world. We appear to have a universe with a begining. So at one point, there was a state at which things had begun to exist before which nothing seems to have existed. This forces us to ask the question "if things can start existing at one moment, for no reason at all, why did only certain types of things start to exist and why don't we see things starting to exist all the time? Or if things began to exist for a reason, what was the reason?"

I don't see how this is essentially a theistic question though. It seems like a natural outgrowth of human curiosity, God(s) or no. — Count Timothy von Icarus

:up:

Mama say what? :yawn: — jgill

Don’t tell Sokal

:up:

And of course the regularities of our world, the seeming logos for lack of a better term, certainly can be used to make an argument about the divine, either regarding its existence or its nature. That's the project of natural theology after all. However, I do not think the recognition mathematics, etc. as, in a way, existing in the fundamental fabric of being, at least as much as we can say anything exists, or even the recognition of some telos at work in nature, necessarily entails any particular theistic or religious attitude.

Like you say, any apparent all encompassing logos can perhaps be paired down into fairly sterile mathematicological idealizations. I don't think you get religion qua religion without the mystical/experiential elements, and that the fear of religion "creeping in the door," of the sciences is greatly overblown, at times a cover for religion-like dogmas.

For one example of an excellent effort on this front, there is Saint Bonaventure's The Mind's Journey Into God.

However, by a more excellent and more immediate method, judgement leads us to look upon eternal truth with greater certainty. For, whilst judgement and analysis arises through a reasoned abstraction from place, time and transformation and, thereby, through immutable, unlimited and endless reason, of dimension, succession and transmutation, there however remains nothing which is entirely immutable, unlimited and endless - apart from that which is eternal; and everything which is eternal is God, or in God. And, therefore, however more certainly we analyse all things, we analyse them according to this reason, which is clearly the reason of all things, the infallible rule and the light of truth in which all things are illumined infallibly, indelibly, indubitably, unbreakably, indistinguishably, unchangably, unconfinably, interminably, indivisibly and intellectually. And so, as we consider those laws, with which we judge with certainty those things which we perceive, while they are infallible and indubitable to the intellect of the one apprehending, indelible to the memory of the one recalling and unbreakable and indistinguishable to the intellect of the one judging, so, because, as Augustine says, no-one judges from them, but through them, it is required that they be unchangable and incorruptible because necessary, unconfinable because unlimited, endless because eternal, and, for this reason, indivisible because intellectual and incorporeal - not made, but uncreated, eternally existing in that art of eternity, from which, through which and consequent to which all elegant things are given form. For this reason, they cannot with certainty be gauged save through that which not only produced all other forms, but which also preserves and distinguishes all things, as in all things the essence holding the form and the rule directing it; and, through this, our mind judges/analyses all things which enter into it through the senses.

What exactly is wrong with the puddle's thought in Adam's analogy? The idea that the hole was made for the puddle is the most obvious target. But the puddle is still in the hole because of what the puddle is and what the hole is, and those seem like phenomena a sentient puddle might well strive to understand.

I don't know how well the analogy generalizes to things like the Fine Tuning Problem though because there the comparison cases seem to be as wide as "all conceivable, describable objects, and maybe inconceivable ones too." And I don't think the pivot to multiverses solves this problem in the least. You just move from, "why this precise universe," to "why this precise universe production mechanism." Because if all possible universes are created, a host of follow on problems show up. I think FTP actually gets at a broader set of problems with naturalism when it is stretched into the realm of infinite abstractions, problems which are currently very poorly defined, rather than being a simple fallacy.

To my mind, this is more akin to the puddle trying to get its bearings by asking, "what is a hole and why is it here? And do puddles make holes (which, to stretch the analogy to the breaking point, puddles do indeed make potholes for themselves to collect in when they freeze, in a sort of self-reinforcing mechanism)?"

And so, as we consider those laws, with which we judge with certainty those things which we perceive, while they are infallible and indubitable to the intellect of the one apprehending, indelible to the memory of the one recalling and unbreakable and indistinguishable to the intellect of the one judging, so, because, as Augustine says, no-one judges from them, but through them, it is required that they be unchangable and incorruptible because necessary, unconfinable because unlimited, endless because eternal, and, for this reason, indivisible because intellectual and incorporeal - not made, but uncreated, eternally existing in that art of eternity, from which, through which and consequent to which all elegant things are given form ~ Bonaventura. — Count Timothy von Icarus

Augustine on Intelligible Objects (clearly showing his Platonist influences):

1. Intelligible objects must be independent of particular minds because they are common to all who think. In coming to grasp them, an individual mind does not alter them in any way; it cannot convert them into its exclusive possessions or transform them into parts of itself. Moreover, the mind discovers them rather than forming or constructing them, and its grasp of them can be more or less adequate. Augustine concludes from these observations that intelligible objects cannot be part of reason's own nature or be produced by reason out of itself. They must exist independently of individual human minds.

