I see you started a similar thread just before this one. But I will quote a bit of that here...

Beyond the limit of existence we said its opposite must lie. This opposite again has a limit, for it is only what it is and therefore exists. As you might be able to see, nothingness is that from which existence comes but that never gets to be per se for when it is it becomes something that exists and therefore never exists and IS nothing. Now this nothingness before the origin must not necessarily be 0 of everything. As I said, it could be everything except the ability to change. I dunno it is as if change were what we call god. Change that arises because the limitation of things forces their existence. It is as if we exist because we have to exist. Makes sense? — Daniel

So I would say you are asking the right questions. Now what suitable answers have some philosophers offered?

One approach is that of metaphysicians like Anaximander in Ancient Greece or CS Peirce in modern times.

Where things begin is in a vagueness or a pure unbroken potential. This is neither a state of change nor stability. Being the unlimited or the indefinite, it has no division in either of these possible directions. It is only the possibility for such a division to manifest.

We are talking of metaphysical qualities that are dichotomous. Each is the limit of the other. So the limit on changing is to be stable. The limit on stability is to be still changing. Thus you need both to “exist” to have either as something that definitely applies in the world. The existence of each secures the existence of the other. We can point to the lack of change when things are stable. And we can point to lack of stability when things change.

But back when things were primally vague, there could be no fact of the matter either way. There was no change to measure stability by, and no stability to measure change by. All you have is mute indeterminacy in regards to either possible question.

So apply that to existence in general. Non-existence must exist to stand as a definite limit on existence. And vice versa. Existence must limit non-existence.

Fine. But note how non-existence is not yet defined in its own way. Are we talking about absolute nothingness. Is it the nothingness that stands outside the somethingness in some spatial sense, or temporal sense, or even a spatiotemporal sense?

We can see that the notion of “existence” does have some inherent problems. Is it properly opposed to nothingness, to flux, to development, to decay, or what? Again, that is why we would want to start by deconstructing the term, discover what we actually think we mean by it. What actually is the limit that makes existence exist. Across that limit must lie its other. But we need to give that other some more concrete definition than saying “it is whatever existence is not”. It must be given a positive character to secure existence as a well defined metaphysical concept.

So anyway, the story would go that everything begins just in an undifferentiated vagueness. Then your key metaphysical polarities are what could emerge in a mutually definitional fashion from that. You get a dichotomy like flux and stasis which describes existence in terms it’s two logical extremes.

So now your reality is bounded by standing within a pair of limits.

You want to draw a circle on a page. That marks off an inside from an outside. And then you want the inside to be existence, the outside to be non existence. Yet that doesn’t really work. You have only marked off a region of a plane in arbitrary fashion. The outside of the circle also actually exists in this tale.

A better conception is a page with a mark, an ink dot. Now there are two opposed extremes. A figure and a ground. An event and a context. The reality goes in two complementary directions. Either it contracts towards the black speck of ink, or it expands outwards to the general blankness of the page. You can’t get more black and inky in one direction, or more unmarked and blank in the other. However neither without the other can properly claim to have its chief characteristic.

A dot of ink without the page it blemishes can be a mark. And a page can’t be definitely unblemished as a definite thing unless there is at least some mark to blemish it and so betray its general presence.

So metaphysically, existence is what we find between two complementary limits on being. The essential relationship is hierarchical rather than spherical. Reality is to be found between upper and lower bounds on possibility. The relation is not between an inside and an outside, but a triadic one where reality is the spectrum of intermediate possibilities that two countering limits definitely create.

So first there is just a potential. Then there is the possibility of some mutually definitional division. And thirdly there is the final outcome of a spectrum of possibilities that those two limits on being can manage to define.

So what if I say that "for existence to exist it must have not existed before? — Daniel

This is a very standard line of thought of course. We believe in deterministic cause and effect. We believe in Leibniz's principle of sufficient reason.

And yet we also we realise that while this can explain existence in terms of particular individuated entities - a world full of objects - there is a problem when it comes to applying the same simple cause and effect logic to "existence as a whole".

You are talking about the central problem of metaphysics. And we know that simple cause and effect stories can't work.

And that is why you would have to start to step back and see what reality is actually composed of. In talking about "existence", you are already presuming individuation and stability ... in the face of an equal amount of development and decay. So "non-existence" looks like that other bit - the change, the possibility, the flux.

The question has to become about why anything might develop and persist in the face of so much action in the other direction. This thing that you presume - existence - then drops out of the picture. There isn't any such thing as "simple existence". That is simply a label you were slapping on the most stable and enduring part of everything that is always changing.

But likewise, "coming into existence", is a problematic idea because it is also true that things do have the tendency to stabilise and find concrete forms that endure. Everything might be changing, but pattern or regularity also can't seem to help emerging.

So to get anywhere on this obvious poser - how could existence first exist? - you have to be prepared to unpick the notion of existence itself.

To me, it makes more sense to understand existence as where the "coming into being" has finally arrived at some stable rest point. So it is not about where existence starts. It is about where coming into being stops.

Our attention can focus on why flux or chaos settles into something stable and persisting. And we have a lot of mathematical-strength models that can speak to that kind of metaphysics.

Is it safe to assume that for something to exist it has to come into existence first? — Daniel

It seems a good assumption just looking around at the evidence. When things exist, we mean that they persist. They hang about in an individuated and stable fashion. But we also can see that things change. Individuation is the result of development. Stability is what can survive lability or corruption.

So what we see is a reality that is stretched between two tendencies. Things persist. And things also develop and perish.

So if that is what we see everywhere we look, then that is what would be safe to assume. Reality is a process in which things can both change and stay the same. Our metaphysics then has to be directed to the "how" of that duality.

Every day to go and expect your car to start you are relying on determinism. And if he fails to start then you rely on determinism to find a solution, such as you forgot to put petrol in it; or you need to change a spark plug. — charleton

So when a radioactive atom decays, are you saying that was determined by a cause? Something suddenly made its decay more probable, nay inescapable, in that moment rather than - as inductively confirmed in the study of these things - that the decay probability does not vary with time? The chance was constant, therefore the determinism was - measurably - zero?

So at some point you have to be able to say in what way you think the neurobiology of brains is informationally deterministic. What does such a claim mean?
— apokrisis

As above really, it means that the next physical state of all the neurons in the brain is determined by the prior physical state of those neurons plus all the universe interacting with them. The change from one state to the next being determined by the laws of physics, which themselves are determined by the initial state of the universe. — Pseudonym

There didn’t seem any point continuing when you just keep making the same bald claim and say nothing about how that could be the case in terms of the actual neurobiology.

