But perception is the result of something acting upon us, as well as us acting upon what acts upon us, and what we seem to perceive is not necessarily precisely the same as what is acting upon us. — Janus

This is because classification involves judgement, that may err, while experience does not. There is a many-to-one map from types of causes to types of experience. E.g., the experience of snakes might be due to reptiles or alcohol.

dimensionally diminished mapping. — Dfpolis

Can you explain this, though? — Noah Te Stroete

Carnap has a model in which the yes or no answers to logically independent questions define different dimensions in the vector space of knowledge. While I see problems with his model, I think it can be a useful analogy. (Also, it can be used in conjunction with Shannon's notion of information.)

So, when we look at the front of a house we have a projection that answers certain questions, and leaves others (e.g. those about the back of the house) unanswered. Thus, our experience spans fewer of Carnap's dimensions than exhaustive data on the house would.

Are hallucinations real? — Galuchat

Yes. They are real experiences potentially informing us of the reality of some neurological disorder. — Dfpolis

So, they are an encountered experience type of experience potentially informing us of the encountered experience of some neurological disorder.

This is nonsense. — Galuchat

That is how implication often works. It allows us to move from the data of experience to new realities, many of which are available to experience. For example, Jane has a hallucination and seeks medical help. The doctors may do blood tests and MRIs to seek the cause. That is medicine, not nonsense.

My point was that while the form of these is different, their matter is the same. — Dfpolis

This makes no sense to me. The first is just a tree. That's all it is phenomenally. The second is phenomenally the tree plus phenomenally the notion of a self, an I, the notion of a perception (or if you want to say a judgment). — Terrapin Station

The tree in the first instance does not simply exist, it exists in relation to me. I can change my relation to it by doing things to myself, not to the tree. So, encountering a tree is loaded with intelligibility about myself:
- As I can change my relation to it, there is a relation to be changed, and thus relata which I choose to name "the tree" and "myself."
- I have encountered the tree, so I am a being with the power to encounter other beings. I can call this kind of encounter "experience."
- I have the power to receive content in experiences and call this kind of receptivity "subjectivity" and so see myself as a subject in relation to a tree object.
- Etc.

All of this allows me to tease <I am perceiving a tree> out of the encounter with the tree. The essential point is than an encounter is not a concept. I can't tease any of the above out of the bare concept <tree>, but, since an encounter is a dynamic relation, I can tease much out of the dynamics present in it.

Once you question realism, you slide down the rabbit hole of solipsism, and there is no such thing as a middle ground (ie. idealism). — Harry Hindu

I think this is right.

Are hallucinations real? — Galuchat

Yes. They are real experiences potentially informing us of the reality of some neurological disorder.

Does it make sense to you that "(Just a) tree" is different than "I am perceiving a tree"? — Terrapin Station

Yes.

So the experience (again, I was trying to avoid that word--we could just say the phenomena) of:

<<(just a) tree>>

would be different than the experience (phenomena of):

<<I am perceiving a tree>> — Terrapin Station

Yes. The first is an experience of a tree, the second the experience of making a judgement about experiencing a tree. My point was that while the form of these is different, their matter is the same. The judgement adds no content. It only actualizes content already present.

What is objective reality, and does it require subjective reality? — Galuchat

Reality is "objective" to the extent that it can enter into the subject-object relation of knowledge, which is to say insofar as it is intelligible. It can be intelligible without being actually known by a subject. So, we know that there is objective reality when we actualize its intelligibility, but our knowing is not a condition of its existence.

My apologies. I am trying to understand you.

I would say that we try to model reality, — Dfpolis

Granted, but what is a model but a construct? — Mww

Models mix abstracted and constructed elements. They are not pure constructs or they would have no relation to the reality modeled. When we combine divers abstracted projections of the same reality, there are invariable gaps because no human understanding is exhaustive, so we fill these gaps with constructs that may not even be consciously added.

Whether model or construct presupposes that which is its cause, which in its turn presupposes a necessary displaced orientation of it. — Mww

I do not understand this sentence. What does "a necessary displaced orientation of it" mean?

