Work on philosophy -- like work in architecture in many respects -- is really more work on oneself. On one's own interpretation. On how one sees things. (And what one expects of them.) (Culture and Value)

OK, I'm on board with that. :up: :smile:

Philosophy is concerned with what was said or printed or argued in the past — jgill

Not in my view, obviously, but I won't try and persuade you — Wayfarer

Isn't that what you are talking about? The issue of the "reality" of mathematical objects. Over two millennia have passed with no consensus. When we speak of Platonism isn't that something from ancient times?

However, quantum theory may ultimately bring some clarity as physicists explore the mysteries between mathematical entities and physical reality. Where in a process does actualization occur? Virtual particles appear to be Platonic rather than physically real - they cannot be observed and yet they are convenient in certain procedures. In QT is where I might expect to see progress in understanding the nature of mathematics, here is where the subject may morph into a kind of neophysical existence. Who knows?

How large a coin would it take for you to squat down and pluck it from the ground?

A nickle for me, a penny for my wife.

Thanks. My question was about the sense in which a domain, such as the domain of natural numbers, is real, but not phenomenally existent. I notice that nowadays it is commonplace to say of anything considered real that it must be 'out there somewhere' - but even though such a domain is not anywhere, it is nevertheless real. See this passage. — Wayfarer

From your link:

Cunningham had unwittingly re-ignited a very ancient and unresolved debate in the philosophy of science. What, exactly, is math? Is it invented, or discovered? And are the things that mathematicians work with—numbers, algebraic equations, geometry, theorems and so on—real?

It may be ancient and unsolved, but that doesn't mean it holds the interests of those involved. What appeals to most mathematicians is the exploration and creation (or discovery) of new ideas - new theory. I was a rock climber for over half a century and what compelled me in both math and climbing was finding out what lies around the bend or over the overhang, whether it's creating or discovery - an argument that few in the profession care diddly about - and this seems to be a major difference between what is being said about philosophy in this thread and what is true of mathematics, save for those few in math foundations: Philosophy is concerned with what was said or printed or argued in the past, whereas mathematics (with the exceptions of a few math historians) always looks toward the future, even when analyzing the present lay of the mathematical landscape.

From "what is new is the exception" to "what is new is the rule".

Foundations and set theory, overlapping philosophy and mathematics, are out of my bailiwick. :cool:

Thus, the physical theory of dynamical systems could be transformed into a model in which that consciousness could be described as an attractor, the physical concept of information (not Shannon!) in connection with information or structure density describes the same dynamic 'center', . . . — Wolfgang

Such a model would be interesting. I've played with dynamical systems in the complex plane for years, and have seen only one instance when a theorem I contributed was extended to the realm of psychology (decision making in groups) - and this was done without regard for the technical hypotheses. That's what seems to happen when math is appropriated by a social science. I doubt things would be much better in a quasi-biological setting.

Your replies are always entertaining, and frequently thought provoking. Continuous mappings, in the context of QM, can mean the topological definition applied to the Hilbert spaces of that subject. Inner products yield norms which give rise to metrics, within which continuity is defined. It's a long way from Aristotle.

I still think much of what is discussed in this forum concerning QM boils down to the problem of unitarity.

I think the issue with the lattice representation is that the designation of a quantum (discrete unit) of space is completely arbitrary, not based on any real attributes of space itself — Metaphysician Undercover

What are the "real" attributes of space?

. . . and internally as will. — KantDane21

Interesting. In my experiences in the Art of Dreaming (lucid dreaming) I become pure will.

I have even heard it said that in philosophy, getting it right is less important than being wrong in interesting ways. — Ludwig V

Delightful! Thanks for a glimpse into the profession. :cool:

then the physicist will continue into that theoretical fantasy land, a fictional world requiring the assumption of "virtual particles", in a pointless attempt to maintain the representation of mass at a point. — Metaphysician Undercover

Lattice field theory avoids virtual particles, which are mathematical conveniences.

the point does not provide a very truthful, or even accurate representation of a body, which really exists in the area around the point — Metaphysician Undercover

I'm curious how you would express what you have said in the context of field theory.