If you believe every thought and choice you could have, every next word you could say, was hardwired into the quantum foam at the beginning of time, then you are asking me to take seriously something that is just too silly.

If you were familiar with biology, then you would find that life actually depends on randomness. It needs material instability so that it can have something to regulate with its information. It is made of molecules that will fall apart and put themselves back together so long as they get the right signals.

So just in that you have the fact that life thrives on the edge of chaos. Where things are the most poised and unpredictable, is where information can then point that constructive energy in a predicted or constrained direction.

That is why I urged you to read Pattee. And your response tells me all I need to know about your interest in any actual challenge to your assumed position.

Sorry. You are not getting it. Biology tells us that bodies aren’t deterministic devices. Life likes to control matter. So it has to separate itself from matter to have that control.

You will find the argument laid out here ... https://www.informatics.indiana.edu/rocha/publications/pattee/pattee.html

How does that explain the problem? The "bang" of the big bang? — TimeLine

I was answering the question of how an inflationary universe could be considered large yet not infinite.

So again you are speaking in non sequiturs. Who was talking about the problem of the bang of the Big Bang? Where are you getting this latest misrepresentation from and what could it even mean?

As I said, it is you that has no clue what he is talking about. — TimeLine

If you believe that statement is wrong, provide a refutation with citations.

The claim of determinism is solely that somehow the state of the universe in the next moment is determined by its state in the previous moment. — Pseudonym

Remember we are discussing freewill. Are you claiming there was a widely discussed problem before Newton’s mechanistic laws of motion?

And while you could take a looser view on determinism - I certainly do - the normal view relies on laws to ensure one state has no choice but to lead to the next.

Nomological determinism is the most common form of causal determinism. It is the notion that the past and the present dictate the future entirely and necessarily by rigid natural laws, that every occurrence results inevitably from prior events.

https://en.m.wikipedia.org/wiki/Determinism

Then what you actually claimed is that there is informational determinism when it comes to the brain. After all, as I pointed out, no one uses Newton’s laws of motions to say that physics determines any putative finite state transitions.

So again, what ensures that neurons behave deterministically if you are claiming it is information and not physics?

As I said, the design feature of computers is that nothing about the physics of transistors should dictate the way a gate decides to open or shut. Only the program instructions are meant to determine the state transitions. So we certainly know how to build a deterministic finite state automata.

However if it is our free choice about what programme code to write, what rules to create, then the freewill issue can’t be solved by pointing to that kind of machine determinism. We still lurk behind the scene.

So at some point you have to be able to say in what way you think the neurobiology of brains is informationally deterministic. What does such a claim mean?

None of this invalidates determinism in any way. It just means we do not yet have all the information necessary to predict 'stochastic' events — charleton

Hmm. To say that events are predictably unpredictable, as a wavefunction does, is merely to say they are constrained rather than determined. You can be certain of your uncertainty. And if that uncertainty is irreducible, then absolute determinism is a dead duck.

But relative determinism, or a degree of constraint, is still a useful thing to have. Just because absolute determinism fails, not all is lost.

But you were going to tell me how my next word could be predicted in principle by a prior neural state. Apparently the information is in my brain and in the entire universe. That seems a little hand-wavy, no?

Remember the question I actually asked.

And how would you know what the previous state was and the next state was of either. Would your "determinism" allow you to predict that using Newton's laws of motion? If not, what laws are you proposing that would connect one measured state to another measured state? — apokrisis

If your version of determinism is informational rather than material, then what law of nature determines the transition from one neural state to the next?

So just saying there is information involved is not an answer. I’m asking what kind of natural law are you imagining ruling the neurobiology. Where is the evidence that the brain is literally a finite state automata that could even sustain that kind of completely constrained or deterministic state mapping?

I don’t follow. Are you being sarcastic?

So fill in the blank. The next word I’m going to write is the word ...

Indeed, and you went on a torrent of abuse because I sought an explanation, and an explanation you still have not given. — TimeLine

I’ve given you an explanation several times now. So you will have to explain what your problem with it is. Otherwise you are simply trolling.

The problem is not that, Apokrisis, the problem is that you are intentionally and incorrectly misunderstanding my comments and then responding to an article I have given you by implying I meant something that I did not mean. — TimeLine

Well explain how that cite meant anything.

How can I have intentionally misunderstand your comment “Here, read.” Clearly I understood. I read.

But what the hell do you think baryon asymmetry has to do with inflation? I’ve asked you to explain. Clearly having stuffed up again, you won’t. You will just huff about with wounded pride and pretend you have been done some dreadful wrong.

'm not. I am interested in what you have to say, but your behaviour and your responses have only made me lose my respect for you completely and I am confident that the reasoning behind that behaviour is because you are uncomfortable with my presence. — TimeLine

Uncomfortable with your presence? You have a vivid fantasy life apparently.

It is as simple as the fact that first you baffled me with your non sequiturs, and then you annoyed me with your strangulated prose, and finally I am tiring of your self-pitying tone.

I’ve asked you for a number of explanations. They have not been forthcoming. I’m not holding my breath.

Here, read. — TimeLine

When you are so deep in a hole, stop digging. You've just cited a paper that is hypothesising about a non-inflationary scalar field that might explain some other issue - the dominance of matter over anti-matter after recombination.

So this scalar field would be a condensate that produces right-handed sneutrinos. It would be carried along for the ride like all other particle fields during inflation - inflation being produced by a different imagined scalar field that Guth dubbed the inflaton. https://en.wikipedia.org/wiki/Inflaton

The logic is the same as I outlined of course. And it is weird that you seem to want to continue to want to challenge that logic in some obscure fashion.

The logic is that observation shows that we have a problem and that then sets up the search for a mechanism that can fix it.

So the isotropic state of the CMB was a puzzling observation. Guth proposed a scalar field with a special property - some kind of repulsive spacetime expanding phase before it decays - as the possible solution.

Likewise, the paper you cited starts with the matter asymmetry problem. It is observed there is matter in the universe and so something is needed to explain how that asymmetry arose. Again, a scalar field - this time a more standard particle one - is being proposed as the get out jail card.

The paper makes this distinction in its first paragraph. It would have been impossible for you to miss it.

In particular, assuming inflation [1] as a solution to the horizon, flatness, and other cosmological problems and as a seed for density fluctuations for later structure formation, we are obliged to adopt scenarios where the baryon asymmetry is generated after the reheating.