That is, because it is reason modeling, the cause absolutely must be oriented exclusive to reason — Mww

Our reason is intentional (manifesting "aboutness" per Brentano). Thus, it points beyond itself.

knowledge of the model cannot be distinguished from knowledge of the cause of the model — Mww

As I explained above, models combine abstracted and constructed elements. Since we can distinguish them, we can differentiate what we add (what occurs in the model, but not necessarily in what is modeled) from the portions of the model abstracted from reality. So, there is no need for epistemological dualism.

But give to his sensibility something for which he has no ready conception, he should be all the more surprised by what little he really knows. — Mww

I agree we know precious little and should always be open to surprise.

whether sometimes the phenomena that are present aren't simply things like trees, rivers, etc. — Terrapin Station

Of course. Sometimes they are experiences of reflective thought, meditation, dreams, pains and joys, etc. Over time we learn to divide the content of experience into "self" and "other" categories. How this is possible is a profound open question in my view.

This is to say that the phenomenon present sometimes is not but simply a tree. — Terrapin Station

I would not call "I am perceiving this tree," a phenomenon, but a refection on a phenomenon. The tree presents itself, is apprehended (or not). Then, we can stop to reflect on the experience, or not. Quine's analysis of introspection in the Concept of Mind is deeply flawed. We don't have separate awarenesses of the tree and of ourselves perceiving the tree, but a single awareness that can be reflected upon and articulated in various ways. Aquinas understood that we come to know our intellectual powers not in se, but in actu, i.e. by reflecting on what we do.

In other words, there's no conscious notion, awareness, etc. of perceiving something per se (or of conceiving, etc.) There's just a tree. — Terrapin Station

I agree that often the intelligibility of the knowing subject is not actualized. Still, the knowing subject is always intelligible in acts of awareness. Awareness makes no sense absent a subject being aware.

If it's the case that the phenomenon present can sometimes just be the tree, then the phenomenon present on that occasion will not be "I am perceiving a tree." So, for those occasions, "I am perceiving a tree" is doing something theoretical (as I'm using that term) that isn't present in the phenomenon it's about. — Terrapin Station

This misunderstands "I am perceiving a tree." It is not a phenomenon, but the result of actualizing/articulating intelligibility already present in the perception of a tree. So, if you see theories as adding content, that isn't happening here. Theory theory is wrong.

"Reality" first means what we encounter in experience... — Dfpolis

I'm waiting for the other shoe to drop.
IOW, is there a second, third, fourth (etc) elaboration of the meaning of reality (what we encounter in experience)? — Galuchat

Of course there is. We call these shoes philosophy and natural science. In my view, the goal of philosophy is to provide us with a framework for understanding the full range of human experience. Natural science seeks to discover general principles for understanding objective reality in abstraction from the knowing subject.

I had a hard time parsing his statement.

This requires a more in depth discussion to distinguish the differences. — Noah Te Stroete

Feel free to ask for clarifications.

Yes, trees are often just present — Dfpolis

Sure. So going from that to "this is something I'm perceiving" etc. is theoretical, isn't it? That is, it's literally invoking a theory about what's going on. — Terrapin Station

...

"Theoretical"--basically in the sense of reasoning about something, coming up with an account of "what's realy going on" contra the phenomena in question, etc. — Terrapin Station

I think it is naming, not theorizing. In what way does "this is something I'm perceiving" go beyond our experience? I think Maritain's analysis is on point. He sees us as mentally dividing in abstraction, and then joining what was divided in the act of judgement.

So, here we are aware of the integrated act of my tree perception; seeing in it mentally separable notes of intelligibility (<this> and <something I'm perceiving>); and finally seeing that these notes are not actually separate, but both evoked by the identical unity, judging <this is something I'm perceiving>. The copula "is" betokens this identity of source.

So, there is reasoning going on -- specifically mental separation and reunification, -- but there is no new, constructive element being added.

It is not an account of "what's really going on." For that you have to wait for something like Aristotle's analysis in De Anima iii. All the judgement is doing is explicating a unified experience.

The point is that phenomena that are present aren't actually always of one as a conscious being experiencing things. The only way to move away from realism with respect to experience is to introduce theoretical explanations for what's really going on. — Terrapin Station

I have no desire to move away from realism. I think you're confusing realism with naivete.