The question is not one about physics, it's one about meaning. — Wayfarer

Unfortunately, it may well be the meaning of the math as one follows that path to actualizations. When does that occur? Beyond me. The math is hard for me to follow. Not so young, anymore. :worry:

Every single moment we're reminded of how small we are while our hearts & minds yearn for the great. Soul-crushing it is (for those who recognize the problem) — Agent Smith

Nailed it, Dude. :cry:

:lol:

The use of "inner" makes it sound like these are properties internal to the point. In reality they are how the point relates to other points (by means of vectors), therefore external relations. — Metaphysician Undercover

Inner product = input vectors into a form producing a real or complex number (scalar). Outer products are matrices or tensors. Word salad.

The problem with vectors is that they represent things (forces and movements) with one dimensional straight lines, when we know that in reality these things act in a multidimensional way. — Metaphysician Undercover

The issue is, as I said at the beginning, the straight line of a vector does not accurately represent a multidimensional activity which has curves inherent within every infinitesimal point. So real movement from one infinitesimal space to the next is not accurately represented with straight vectors, and the longer the vectors are, the more the inaccuracy is magnified. — Metaphysician Undercover

Oh my. This is dreadful, I fear. :gasp:

Whereas the simplest vector spaces (in R^2 or C) have vectors which can be represented by little arrows in the Euclidean or complex planes, most vectors in QM go far beyond this and cannot be so described. See Hilbert space. But, if I read between the lines you write I think what you may be getting at is the fact that linear maps are fundamental in applications.

Working with complicated functions in math one frequently tries to approximate little parts of these functions with linear functions, which are so much easier to work with. That's what happens, say, in finding a distance an object has traveled, D=Rt. If R is constant, we have R(t1+t2)=Rt1+Rt2. But if R varies we go to a definite integral, which, itself, consists of adding tiny parts of time with constant rates applied.

I've wondered about this linearity feature of QM and why it is so fundamental to the subject. But I am not a physicist. Here is a comment found in Wikipedia.

Oh Brother, Where Art Thou? is my favorite of all time. I've watched it a dozen times. Mostly the wonderful music. :smile:

Politics is easier than science. The reason: It's easier to lie and get away with it in politics.

A physicist, especially one who is a genius, can manage to be an eccentric, offputting, raw truth blurter with poor hygiene, even — Bylaw

Further a physicist might be terrible at reading people's emotions. They might react with tremendous confusing when encountering subcultures other than their own and might have no interest in trying to understand them — Bylaw

They might be utterly incapable of speaking in different ways to children, poor people, working class people, rich people, people going through trauma and so on. Another way to more neutrally put all this is they could be socially rigid. You could say, such a physicist is socially honest. Or you could say they are a very poor communicator. — Bylaw

Whew. You have a thing about physicists. The ones I've known had none of these characteristics. :roll:

Philosophy is self-reflexive and dialogic. What others have said is not separate from what one says about world, existence, reality and truth.

Original ideas and concepts have always been the exception. — Fooloso4

Thank you for this moment of clarity. In math what has come before is a stepping stone to advancements. The actual words of the pioneers are immaterial.

The word domain has several meanings in math. In number theory you have integral domains and when speaking of functions of one sort of another it refers to a set, let's say, of x's for which f(x) is defined.

Basically, it's just a set of objects defined in some sort of space. Not meaningful by itself.

Have you ever happened across Wigner's essay — Wayfarer

Yes, some time ago, but nothing stuck, so I guess I wasn't moved by it.

↪jgill
Coming to think of it, here's a legitimate question within your area of expertise: there is a 'domain of natural numbers', is there not? And there are numbers outside that domain, like the imaginary number −−−√1 which is used in renormalisation procedures in physics. — Wayfarer

You must be referring to integral domains, commutative rings, generalized from the properties of natural numbers. From natural numbers one enlarges to rational numbers, then real numbers. And then extending this to complex numbers. Complex numbers are used as a powerful tool in QM.

Is there a question here?

I think that deep within the mathematical structure of QM is where superposition or assumed existence in two "separate" states simultaneously occurs, or a mixture of states. The process begins with Hilbert spaces and their inner products (in C these might be thought of as the power of combined vectors). States of a system are subspaces of these. A pure state is determined by a unit vector in the Hilbert space. Combining systems is interpreted as taking tensor products of two Hilbert spaces. The probability of a property when the system is in a pure state is given by the inner product.

It seems to be a mathematical thing and perhaps someday a different math approach will clarify this. Schrödinger's cat deserves a bowl of milk and gentle scratching around the ears.