So because the inflaton can't explain the matter~antimatter asymmetry, something else after inflation would have to be the mechanism. Some particular particle condensate with a right-handedness that broke during recombination.

If you still think that your citation is any kind of argument against something I said - in particular, that observation of a problem is the reason we impute some scalar field as a mechanism - then you will have to explain yourself further.

Now, I could turn around and say something like just because you go over the heads of others, doesn't mean you know what you are talking about or screaming like a little baby boy doesn't actually suddenly make you right but I am going to ask you once and once only, speak and question properly. If you do not understand something, it is you that has the problem and because you know a bit of physics, your attitude is nevertheless ungenerous. — TimeLine

And here you go with your usual hyperbolic attack as soon as you encounter the slightest pushback on your posts. But I'm sorry. You are giving me no reason to think you understand the issues in question.

The paper you just cited to "prove your case", again proves mine. And you can use your moderator position to hound me all you like. I'm not going to pretend you are correct about things when you aren't.

Why do you repeat what I say and then scream that you don't understand? — TimeLine

Remember that you decided to focus on my use of the term "humongously large". You were asking relative to what? I answered several times. Obviously the comparison was between the size of the visible universe at the end of inflation compared to the inflated whole.

So do you accept that as correct now? If so, why are you trying to pretend I was agreeing with something you said?

Determinism is a fact of the universe it does not have an opinion. It's true whether you believe it or not. — charleton

Does science talk about discovering true facts or arriving at the most broadly based unfalsified beliefs?

You are adopting an absolutist position on determinism as a known metaphysical fact. And it is no longer even a reasonable metaphysical belief, given quantum indeterminacy and the measurement issue in general.

It is all well and good that observable fluctuations and perturbations in scalar fields in the CMB radiation can explain the isotropy and homogeneity along with the massive size, as well as the expansion of the universe as accelerating, — TimeLine

What is it with your bad writing? Every sentence lacks logical argumentative structure. It's all a garble of buzzwords and not a proper response.

How do the fluctuations and perturbations in scalar fields in the CMB radiation "explain" the isotropy and homogeneity, and the massive size?

It is the fluctuations of the CMB we observe. Any scalar field responsible for inflation is then imputed via theory.

And it is the isotropy of the CMB we observe, thus making homogeneity a reasonable belief. And likewise, the massive size (much bigger than just the visible universe) a reasonable belief.

Likewise, how do the fluctuations themselves "explain" dark energy? The original observations that spoke to a cosmological constant were of surprising supernovae redshifts. It took another theoretical mechanism - the Sachs-Wolfe effect - to then "see" a background acceleration in the CMB data.

So you are name-checking familiar bits of the cosmological puzzle. But that's it. There isn't the logical connections that would show you understood how these bits of the puzzle slot together.

You stated that the initial region that "banged" was already massive. Going back 13 to 14 billion years, this makes no sense. If the universe was large and infinitely dense, you are merely comparing the size or shape to the observable universe. — TimeLine

It is you who continue to fail to make a coherent response.

First, I stated that the initial region in the original inflationary story was very small. There was a pre-inflationary phase that lasted from the first Big Bang event - the symmetry-breaking that split gravity from a vanilla GUT force. Then this GUT force broke down into the strong and electroweak force an instant later, starting the inflationary period - according to the standard mainstream telling of this form of inflation.

So the usual tale is that the inflaton field was some kind of initial quantum fluctuation - about a teaspoon of matter. And then inflation was an exponential doubling in size of this field, without any dilution of energy density. It is quite easy to fit 50 to 60 e-doublings between the likely times for the GUT symmetry breaking and the next symmetry breaking - the Higgs/EW one - where inflation must have come to its end. Hence we can compare our visible universe region to the total inflationary expanse by counting up the number of supposed e-doublings. That gives us a 55 orders of magnitude difference. Plenty to do what inflation is meant to do in terms of the obseverable degree of isotropy and homogeneity in the CMB.

And all this is just what any popular science book on inflationary cosmology will tell you.

That you say: "This is odd. It also explains nothing," shows you have a flakey grasp of the cosmological arguments being made.

Going back 13 to 14 billion years, this makes no sense. If the universe was large and infinitely dense, you are merely comparing the size or shape to the observable universe. — TimeLine

It is your sentences that make no sense.

What size do you think the observable universe was relative to the inflated universe back then just after inflation ended and recombination got visibility itself started?

If you could write proper sentences, then it would be clear what you think should be compared to what. You wouldn't rely on ambiguity to make it sound as if you had some valid criticism of my account.

Well that is just your first paragraph. And it continues the pattern of being so garbled that it is a huge waste of time untangling your out-pourings for you.

As I have already said, I appreciate Guth' suggestion that the early conditions were about the size of 10^-28cm - the size of a marble - and with energy at 10^16 GeV the scalar field in this false vacuum state dominates the total mass-energy density enabling the volume to expand at a constant; the negative pressure enables it to grow exponentially and no energy is actually needed, or at least the energy of empty space (dark energy) and something we still have no clue as to what it is. In a fraction of a moment, the universe expanded at the speed of light, actually probably faster than light because there are no limitations to how far the universe can expand according to GR. Then the repulsive gravity begins to decay at 10^-33 seconds after the big bang and we get what we have now in the observable universe. — TimeLine

Are you implying I argued something fundamentally at odds with this? Again, you are sticking in a lump of text that does not contest what I said, and doesn't explain what you think you might be criticising when you accuse me of "This is odd. It also explains nothing."

I get that inflation is the physics of matter and scalar fields and that the particles that make universe from initial conditions to the big bang is in the Higgs fields, but these separate suggestions are intentionally fused to help ascertain a number of other factors that have - like the flatness problem - but also have not yet been raised in this discussion; as mentioned earlier, the second law of thermodynamics and the arrow of time, the low-entropy early conditions, cosmological parameters and these problems in inflation also need to be considered, hence the fusion and I believe that I have already made it clear that I appreciate Guth. — TimeLine

Wow. What a dog-turd of a sentence.

OK. So there is a flatness problem - from observation we see the universe is as flat as possible. And there doesn't seem enough gravitating mass to brake an exploding big bang with such exact precision.

Another part of the flatness problem is that the density of any gravitating mass looks evenly thermalised. The universe in one direction looks the same as the universe in the other. And if we believe in the Big Bang, that raises a further issue of how our neighbouring regions could be thermally the same having never shared the same lightcone. We need a mechanism that explains that.