Minor distinction, perhaps. I consider projections of reality our expressions about it. Reality itself is that which is given to us. Reality comes in via perception, projections go out via understanding. — Mww

To me a projection is first some aspect of reality existentially penetrating us -- projecting itself into us -- and second, our fixing on some part of that presentation and projecting it into our conceptual space. Each of these steps is represents a potential loss of content and so is a projection in the mathematical sense of a dimensionally diminished mapping.

Thank you, both. — Noah Te Stroete

You are welcome. The term was "radiance of action."

I support different projections of reality, but adhere to the thesis that because there is some general empirical data, re: experience and therefore knowledge, potentially common to all rational humans, reality in and of itself is most probably one iteration of all those various and sundry individual projections. — Mww

I am not sure I understand this. Are you saying, that as a projection, reality is a construct? That seems odd for an empiricist, for to be an empiricist, one must stand ready to be surprised by reality, and our own constructs have a hard time surprising us.

I would say that we try to model reality, and the more projections we incorporate into our model, the more adequate to reality it will be.

Calling it “instinct” or “innate knowledge” is splitting hairs in my view. — Noah Te Stroete

What are they aware of? Not some intellectual content, but a desire. In a sense it is knowledge, but not in the same sense that awareness of intelligibility is.

is there knowledge that can come from something other than sense data, or that doesn’t have as its foundation, sense experience? — Noah Te Stroete

After reading W. T. Stace, I started taking mystical experience seriously. I now think it is veridical, but not (usually) informative. It is veridical in that it is exactly what one would expect from an experience of God, but not informative because God is unlimited and information is the reduction of possibility. I think that a few mystics, such as John of the Cross, have grasped empirical reality via their awareness of God, but that this is extremely rare.

My other question is: in the case of JF Nash, he had insight into his illness. Someone else may not have this insight. Does someone who hallucinates and doesn’t recognize it not have useful knowledge of reality? — Noah Te Stroete

I don't know that "useful" is a relevant criterion for knowledge. I would say that if you don't know you are hallucinating, you could learn to recognize it, as Nash did, but in the meantime, you will be holding false views.

For example, how does a baby know how to suck on a bottle? Isn’t this an example of innate knowledge? — Noah Te Stroete

It is an example of instinctive behavior. If the child were old enough, it could know that had such instincts. I do not think that we should confuse behavioral propensities/desires with knowledge. For example adolescents have a sex drive, but not an innate knowledge of the mechanics of intercourse. It is rather that the things they want to do will get them there.

The "God's Helmet" experiments could not be replicated and are now considered debunked (by researchers in Holland, if memory serves -- I wrote about it in my book). The "results" were explained by suggestion.

But, supposing we had such a propensity, we would learn of it when we experienced its activation -- just as male transsexuals learn that they are "girls." Many people see religious behavior as a reflection of such a propensity.

My question is: is this empiricism, rationalism, or neither (such as in Kant’s view)? — Noah Te Stroete

The argument is mine. I'm a moderate, Aristotelian-Thomistic realist, who thinks that we can have different projections of reality, which is to say that we can represent the same reality using different conceptual spaces.

If there is no data outside our experience we are presented with two absurdities, 1.) we should know everything because all the experience we have is all the data there is, or 2.) data and experience are congruent which would force the impossibility of misunderstandings. — Mww

1. I have not assumed or implied that our experience exhausts being. I have only said that our concept of reality begins with what we experience. ("'Reality' first means what we encounter in experience.") We say "seeing is believing," not because seeing is exhaustive, or even inerrant, but because our concept of reality begins with things that can act on us in experience. I left out that we expand the extension of our concept of reality (being) far beyond this humble beginning because I was discussing the relation between experience and reality.

I think the problem is that we are not defining "data" in the same way. I am defining it as what is experienced, not things that could be experienced or known indirectly. You seem to be defining it as what we could know. I agree that\ much more is intelligible than we actually know, than our actual data.

2. I agree that being is not fully congruent with human understanding, but I think every experience is caused by an existent adequate to cause it. Our errors of understanding are due to misjudging/interpreting/classifying what we experience -- not to mis-experiencing. The adequate cause of my experience might be a neurological disorder -- and in time I might learn to recognize it for what it is. (As John Forbes Nash did.) Usually, the cause of my experience is just what I judge it to be.rly.