Thus we have agnostic realism about the mathematical world: numbers are real but we must be agnostic about the intrinsic character of numbers—as we must be agnostic about the true nature of what we call “matter”.

Well, I would say the "intrinsic character of numbers" is irrelevant to the subject, and an unfruitful environment for agnosticism. Can philosophy bring any clarity to something that exists only within its practice?

I posted a question about philosophy of maths and the ontological status of number, which was frozen because, the moderator said, there was no-one there qualified to address it — Wayfarer

I wonder what would happen if this were posted on a math forum. Probably the same result. There do seem to be ontological questions arising about sets, and numbers can be interpreted as sets.

I am somewhat saddened that the logic and philosophy of mathematics and philosophy of science categories never receive much attention or forum posts. — Shawn

The philosophy of mathematics is largely foundation theory, and this is a very technical subject. I was a math prof but beyond naive set theory I know little of foundations. In the past the forum had several participants who seemed quite knowledgeable in the subject, but, apart from Tones in a Deep Freeze they don't seem to be active. Beyond foundations I suppose one looks into the historical origins of the subject, arguing what Aristotle really meant by something attributed to him, etc. Not much there in my opinion.

As for science, threads on quantum theory spur a number of posts, many of which appear authoritative, but I have my suspicions. We have had a few actual physicists active here, but they seem to have at least momentarily fled the environment. It's an arena of discussion that beckons those who enjoy batting around the quaisi-woo some actual luminaries lay out - seriously or frivolously.

Philosophy is laugh-out-loud good times for those who love it, especially in the heat of battle with all marbles on the table. — ucarr

I've wondered what happens to those when a philosopher loses them. Now I see where they end up.

There were lots of basic topics covered, down to interpretations of time near the bottom, but I didn’t see quantum interpretations mentioned at all, which requires probably a whole separate course — noAxioms

Might be hard to find a faculty member of a philosophy department capable of this. :cool:

I would say any university with a good philosophy program, and adequate courses in metaphysics. — Metaphysician Undercover

Amongst the myriad of courses in numerology, astrology, meditation, noetic sciences,chakras, auras, divination, spiritualism, angels, etc., I found an introductory course at Oxford that looks legit:

Introduction: what is metaphysics? An introduction to the distinctive character of metaphysical questions: the history of the idea of metaphysics, understood as the most general and abstract inquiry into the nature of reality.

Existence: what is existence? What is it to exist? People disagree about what exists; but how can we understand this disagreement? Are there things which do not exist?

Universals and particulars: in addition to particular objects and events, our world seems to contain general or universal features of things, like their colours and their shapes. Is this an illusion or does the world really contain such features, known as 'universals'?

Realism and idealism: does the world exist independently of our minds? Realism is the view that it does; idealism is the view that reality is mind-dependent. Are any features of the world mind-dependent?

The freedom of the will: we think our actions and decisions are free, or up to us, but this idea seems to be in conflict with the apparent fact that everything which happens is determined by what happens before it (this is known as 'determinism'). Does determinism imply that free will is an illusion, or are free will and determinism really compatible after all?

Cause and effect: what is it for one thing to cause another, or to make something happen? Is there more to cause and effect than the mere regularity of things happening after one another? If so, is causation a physical process, or is mental causation also possible?

The nature of time and space: what are time and space? Is there no more to them than the temporal and spatial relations which hold between events and objects? Or should they rather be conceived as the 'containers' in which things exist and events occur? Are the past, present and future genuine aspects of reality, or are they merely 'subjective' features of our experience of time?

We strongly recommend that you try to find a little time each week to engage in the online conversations (at times that are convenient to you) as the forums are an integral, and very rewarding, part of the course and the online learning experience.

I encourage any Q-physicist reading this post to consider enrolling in this course. :cool:

(or simply pull up all the threads on TPF relating to these subjects. Much profound stuff therein.)

You're dealing with probabilities in the quantum world, not deterministics. The probability of the cat being alive might be .3 and dead .7. Doesn't mean the poor cat hovers between life and death. It may be alive.

Wikipedia:

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics.

I grew up as an only child and I did feel that was hard. It is also probably why I am better able to do things by myself as I was got used to it — Jack Cummins

Me too, but I did not feel it was hard. I learned to talk to myself, and made friends with that inner companion. I still do when I'm alone, and my inner friend supplies me with mathematical ideas. Also, I became a solo climber and relished being entirely alone high up on a piece of granite.