So two big problems. And inflation would help explain both.

You smoosh everything together, killing the logical story science wants to tell. You ought to be making it clear that you appreciate the parts of the puzzle when you write your replies. Otherwise there is no possibility of you making some actual counter-argument or criticism of the science as I explained it.

Your throwing in the arrow of time, entropy, cosmological parameters, etc, is just adding to the confusion you have already created.

More buzzwords that are irrelevant to any thread of argument you might be trying to sustain in your mystifying attack on me. If you think I should have added something further on these issues to explain the cosmology, then pin-point the difference they make. Otherwise it just seems you are trying to sound impressive by name-checking every damn buzzword you can think of. A childish rhetorical tactic.

From my understanding, it does; when you consider the effect of the cosmological constant as it explains the rate of expansion with time, particles that make up the universe following inflation are merely the quantum explanation of a Non-Zero Higgs field that forms elementary particle masses; it has positive and negative contributions at a constant at every space time point, which would mean that omega would equal to omega(m) + omega (lambda) as it explains the rate of expansion with time. I get what you mean, but there is no distinction. — TimeLine

No, you really don't get what even your own citation is saying if you believe that a distinction between omega(m) and omega (lambda) is not in fact a distinction mentioned for good reason.

And given that the simplistic focus of your attacks on me became about this issue of a "humongously larger" inflationary universe, how is this even relevant to that?

You are now conflating the issue of the late dark energy dominated era of the Cosmos with the brief inflationary event hypothesised to better explain its first moments.

Now I find it very reasonable that if there were inflation (a big if), then it is very appealing that dark energy may turn out to be a remnant effect of some kind. So future science may establish a connection.

But here, in your replies, you don't even seem to realise how your mind skips from one thing to the next without paying proper care to the distinctions involved.

You shit out another dog-turd of a sentence that is so scrambled that it can have no possible bearing on whatever it was that I was saying. It makes no definite argumentative point. And that has been the pattern of your every response so far.

Sorry to be blunt. But that's what you get for being blunt, isn't it?

I'm not making any claims, — Pseudonym

Well you are in insisting that brain function is deterministic, even if that just means a deterministic computation, and even if that in turn just means the computations are deterministic guesswork about an undetermined reality.

So you are very determined to make determinism true here, and reject my constraints-based, semiotic, approach where - as a metaphysical generality - all events can be only relatively deterministic and are unable to be absolutely deterministic.

All you've presented so far is a vague "because fundamental particles cannot be measured, we must have free-will", which is fine if you're looking to simply justify an already held belief in indeterminacy, but not really a sufficient argument to ground its necessity. — Pseudonym

Haven't you got that back to front? If my position cashes out at a general metaphysical level against determinism, then in fact it is a necessity that some local bit of complex machinery - like a brain - operates with a constraints-based causality and not a mechanically determined one.

So yes, quantum level indeterminacy is exhibit A. And then chaos theory and non-linear dynamics would be exhibit B.

For me to take a strong position here, it is important that modern physics is now evidence against the Newtonian classical deterministic paradigm.

If the answer to your question helps you to explain your argument somehow, then for me information is the state of a collection of neurons, no different to the way information is the state of a collection of transistors in a computer. That state, together with inputs from the external system, determines the state in the next moment. Of course, given that this is a transition from one state to another, it could also be described as a process, but I see that as a semantic issue, not a metaphysical one. — Pseudonym

So how would you go about measuring the state that is a collection of neurons?

Or in a collection of transistors in a computer.

And how would you know what the previous state was and the next state was of either. Would your "determinism" allow you to predict that using Newton's laws of motion? If not, what laws are you proposing that would connect one measured state to another measured state?

If you can't answer these questions, you haven't got an argument.

How is the brain's model of the future not determined entirely by the information it has at the current time and the neurological connections which represent its current responses to all the multitude of stimuli presented in the model? — Pseudonym

Explain to me how you think information exists in brains. What is brain information in your book - the kind that you are claiming to be mechanically deterministic?

The rather clichéd "Our language/culture is more complex" is pretty weak without defining the level at which this happens and why. — Pseudonym

Cliched? Human language is articulate and syntactic. It is rule based symbolism so capable of unlimited combination. You are talking apples and oranges in claiming other species have “language”.

You have to presume, for this to work, that moral behaviour is in some way opposed to natural instinctive behaviour. I don't see any evidence for this. — Pseudonym

It should be enough to mention #MeToo.

Why would we presume that the brain's ability to model the future isn't entirely determined by the information is has gained up to the present and the current state of it's neural connections which together determine the picture it will generate of the future world? — Pseudonym

Yeah. We might make a guess that is determined by our best information. And then the guess turns out to be wrong.

So I’m not arguing against the ability to constrain uncertainty. I’m attacking the presumption of absolute determinism - mechanistic understanding of physical and informational processes.

The point of having a brain is to make the best choices, given an uncertain world. You seem determined to recover some kind of actual determinacy in what the brain does. But I am arguing from a systems science or hierarchy theory perspective where the causality of reality in general is understood in terms of constraints on degrees of freedom.

It’s not just neurobiology. Even physics is not deterministic.

The question then arises, 'what is the nature of number?' Conjecturally, one might say, number is a series of equal values (quantity). Hence, Pythagoras' and other ancient mathematicians' inclination to render number as equal, whole values. If this is an accurate description of number, then it follows, the concept of number is tied to the idea of a 'unity' value (unit measure). — cruffyd

Yeah. The historical view is a good way to get at it. There was a reason why the Greeks were so horrified by the notion of an irrational number. That very reaction betrays the underlying belief about what a definition might be.

And so we have "oneness" as the central object of arithmetic. And we have "a dimensionless point" as the central object of geometry.

The Greeks were discovering what the maximally invariant mathematical objects looked like - the ones that had irreducible identity despite all possible operations that might attempt to change that in one of the mathematical families.

Having established the highest symmetry identity operations, then maths could progress by identifying and relaxing the various constraints that ensured the existence of these ideal objects - the 1 and the point.

Geometry could go non-euclidean and topological. Numbers could loosen to include negatives and irrationals.

Bourbaki's talk about the three mother structures makes me wonder where order structure fits in to the Ancient Greek story. I guess Aristotle's work on the logic of hierarchies - the [genus [species]] relation - does describe what is the most primitive notion of set theory.