Be that as it may, I accept the gist of what you’re saying in the OP, so my little foray into the sublime can be disregarded without offense. — Mww

Even misunderstandings are opportunities for both parties to learn to communicate more clearly.

es, trees are often just present — Dfpolis

Sure. So going from that to "this is something I'm perceiving" etc. is theoretical, isn't it? That is, it's literally invoking a theory about what's going on. — Terrapin Station

It depends on how you define "theory." If you mean a hypothetical structure, then, no, it is not a theory. If you mean a way of organizing experience, then yes, noting that certain things (trees) are equally capable of evoking the concept <tree> does organize our experience.

So far we seem to share similar views, though I would not mix modes of neural response with modes of intentional response. (Not that I think that intentional response is independent of neural processing. I don't. Rather, they depend on different kinds of analysis, and if we are dealing with the question of realism, we have a lot of ground to cover before we can justify neuroscience.)

I am sorry that we have not been able to resolve our differences.

If one is positing that one has a body and is perceiving things via one's senses, etc., then one is already assuming realism, by the way. — Terrapin Station

I don't think we start by positing that. Rather we seek to organize our experience by classifying it, and in doing so we come to concepts that include our body. We come to understand things in terms of objects (ostensible unities) that persist and learn the conditions under which we can and cannot encounter them. It is out of such considerations that we develop notions of body, senses and sensible objects.

This is one reason the question of whether it's always the case of not just "tree" but "I'm conscious of a tree" (see my post above) is important. — Terrapin Station

You will need to expand on this, as I don't see your point. The center of our subjectivity is not given as material and so not as a body.

Excuse me for not quite seeing your point. I was not suggesting we really stop thinking, only that all the content we think about is experiential. So, if we were not thinking of content traceable to experience, we would have nothing to think about.

"Data" means what is given, and it is given exclusively in experience. I do not see any other way for there to be data. We even find out about our innate capabilities/propensities in the experience of using them. If, for example, I had an innate fear of 8-legged things, I would find out in experiencing my response to one -- and not as a priori content independent of experience.

I don't think that reflective thinking is the means of experience. I think that reflective thought is how we seek to integrate experience into a comprehensible whole.

Please forgive me if I missed your point.

If I make:
1) Reality synonymous with actuality,
2) Experience an awareness event, and
3) Awareness a perceptive and/or cognisant condition,

have we made similar assertions? — Galuchat

It depends on how you explicate your terms.
1) What does "actuality" mean to you? Is it accessible, or quarantined?
2) Are you thinking of "events" as disjoint, or simply points in a continuum we happen to be fixed upon? And, how do you conceive awareness?
3) By "Awareness" i mean what makes intelligibility known. So, it rises above sensory perception in that we can perceive and respond in complex ways without being aware in the sense required to know.

If I've over analyzed what you said, forgive me.

For example, it's never for you just that there's a tree, say. It's always that you have something like "I'm a conscious entity, aware of a tree" present? — Terrapin Station

For example, it's never for you just that there's a tree, say. It's always that you have something like "I'm a conscious entity, aware of a tree" present? — Terrapin Station

Yes, trees are often just present. Often they are not even identified. It is only when we fix on this or that aspect of experience that we distinguish trees and even ourselves as subjects. We are aware of the whole complex, but that does not mean that we have focused on any aspect of it so as to conceptualize/categorize it.

Here is the problem in a nutshell. You refer to your "analysis" as if it is not based on your own dogmas and beliefs. The fact that you indefatigably argue them demonstrates nothing more than your willingness do so. — Fooloso4

I have explained how ere abstract concepts such as that of number from the realization that counting does not depend on what we count. You have not shown that this is an inadequate explanation of our natural number concept.

Seriously, this impossibility of self-inquiry is an enormous flaw in the scientific method. — alcontali

I think the flaw is seeing the scientific method as the only acceptable means of inquiry. In its proper domain, the scientific method is fine.

I would simply say that one can't deny this without twisting the meaning of "reality" as what is revealed by experience. — Dfpolis

This is really a fundamental point. What you're arguing is British empiricism, per Locke and Hume. — Wayfarer

No, I am not. I am arguing Aristotelian moderate realism.