But living alone is another dimension, and I truly appreciate my companion, my wife.

Metaphysics consists of different principles which physicists have not been trained in. — Metaphysician Undercover

Suppose I am a typical Q-physicist, following the mathematics but paying little attention to authorities in my subject babbling woo about interpretations. Please elucidate the training program in metaphysics I would need to complete to be considered competent in metaphysics. Be specific as possible.

Would I need to attend the University of Metaphysics? Would a bachelor's degree be sufficient?

↪jgill
Well then what explains all the Sturm und Drang mon ami?! Why the hullabaloo if the cat is simply dead OR alive? — Agent Smith

No one really knows exactly whats going on at the quantum level. If you simply follow the math and avoid all this metaphysical stuff, you do well at predicting. Apparently. Once the science popularizers get into the game, however, you see the Earth in basketball nets. Best to let the Q-physicists argue it out. My opinion. FWIW. Not much.

I thought that superposition is a fact and not just a hole in our knowledge. In other words the coin is heads and tails and not that it's either heads or tails, only we don't know which. — Agent Smith

Wikipedia:

Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution(s)

. . .

In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system

The cat really is either dead or alive, not in some mystical sense, both. Probabilities, on the other hand, are not definitive.

To come to a universal consensus regarding the definition of metaphysics.

I take it you've appealed to your dojo? In that case I don't think The Philosophy Forum can help your cause. Good luck.

But even if you're not going to earn any more ranks after first degree black belt the fact of the matter is that you're just getting started. There is no end — HardWorker

Yes, I'm familiar with most of what you've said. In the Air Force in the late 1950s my best friend was a black belt in Karate.

You need to appeal to the American Karate Association for a change of their philosophy.

However perhaps that's because we haven't developed formal computations complex enough to bridge that gap to subjective states — Benj96

When I was young I never expected mathematics to become so diverse and abstract. Now, with over 26,000 pages on Wikipedia trying to guess what's coming next is nonsense. :cool:

By deaths of despair I mean suicides, including mass shootings, and drug overdoses . . . . . it’s fairly obvious to me based on common sense and the evidence: it’s the guns. — Mikie

Guns cause drug overdoses?

But generally speaking you're correct. Unfortunately, there's no way to round up close to 400,000,000 guns. And they are made so well they last so long.

:up:

I hope that explains how 1 +1 =3 — Benj96

Well, no. But "The whole is greater than the sum of the parts" seems more or less to be what you are saying. And, yes, in a sense that's true of integers. For example, 2+3=5, but 2*3=6, so that the sum of the prime factors of 6 is less than 6.

However, I believe you are thinking of a more philosophical idea. And that's fine, just don't try to make mathematics conform to your notions. :cool:

Success lies neither in being appropriated by some arbitrary cultural notion of success nor by giving in to helplesness and misery. E.g. The best free climber in the world, Alex Honnold, was, initially, virtually unknown, had no money and lived out of his car. He neither dumped his passion to pursue more traditional forms of success nor spent his time fretting over useless self-defeating philosophies. And I very much doubt he stole his desire from a self-help cookie jar. — Baden

I like it when specific examples are given to cut through endless dialogues about abstractions. I know Alex and have done a podcast with him. He would shy away from "best free climber", but he could not dispute the fact he has done the most amazing climbing in the history of the sport. His sponsorships, now, I'm sure are substantial, but he certainly didn't set aim for monetary riches. However, I don't think he started out being helpless and miserable.

I've known quite a few "dirtbag" climbers over the years and for most their way of life is not the result of cultural conflicts, but rather a calling. Another friend, a "dirtbag" living on less than a half dollar a day, when I had the luxury of a dollar a day, eons ago, pursued somewhat different goals and ended up a billionaire who recently formed a foundation to protect the environment. But climbing reaches deep within you and you find a way to make a life that at least includes it.

Nevertheless, there is always one form or another of competition underlying the lifestyle. And most have to do with exploring the unknown or pushing boundaries, either by advancing one's credentials by identifying with a certain quantified level of difficulty - a little like a Karate student reaching Black Belt levels - or making a first ascent, or doing something else seen as admirable by the community.