Temporal construction is such that inequality defines its nature. Equality, on the other hand, can only be outside of temporality. One might say: 'equality can only exist eternally.' — cruffyd

I get what you mean but in that direction can lie hard Platonism. However the altermative I prefer is another long story.

Have I once demanded that you "provide me with a proper theory of what constitutes this you"? — JustSomeGuy

And why not? That would be perfectly reasonable.

Freewill is a debate that comes up every week here. Just last week I gave this general account that is worth recycling.

Get back to basics. The sense of self is a perceptual contrast the brain has to construct so as to be able to perceive ... "the world". Even our immune and digestive systems have to encode some sense of what is self so as to know what is "other" - either other organisms that shouldn't be there, or the food the gut wants to break down. And so too, the brain has to form a sense of what is self to know that the world is other.

A second basic of the evolved brain is that it is needs to rely on forward modelling the world. You probably think the brain is some kind of computer, taking in sensory data, doing some processing, then throwing up a conscious display. Awareness is an output. But brains are slow devices. It takes a fifth of a second to emit a well learnt habitual response to the world, and half a second to reach an attentional level of understanding and decision making. We couldn't even safely climb the stairs if we had to wait that long to process the state of the world.

So instead, the brain relies on anticipation or prediction. It imagines how the world is likely to be in the next moment or so. So it is "conscious" of the world ahead of time. It has an "illusion" of the next split second just about to happen. That creates a feeling of zero lag - to the degree the predictions turn out right.

And this forward modelling is necessary just to allow for a continual perceptual construction of our "self". We have to be able to tell that it is our turning head that causes the world to spin, and not the other way round. So when we are just about to shift our eyes or move our hand, a copy of that motor instruction is broadcast in a way that it can be subtracted from the sensory inputs that then follow. The self is created in that moment because it is the part we are subtracting from the flow of impressions. The world is then whatever stayed stable despite our actions.

It is not hard to look at the cognitive architecture of brains and see the necessary evolutionary logic of its processing structure. And a running sense of self is just the flipside of constructing a running sense of the world.

Then on top of that, brains have to deal with an actual processing lag. And the best way to deal with that is to forward-model the shit out of the world.

Then on top of that, it is efficient to have a division of labour. The brain wants to do as much as it can out of learnt habit, and that then leaves slower responding attention to mop up whatever turns out to be novel, surprising or significant during some moment.

That leads to consciousness having a logical temporal structure. You have some kind of conscious or attention-level set of expectations and plans at least several seconds out from a moment. About half a second out, attention is done and learnt, well-briefed, habit has to take over. It does detailed subconscious predicting and reacting. If someone steps into the road while you are driving, you hit the brakes automatically in about a fifth of a second. After that, attention level processing comes back into it. You can consciously note that thank god you are so quick on the brakes, and what was that crazy guy thinking, and why now is he looking angry at me, etc.

So [conscious prediction [subconscious prediction [the moment] subconscious reaction] conscious reaction].

This is all proven by psychological experiment. The whole issue of reaction times and processing times is what got experimental psychology started in the late 1800s.

Where does human freewill come into it? Well what I've outlined is the evolution of the cognitive neurobiology. The basic logic is the same for all anmals with large brains. They all need to construct a running sense of self so as to have a running sense of what then constitutes "the world". They all have a division of labour where they can act out of fast learnt habit or slower voluntary attention.

But humans are different in that we have evolved language and are essentially social creatures mentally organised by cultural evolution. Yes, memes.

So now our perceptual sense of self takes on a social dimension. We learn to think of "ourselves" in terms of a wider social world that we are representing. We learn to "other" our biological selves - this running perceptual self with all its grubby biological intentionality - and see it from an imagined social point of view. We learn to be disembodied from our own bodies and take an introspective or third person stance on the fact we can make choices that our societies might have something strong to say about.

So freewill is a social meme. It is the cultural idea that being a human self involves being able to perceive a difference between the "unthinking" selfish or biologocally instinctual level of action and a "thinking", socially informed, level of self-less action.

An animal is a self in a simple direct fashion - a self only so far as needed to then perceive "a world". A human, through language, learns to perceive a world that has themselves in it as moral agent making individual choices. That then requires the individual to take "conscious responsibility" for their actions. Every action must be judged in terms of the contrast between "what I want to do" and "what I ought to do".

So the idea of freewill is an ideal we strive to live up to. And yet the temporal structure of actual brain processes gives us plenty of dilemmas. We do have to rely on "subconscious" habit just for the sake of speed and efficiency. The gold standard of self-control is attention-level processing. But that is slow and effortful. However - as human culture has evolved - it has set the bar ever higher on that score. As a society, we give people less and less latitude for sloppy self-control, while also making their daily lives fantastically more complex.

A hunter/gather level of decision making is pretty cruisey by comparison. You go with the flow of the group. Your personal identity is largely a tribal identity. You get away with what you can get away with.

But then came institutionalised religion, stratified society, the complex demands of being a "self-actualising" being. A literal cult of freewill developed. The paradoxical cultural demand - in the modern Western tradition - is that we be "self-made".

So sure, there must be some evolutionary logic to this. There must be a reason why the freewill meme is culturally productive. But the point also is that it is a psychologically unrealistic construct. It runs roughshod over the actual cognitive logic of the brain.

We just shouldn't beat ourselves up for not being literally in charge of our actions at all times. We are designed to be in some kind of flow of action where we let well-drilled habit do its thing. And of course our minds will wander when we are being expected to consciously attend to the execution of stuff we can handle just as well out of habit. The idea that we can switch our concentration off and on "at will" just cuts against the grain of how the brain naturally wants to be. Attention is there for when things get surprising, dangerous, difficult, not for taking charge of the execution of the routine.

So "freewill" sits at the centre of so much cultural hogwash. There is good cultural reasons for it as a meme. It is really to modern society's advantage to have us think about our "selves" in this disembodied fashion. It allows society to claim control over our most inadvertent or reflexive actions.

But it is also a demonstrably unhealthy way to frame human psychology. If we just recognise that we have slower voluntary level planning and faster drilled habitual responses, then this unconscious vs conscious dilemma would not create so much existential angst.

We are not a conscious ego in possible conflict with an unconscious id (and also under the yoke of a social super-ego). Our "self" is the skilled totality of everything the brain does to created a well-adapted flow of responses to the continually varying demands of living in the world - a world that is both a physical one and a social one for us as naturally social creatures.

The actual freewill dilemma arose because Newtonian determinism appeared to make it paradoxical. If we are just meat machines, then how could we be selves that make our own rational or emotional choices?