But does sensory apprehension qualify as 'revealed truth'? Certainly through scientific method, we can discover truth, but the assumption of the 'reality of the given' is precisely what is at issue in philosophy. — Wayfarer

Experience is the data we have to work with. One can either work with experience, or one can simply cease thinking. The scientific method does not get one past this, as all it does is compare hypotheses to experience. Whatever you think reality is, experience is how we humans relate to it -- and we can only deal with it as we relate to it.

We do not and cannot have omniscience, so it is a trap to make omniscience the paradigm case of knowing. "Knowing" names a human activity. So as soon as you say "we do not know," you are abusing the foundations of language. "Reality" first means what we encounter in experience. So, if you say "we do not experience reality," you are again abusing language.

When you make "reality" mean more than, or something other than, what we encounter in experience, you are creating a mental construct. If you create that construct, and then claim that what you have constructed is inaccessible, you have said absolutely nothing about what we encounter in experience.

Doubt is an act of will. I can will to doubt anything, including my own consciousness, as eliminative materialists such as Dennett have chosen to do. What one cannot do is eliminate what we experience. We experience ourselves as subjects and everything else as objects. I know what I experience and no act of will, no doubt, can make me not know it.

Of course, I may misinterpret what I experience. I may think the elephant I experience is in nature rather than the result of intoxication. Still, if I did not have experiences I know to be veridical, I could not judge others to be errant.

the assumption of the 'reality of the given' is precisely what is at issue in philosophy. — Wayfarer

Only in post-Cartesian philosophy. The focus of pre-Cartesian philosophy was and continues to be being.

Again I'm no Aquinas scholar, but I think I grasp some of the rudiments of his hylomorphism, which says that — Wayfarer

What you quoted was a "difficulty" or objection Aquinas intends to resolve, not his position. His response is:

Although bodily qualities cannot exist in the mind, their representations can, and through these the mind is made like bodily things. — Aquinas De Veritate

And this is because, in the view of Christian philosophy, material things have no intrinsic reality; creatures are, as Aquinas' Dominican peer Meister Eckhardt said, 'mere nothings'. — Wayfarer

Eckhardt's is not Aquinas view. He sees material things as real and intrinsically good, as does Gen. 1, which sees God as judging each stage of creation as good.

Corporeal creatures according to their nature are good, though this good is not universal, but partial and limited, the consequence of which is a certain opposition of contrary qualities, though each quality is good in itself. To those, however, who estimate things, not by the nature thereof, but by the good they themselves can derive therefrom, everything which is harmful to themselves seems simply evil. For they do not reflect that what is in some way injurious to one person, to another is beneficial, and that even to themselves the same thing may be evil in some respects, but good in others. And this could not be, if bodies were essentially evil and harmful. — Aquinas ST I Q 65 Art 6 ad 6

I think it's more likely that you're misunderstanding Kant. — Wayfarer

If Kant is saying that we can know noumenal reality, but not exhaustively, I have indeed misunderstood him. I do not think he is saying that, do you?

And how do we come to posit the parallel postulate, if, according to you, it is not an abstraction from reality? — Fooloso4

You seem to have forgotten the OP, where I used it as an example of a hypothetical postulate. It is derived by assuming that our small-scale experience with parallel lines can be extended to infinity.

Its negation is not an abstraction from reality either. Both, however, have their application in reality. — Fooloso4

Whatever we know can be truly applied to reality can be abstracted from reality. We do not and cannot know that the parallel postulate is true because our experience is finite. We can only know if the space-time metric is approximately Euclidean.

We can abstract non-euclidean geometries from spherical and saddle shaped surfaces.

It is not a name assigned to a ball that came to exist independent of the game. It is the name of a ball specifically designed and made to be used to play the game of baseball. If not for baseball the ball would not exist. — Fooloso4

I agree with all of this, The point is that none of it, including the name, is intrinsic to the ball.

---

First, by derived I mean abstracted. — Fooloso4

When intelligibility is abstracted it ceases being potential and commences being actually known. The whole point of intelligibility is that it is potential, not actual, knowledge.