2. Intelligible objects must be incorporeal because they are eternal and immutable. By contrast, all corporeal objects, which we perceive by means of the bodily senses, are contingent and mutable. Moreover, certain intelligible objects - for example, the indivisible mathematical unit - clearly cannot be found in the corporeal world (since all bodies are extended, and hence divisible.) These intelligible objects cannot therefore be perceived by means of the senses; the must be incorporeal and perceptible by reason alone.

3. Intelligible objects must be higher than reason because they judge reason. Augustine means by this that these intelligible objects constitute a normative standard against which our minds are measured. We refer to mathematical objects and truths to judge whether or not, and to what extent, our minds understand mathematics. We consult the rules of wisdom to judge whether or not, and to what extent, a person is wise. In light of these standards, we can judge whether our minds are as they should be. It makes no sense, however, to ask whether these normative intelligible objects are as they should be; they simply are and are normative for other things. In virtue of their normative relation to reason, Augustine argues that these intelligible objects must be higher than it, as a judge is higher than what it judges. Moreover, he believes that apart from the special sort of relation they bear to reason, the intrinsic nature of these objects shows them to be higher than it. These sorts of intelligible objects are eternal and immutable; by contrast, the human mind is clearly mutable. Augustine holds that since it is evident to all who consider it that the immutable is clearly superior to the mutable (it is among the rules of wisdom he identifies), it follows that these objects are higher than reason.

Cambridge Companion to Augustine.

to stretch the analogy to the breaking point, puddles do indeed make potholes for themselves to collect in when they freeze, in a sort of self-reinforcing mechanism" — Count Timothy von Icarus

Snap

But nicely said. Perhaps puddles are aliens in disguise. Clever little buggers.

deleted by author

What exactly is wrong with the puddle's thought in Adam's analogy? The idea that the hole was made for the puddle is the most obvious target. But the puddle is still in the hole because of what the puddle is and what the hole is, and those seem like phenomena a sentient puddle might well strive to understand. — Count Timothy von Icarus

Going back to Wigner's argument, and considering how reasonable or unreasonable the effectiveness of mathematics is...

Our being here (from a naturalistic evolutionary perspective) is only possible because there are regularities in the universe. The theory of evolution only makes sense in a world with regularities. So the anthropic principle applies. If our thinking is the result of biological evolution, then it is not unreasonable to find that we are in a world with regularities. With that in mind, it is not so remarkable that we have found a way (mathematics) for utilizing our symbolic cognitive capacities, to discuss such regularities with some degree of accuracy.

So why think it is anymore remarkable that mathematics is in the world, than that a puddle has the shape of the hole it is in? What is wrong with the puddle's argument is that it doesn't consider the possibility of having the causality backwards.

And do puddles make holes (which, to stretch the analogy to the breaking point, puddles do indeed make potholes for themselves to collect in when they freeze, in a sort of self-reinforcing mechanism)?" — Count Timothy von Icarus

Well, we still might want to take a closer look at the causality. Do puddles cause heat to be removed from themselves in order to freeze, or is the hole the cause of the movement of heat?

It seems to me like this is partially right, and partially missing something. Sans some interpretation of consciousness where mind does not emerge from or interact closely with nature, it would seem to me that our descriptive languages have a close causal relationship with nature. — Count Timothy von Icarus

To this point, I would argue that thinking of math as a "closed," system can be misleading in this context. — Count Timothy von Icarus

I don't think it's causal connection. Zero does not exist in nature. (Contrast that with "there are two apples on the table", which you could actually count) Certainly, saying that a 'nothing' exists in nature is a human invention. And the system of math did not include zero for thousands of years. Zero is a modern invention.

I don't know how to define "closed" in this context, but I agree. With over 26,000 Wikipedia pages, and counting, mathematics continues to expand its realms, especially into abstractions and generalizations. I suppose "closed" could mean based on axiomatic set theory, which it normally is, although frequently some distance from Cantor's creations. — jgill

Yes, our math is axiomatic. The initial axioms drive the succeeding mathematical formula.

At Home in the Universe
— Patterner

I've been reading a lot of science lately - switching from my usual fiction. I'll add this to my list. It was written in 1996, do you think it's out of date? Do you know any good, more recent books. — T Clark

I just learned about his new book. Haven't looked at it yet.
https://www.amazon.com/World-Beyond-Physics-Emergence-Evolution/dp/0190871334/ref=mp_s_a_1_2?dib=eyJ2IjoiMSJ9.85qJ-oJohxHqrtzQatdovH7-dUrh6pZfdaShFwzJL6StLg9LlVDShzZjYaBGq2UlzvY3W1Jfo48PeDf-v8J_mKZqjwwbDWBD-XwFeDf0YRYrAY3HnM4NimmMvWVMqArNN6vktkI1IER1IcSHpgx_ML5gzRem52uJukbXLbObn0sLoDoIW2H92N7pPYYxbb7a1PZSBd-tyHJDmWRCnUy0Nw.vRTBcrPAUfePwOIC_XkMsJF7AFsT_G81TdGX-P53OF8&dib_tag=se&keywords=Stuart+A.+Kauffman&qid=1708716213&s=audible&sr=1-2-catcorr