But physics has gone past such determinism. And the very fact that the brain has to forward model to keep up with the world means that it is not being neurally determined anyway. Its knowledge of how the world was an instant or two ago is certainly a constraint on the expectations it forms. But the very fact it has to start every moment with its best guess of the future, and act on that, already means we couldn't be completely deterministic devices even if we tried.

Universal computation is logically deterministic. A programme - some structure of set rules and definite data - has to mechanically proceed from an input state, its initial conditions, to an output state.

But the brain is not that kind of computer. So it is neither physically deterministic (as no physics is that in the LaPlacean sense), nor is it computationally deterministic.

Thus "freewill" just isn't a real ontological problem. There is no metaphysical conflict. (Unless you are a dualist who believes "mind" to be a separate substance or spirit-stuff. And of course there are many who take that essentially religious view still. But for psychological science, there just isn't an ontological-strength problem.)

Your complete misunderstanding and lack of comprehension of category theory and mathematical structuralism was evident to several other posters the last time we discussed this. — fishfry

Here we go. You and your circle of imaginary friends.

I'm done responding to your posts on this site. — fishfry

Funny. I was waiting for you to start.

I did not write the quote you attributed to me. What is your attitude problem? — fishfry

I get a bad attitude pretty fast when someone like you plays cute with a quote. If you leave off the important part of what my sentence said, that is flat out misrepresentation. Expect a swift kick in the arse.

Nobody has provided a counterexample and you now seem to agree. — fishfry

Keep trying the same trick. You are looking worse and worse.

If you choose category theory as your foundation, there's still no general definition of number. — fishfry

Your inability to discuss the foundations of maths is noted.

"You" is in reference to your person. Your self, comprised of your body and everything in it. This isn't something I should have to explain. — JustSomeGuy

Unbunch your panties a little. If you are going to talk about this "you" who decides to push the button, you have to have a proper theory of what constitutes this you. Your hand-waving approach is not good enough for philosophy or science.

Again, this is all just restating what I already said. — JustSomeGuy

Yeah. But minus the hand-waving. So with the missing rigour.

DNA, as I already stated, is the origin of these "programs". Your DNA determines the "code" for your brain and how it processes things. And what wrote this code into your DNA? Nature. Evolution. — JustSomeGuy

Yeah, nah. If you are talking about this mysterious self that runs the show (according to folk psychology), then the full story has to bring in the several levels of semiosis or code.

So yes. There is the DNA and its evolutionary history. But then there is the neural code and the brain's developmental history. And with humans, our linguistic code and its cultural evolutionary history.

Don’t be a dick and misquote me.

I said you seem to think that a definition would be in terms of the mathematical objects involved, and not the structure of relations needed to produce them via a holistic system of constraints.

A reply that makes some contact with the relevant philosophy of maths would be appreciated if of course no longer expected.

Good idea and a very natural attempt; but arithmetic properties aren't sufficient. Weirder still, there are numbers that lose associativity as well, such as the octonions. — fishfry

Wasn't that my point. You can still be a numerical object even if you don't qualify for the full checklist of arithmetic properties. So the octonions lack a particular property. But they still count as part of the algebra family which takes numbers as their relational objects.

It probably helps that we can see why octonions lack this further constraint. We get the feeling they would express this property if only they could, as that is the general direction they are headed. But their own nature prevents fulfilling that goal. Therefore they qualify to be part of the family even if they can't tick every last box of some ideal definition.

Do you know much about Bourbaki structuralism - the three mother structures of algebra, topology and order - or category theory structuralism?

As I've been saying, you seem to want a definition founded on the mathematical objects rather than the mathematical relations or structures. But that just seems an antiquated notion.

And what is true in philosophy of maths is true of metaphysics generally. Nature is becoming understood in terms of its global structure rather than its local atoms.

That has been the recurring sticking point in any discussion we've had. You just presume the correctness of a reductionist or atomistic metaphysics. You then seem to have no understanding of the alternative view that is that of the structuralist, process philosopher or systems scientist.

In short though, mathematical structuralism is more subtle than just listing arithmetic properties like associativity.The kinds of properties that they use in category theory are ... well, they're kind of weird and nonintuitive when you first see them. The structural relations they have in mind are various types of universal mapping properties. It's hard to do justice to what this means in a simplified format but I might take a run at it once I get into responding in detail to your earlier post on structuralism. — fishfry

Maybe just focus on that. Structures are the objects now. Then morphism is how structures have a relational structure that allows acts of mapping.

So the essential property that founds the whole business is closure or symmetry. Hey, just like physics!

(And then I should add that the fundamental question becomes how could closure emerge? What constrains the openness that seems the alternative?)

I'm not sure what you mean by "next physical state", but the "program" in my example would clearly be the software in yours. — JustSomeGuy

Well you were replying to the point that I made about freewill being problematic because of the LaPlacean implications of Newtonian determinism.

So if physicalism is just about "hardware", then there is a problem. And the computational analogy is a way to show that the physics of matter doesn't get to control everything. There is also the physics of information.

So yes. The program determines its own next physical state. The hardware doesn't. Unless the circuits start misbehaving due to stray cosmic rays or something.

It's not a "folk psychology misconception", it's just how we talk about these things. It has to do with language, that's all. I think you're the one getting dogged by being nit-picky about language. — JustSomeGuy

So now you want to complain about introducing the philosophy that motivates the common conceptions? Are you in the right place?

Using the computer analogy, if you're running a program on some hardware, that program has to be pre-written to follow certain parameters and do certain things, and everything it does is a result of the program's code. Even if you bring artificial intelligence into it, a program that can learn, it still does everything it does based on the initial code you wrote. Every "decision" it makes is a direct result of following this code. It is all determined by the code (as well as other environmental/outside factors). — JustSomeGuy

Yeah. So now let's again talk about this mysterious "you" you keep wanting to introduce into the scientific or natural philosophy account.

Sure, the formal and final cause of a "program" do come from outside it. It has to be written with a certain design that serves a certain purpose.

The program itself is simply a pattern of material/effective causal entailment. A set of instructions that maps one physical machine state to its next. So that is why computers are only a weak analogy for the neuroscience. It is information processing without the designer or intender.

Actual neuroscience needs to account for that other bit of the puzzle. How and why does the nervous system "write its own meaningful programs"?

To cut to the chase, that is where I would bring up Peircean semiotics and other current neurobiological conceptions of what is really going on with a mind that has "a self that can form plans to meet goals".