Second, if the mathematical structure is in nature but that structure is knowable without being abstracted from nature then there is reason to think that structure might be independent of nature. — Fooloso4

I do not understand this at all. If it is in nature, there is no reason to think that it is not intrinsic to nature. Green leaves are in nature and intelligible. Does that mean they also have a Platonic existence independent of nature?

With regard to Zeno, it is the divisibility that is infinite. — Fooloso4

Yes, the potential to divide a continuous span is unlimited; however, any actual division is only finite. As we can only know what is actual, we cannot know anything infinitely divided. (Imagining an infinitesimal is not knowing it.) As I told you earlier, this is the reason for all of the epsilons and deltas in the definitions of calculus -- and it was to see those types of definitions that I referred you to a calculus book.

With regard to infinitesimals the quantity is smaller than can be measured. — Fooloso4

The question is not measurability, which is one for physics, but of being finite or not. Any actual quantity quantity greater then zero is finite. If we use '0' to define the concepts of calculus, they will be indeterminate. So, we us the limits of finite quantities tending to zero.

First, Zeno's paradox is not something abstracted from nature. — Fooloso4

I did not claim it was.

Second, both Newton and Leibniz used a concept of infinitesimals that was not abstracted from nature given that the infinitesimal is not measurable. — Fooloso4

I have not read their derivations. I know that they were defective and have been replaced by those now found in most calculus texts.

Third, the question of whether reality is continuous or discrete is something that is dealt with in physics not mathematics. — Fooloso4

Physics might well find limits to what is actually measurable, given the laws of nature. That is not deciding whether reality is continuous or not. The concept of continuity abstracts from the question of actual measurability.

Your claim is that mathematics is an abstraction from experience. ...
— Fooloso4

Reread the OP. — Dfpolis

If you are referring to 2a, an axiom or postulate is not a hypothesis. — Fooloso4

Regardless of whether I am right or wrong, I did not claim that all mathematics is an abstraction.

Of course it is not creatio ex nihilo! He did not mean it literally. — Fooloso4

If he did not mean it literally, does not support your position. If he would agree that he was imposing new form on old matter, then he might agree that the matter of math was abstracted from experience.

You keep repeating your dogmas, but you do not support them with arguments. You have not said why my analysis does not work beyond saying it does not agree with your belief system. I agree, my analysis is incompatible with your beliefs.

You made a number of unargued claims I will not respond to.

...empirical reality has a mathematical intelligibility. — Dfpolis

And in this case an intelligibility that was not empirically derived, suggesting that the physical world is structured mathematically, that the mathematics are fundamental, formative. — Fooloso4

Intelligibility is a potential that exists prior to being actually known. So, it is not "derived." It is in nature.

Since they do not exist, they are not constructs.The theory uses small quantities tending to zero, while always remaining finite. — Dfpolis

This is nonsense. — Fooloso4

I suggest you read a calculus book.

Having read Kant's reasoning, he seems to have been unaware of the errors he was making. — Dfpolis

What do you provide in support of that? — Fooloso4

I was challenging any Kantian to provide what they believed was an adequate argument. When an argument was provided I rebutted it.

Your claim is that mathematics is an abstraction from experience. But now you say that the parallel postulate cannot be abstracted from experience. — Fooloso4

Reread the OP.

I have discovered such wonderful things that I was amazed...out of nothing I have created a strange new universe.

One can be right about some things, and wrong about others. While I am happy to allow Bolyai his joy, his assessment is clearly inaccurate. Human creativity consists in imposing new form on old matter, not creation ex nihilo. Most of the axioms in non-Euclidean geometry are from Euclid. Concepts derive meaning from experience. So, his achievement was to impose new form on prior, empirically derived, content.

Clearly they were not hypothesis about the physical world, or, as your prefer, reality. They were neither abstracted from or hypothesis about the physical world. — Fooloso4

Yes, and no. I grant that most modern mathematicians are not thinking of the real world when they work. That does not mean that the content they work with is not derived from our experience of reality.

To be continued ...

Could these mathematical discoveries still be used in, say, cryptography? — Noah Te Stroete

It is had to say without even knowing the area of research.