To use the computer analogy, does the hardware determine its own next physical state or is it the software that determines that?

Point being, if your brain's processing and decision making are a product of this program, they do what they do automatically, meaning none of your decisions are true decisions because you could not possibly make a different decision than the one you make. — JustSomeGuy

Yep. So now we have to understand information processing as something more interesting than Turing universal computation.

Also note that you insert this "you" into your questioning as if there really is some dualistic mind-stuff or spiritual element - a res cogitans. So already your metaphysics is presuming a supernatural ontology and abandoning any hope of a properly naturalistic one.

Is this "you" you want to claim the whole of me? A part of me? Do you want to identify your essential being with your attentional-level processes and so exclude your habit-level organisation - all the accumulated wisdom of past attention-driven learning? Is that other half of you some robotic, unthinking, not-you that somehow shares "your" body?

Philosophy of mind is dogged by these kinds of basic folk psychology misconceptions. They are grounded in theology rather than science.

You are talking rubbish and I am probably one of the few people here who can see straight through you. — TimeLine

If you think so, then make your case properly. Don't waste my time with ill-written rambles.

This is the third time I am going to ask you:

What is this "humongously" large you are speaking of? What are you comparing it to, exactly? — TimeLine

Well in comparison to the light cone of our visible universe obviously. It has to be at least several times bigger for our own light cone to look equally thermalised in all directions. The famous cosmic background radiation.

And the original inflation story - not the one Linde is pushing that is the subject of the OP - speculated the extent of the scalar field would double every 10^-37 seconds or so. That was its exponential rate of growth. So presuming the decay of the grand unified field into the strong and electroweak fields happened at 10^-35 seconds after the birth of the universe, thus triggering the onset of inflation, followed by the further decay of the inflaton field by about 10^-32 second, then you could easily get 50 to 60 doublings into that fractional period.

So old school inflation says the visible universe is just 10^-55ish of the whole shebang. Hence the whole is "humongously larger", but not infinite, to use the technical description for that cosmic scenario.

The idea in inflationary terms is that the total energy at the beginning was 0 where the negative contribution to the energy of the cosmic gravitational field - as in gravitational repulsion where the energy density produces these gravitational fields - cancels the energy of matter or the positive energy. Inflation thus becomes eternal because as mentioned earlier the matter is being created by the inflation but controlled by the non-uniformity. — TimeLine

You see how right from the beginning you were mangling the science. The free lunch story is that the kinetic mass of the universe nicely balances its gravitational potential. So the energy to drive expansion is matched by the energy wanting to re-collapse that expansion. However, gravity is held in suspension until the electroweak symmetry breaking releases a flood of gravitating particles via the Higgs mechanism. It is only then that the potential is actualised and collapse becomes a real issue. Mass can start to clump and unbalance the expansion.

So story one is inflation-less. You have a positive inertial expansion due to an initial energy density vs a countering negative gravitational contraction. To have then a flat outcome - a universe cruising towards the halt of a heat death at the end of time - these two tendencies have to be miraculously balanced from the first Planckian moment. And astronomical observation then found a lack of the necessary mass vs gravity balance. There wasn't enough mass to achieve the necessary amount of gravitational braking we could observe in a universe that looks as flat as it does. So Houston, we had a problem.

Then came inflation theory. Even with a perfect initial balance, there would still be the inevitable inhomogeneities of mass density due to quantum fluctuation. Something further had to kick in soon after the Planck scale birth to stretch the universe so big and flat it couldn't immediately collapse due to that.

On top of all that, dark energy was then discovered. That looks like a remnant inflation field - a faint continuing extra acceleration laid over the top of an under-weighted inertial expansion due to a "too thin" initial mass density. So some kind of inflation still rescues the general "Omega" picture of a perfect balance between the positive energy of inertial expansion and the negative energy of gravitational collapse. Counter-intuitively perhaps, the faint dark energy repulsion counts as a pervasive presence of an energy of pressure. And as energy has gravity, the missing gravitational braking could now be supplied to achieve a flat balance and arrive back at where we need things to be.

So you have managed to smoosh at least three separate cosmological stories into one garbled paragraph.

And luckily I'm one of the few people here who can see straight through that. :)

If inflation is pushing omega to 1 with omega being the mass density divided by critical mass density, it means a universe with 0 matter density and critical mass density in the cosmological constant; the expansion of the universe is accelerating and the vacuum energy of this empty space has a mass density (which would mean that it is not actually empty). So Omega is relevant. — TimeLine

Inflation doesn't push omega anywhere. It washes out the early fluctuations that would have destabilised the show. So the problem is that overall, on average, the Big Bang could have had a perfect flat balance of omega = 1, but quantum fluctuations would have made it grainy. So it would have been unstable due to inhomogeneity. You need inflation just to deal with that separate problem.

Your own citation says this - carefully distinguishing between omega(m) and omega(lambda), or the critical density of the mass contents and the critical density of the dark energy:

Clicking on the graph shows that (nearly) all universes start at the Einstein-de Sitter point with Omega(m) = 1 and Omega(Lambda)=0. This is because if there is a Big Bang (R goes to zero) the density, hence H, hence the critical density, all tend to infinity at R = 0. So Omega(Lambda) tends to zero, while the matter density tends to the critical density.

Whoah, you are a cranky one. But really, your posts on cosmology are a garbled mess. And being polite to you was clearly wasted breath.

But the freewill deal is the fear that our decisions might be physically deterministic. So as soon as you view the brain in information processing terms, that issue is already dead.

The issue after that concerns people’s dualistic take on conciousness. So they want awareness to be something above and beyond the meat machinery of habit and attention.

Yet that again is to fail to understand an information processing functionalism.

So it is just science vs folk confusion. And the experiments aren’t great as they buy into the confusion.

If you just want to study the neurobiology of voluntary control, that’s what you should do as a scientist. And that’s what the mainstream does.

Sorry. Your post is a torrent of incoherence. I can’t be arsed untangling it for you.

I’ve not heard of sleepwalkers doing anything novel or useful. So no. It is just being awake enough to react automatically to familiar cues.

And to sleepwalk more than a few moments would only happen in adults with a neurological condition or in kids with, presumably, less developed habits of conscious self regulation.

As far as these experiments tell us anything about free will, they really should be seen as part of a continuum of study on the neurological markers of decision making processes, rather then in isolation. — Pseudonym

Yes. I’ve been following this story since the 1980s. The important thing is that the subjects are always fully conscious of the experiment’s demand to “let an impulsive choice surface”. And surprise, surprise, we can choose to do just that. We can disengage a sense of oversight.

Readiness potentials were uncontroversial when Kornhuber and Grey Walter reported them. They slotted nicely into the dominant behaviourism of the time. But then Libet came along with his dualistic agenda and managed to create a little sensation in philosophy of mind circles.

So it’s all social history as much as science. ;)

I think you just want all the glory or something, hence why you are trying to answer questions directed to me. — TimeLine

My goodness. Is that what it is about? Hilarious.

Your shape and size of the universe is the observable universe of 46gly from earth and just to help ameliorate your understanding, the singularity - whilst it does not reference a single planck point - is a physically impossible point that we use to explain how the universe came to be. So the assumption is that the early conditions were infinitely dense at the size of 10^-28cm (with energies at 10^16 GeV) and that would mean that anything larger or smaller would blow the universe apart or suck it away — TimeLine

Who mentioned singularities? I didn’t. And what is the relevance of a length scale 100,000x the Planck length? I’m not following you at all. This is another series of irrelevancies.

What? First of all, inflation is pushing omega to 1 and the asymptotic curvature would therefore be flattened by the expansion, thus the curvature would equal 0 or at least be very close to 0 and this would cause infinite expansion. The symmetry between these points is explained by fluctuations in the anisotropy of the cosmic microwave background and so the universe is isotropic and homogenous; the best way to explain thermal equilibrium (actually the only as far as I know) is inflation. — TimeLine

Inflation doesn’t have to balance the kinetics of its expansion with its gravitational attraction. So an Omega balance is irrelevant. Inflation is about a scalar field that stays the same energy density while expanding exponentially. Repulsion dominates and gravity is simply impotent.

You are mixing up quite different things.

In sleep, you don’t form long term memories. And also there is a dissociation, or lack of integration, more generally. That is why in dreaming sleep, what you are thinking about your dream imagery has only a loose connection to that imagery. You are making up some kind of story, but it doesn’t closely follow “the facts”.

Thus in sleepwalking, you can be semi awake with some confused intentionality that has some very loose connection with the facts, and yet quite capable of acting with awake levels of habit. Some sleepwalkers have got in cars and driven miles.

So the attentional level of forming intentions and remembering consequences might be dazed and confused. But habits just need the eyes open and the body awake enough to respond automatically to a world of familiar clues.

There is this great tale of A.A. Gill cooking elaborate meals during alcoholic blackouts. A similar story... http://www.esquire.com/food-drink/a46904/a-a-gill-memoir/

Huh? You do write weird. I asked what difference did your comment make. I did not say your comment was no different. So I was saying your comment was a non sequitur as far as I could see as it did not follow from mine in any useful or relevant fashion.

But if you think it did qualify my remarks in some meaningful fashion, could you explain in what way.

You will have to explain why your comment makes any difference to my comment.

Observation says the geometry is almost perfectly flat with just enough hyperbolic curvature to count against any gravitational collapse (and so any reheating of the universe and its contents).

Thus I don’t understand what you are getting at here.

It seems that, by current findings, big bang inflation + expansion does not account for the spatial extent of the universe. — jorndoe

Inflation definitely does. But then inflation is hardly a proven story. And also inflation can produce as big a common starting point as you like. Just leave inflation running a few more ticks of the clock and you get exponentially more growth.

So inflation is a free parameter. You can just dial it up as much as you need.

Then the eternal inflation article you referenced is another story again. It presumes inflation keeps happening forever and keeps spawning an unlimited number of big bangs. Ours is just one infitesimal region of the inflation that has cooled and slowed enough to bud off. There would be an unlimited number of other similar universes being created.

So the eternal and infinite version of inflation depends on an inflation event that spawns an unlimited number of big bangs. Ordinary inflation says our Big Bang suddenly took off and inflated a split second after it was first born. It wasn’t born inflating, but then inflation came along to make the universe sufficiently big and ensure that any local wrinkles were smoothed out and make the whole thing look as if it started off as perfectly flat and thermalised as possible.

So either inflation is eternal and we are a spot that dropped out of its exponential rate expansion with no cooling, to be a Universe with a steady rate expansion and cooling. Or inflation kicked in just after the Big Bang for a split second, which would still be enough to stretch out and flatten spacetime as far as the eye could ever see.

When we say "infinite" do we mean infinite volume or infinite mass? Both? Or something else? — T Clark

It would be both. For those arguing for an actually infinite extent, it would be just as unexpanded at every point, and so just as maximally dense and hot at every point, hence just as massive or energetic in its "explosiveness".

But as I said, any such extrapolation from our rather classical view of the Universe - one in which distances and energies have some relative value - really becomes quite moot if we are talking about an initial conditions where there just is nothing for distance and energy to be relative too, as yet.

So the infinity of the initial conditions would have to be infinite in some more general sense that we aren't good at describing in classical terms. A theory of quantum gravity would probably help that ... if not rely on that kind of re-conceptualisation.

My remark is entirely agnostic of foundational approach, a point apokrisis does not sufficiently appreciate.

There is no general definition in math that tells us what a number is. — fishfry

Or maybe I'm just pointing out that the idea of "numbers" speaks to a family resemblance. No single definition could hope to pin down "numbers" in some exact sense. But there is a constraints-based definition, or a structuralist definition, in that numbers are whatever it takes to get certain number-like operations - like those that preserve certain global symmetries, such as commutativity or associativity.

So you wouldn't expect a hard and fast definition of something general. As a foundational fact, all we can talk about is a family resemblance which emerges as we enforce greater and greater constraint in terms of bounding symmetries. Then in the limit, we arrive at associative division algebras.

So the octonions are not associative but they answer to the weaker constraint of being alternate. They still deal in numbers, but a slightly less constrained version.

The general definition is thus inherently fuzzy. The most highly constrained or specified kind of number system isn't broad enough to capture the weaker kinds that are possible with some of the constraints relaxed or even absent. And yet at some point the "general definition" is so weak that it doesn't then capture the essential operations that do define being part of that general family.

This is a familiar issue when framing scientific law. Philosophy of science says exactly the same thing.

So you may be agnostic about foundational approaches. But philosophy of maths can't afford to be. And I think the same understanding of the trade-off between the general and the particular applies across all the rational disciplines.

You are simply looking for the wrong kind of "general definition". Structualism is needed because that focuses on generic relations of which numbers then can be the various possible kinds of object.