Who came up with this? Was it you? Also, could you flesh this out for me so I can understand it better: “Every physical object is surrounded by a radiance of action, which is the indispensable means of our knowing it.” — Noah Te Stroete

I came up with it reflecting on Aristotle and Aquinas. Aristotle classes action as an accident as something inhering in a substance. If we reflect on any object that we encounter, we see that it is inseparable from its environmental effects -- its radiance of action. This includes its gravitational field, the light that it radiates and scatters and the odors it emits -- all the means making it sensible, observable. The quantum description of matter also shows no hard boundaries -- its material fields extend becoming ever more tenuous. This action on us modifies our our neural state, and that modification of our neural state is identically our neural representation of the object. So, so that part of us is also the object's action.

We can and usually do abstract the object from its radiance of action, leaving us with the impression that it is no more than a core with well-defined boundaries. Still, if we remove the radiance of action from an actual object, it no longer acts as it does and no longer is what it is. Instead of being an integral part of reality, it becomes an isolated monad.

Couldn’t it be the case that mathematics was first derived from empirical experience, and that newer maths were abstracted from these more fundamental maths? — Noah Te Stroete

Yes, I think this is the case, for example with the structures studied in abstract algebra. Ultimately, however, the foundations can be traced to abstractions from reality or to hypotheses.

Truth is not a value, but a relation between mental judgements and reality. — Dfpolis

But there's a subtle recursion in this understanding, because it presumes we can attain a perspective where 'mental judgements' can be compared with reality — Wayfarer

The statement presumes that experience gives us access to reality -- which is an independent, not a recursive, assumption. Books have been written on this assumption, but that is a topic for another thread. I would simply say that one can't deny this without twisting the meaning of "reality" as what is revealed by experience.

For since the object is outside me, the cognition in me, all I can ever pass judgement on is whether my cognition of the object agrees with my cognition of the object” — Wayfarer

This is why it is important to recognize that in both sensation and cognition we have an existential penetration of the subject by the object, Thus, Kant's claim that "the object is outside me" is only partly true. Every physical object is surrounded by a radiance of action, which is the indispensable means of our knowing it.

Kant's basic problem is that he wants knowing to be independent of knowers when it is actually a subject-object relation. Or, perhaps, he wants us to have divine omniscience of the noumena when we only have human knowledge -- knowledge, not of how reality is in se, but of how it relates to us. Yet, knowing how reality relates to us is exactly what humans need to know to be in reality.

How reality informs me, how I interact with its radiance of action, is immediately available to awareness -- not "outside me." So, Kant has misunderstood the issue.

I do want to add that I was was unclear in discussing the relation of aleph-1 to the cardinality of the reals and that your point on that confusion was well-taken. Mea culpa.

There is no judgment of the truth of the deductions of non-Euclidean geometry that independent of reality, unless of course you maintain that there is a mathematical reality. They are formal logical truths. Whatever your theory of truth may be, non-Euclidean geometry works. They find their application in reality. — Fooloso4

This is a very confused statement. If a mathematical theory applies to reality accurately, it is instantiated in reality and the adequacy of the theory to that instantiation shows the truth of the theory with respect to that instantiation. Further, since we presumably know the instantiation, we can abstract the theory from it. So, one need not "maintain that there is a mathematical reality." only that empirical reality has a mathematical intelligibility.

There are no actual infinitesimals in calculus. — Dfpolis

The point is that they are theoretical constructs. They are not abstracted from nature. — Fooloso4

Since they do not exist, they are not constructs. The theory uses small quantities tending to zero, while always remaining finite.

Him and several generations of Kant scholars. When are you going to publish your findings in a peer reviewed journal? — Fooloso4

Do you think that I'm the first to notice that Kant's arguments are inadequate?

I said that non-euclidean geometries could be abstracted from models instantiating them. — Dfpolis

But the fact that you are trying to dance around is that they didn't. — Fooloso4

I have not read the original papers, so I don't know if they did or did not. I do know that the parallel postulate has been suspect since classical times precisely because it cannot be abstracted from experience -- which was my point.

They did not have a hypothetical status because they were not hypotheses. They were formal logical systems that were not intended to relate to anything else. — Fooloso4

That is you view. I already noted that Bolyai discussed which geometry described reality, which means that he saw geometry as potentially reflecting reality, and the status of the parallel axiom as a hypothesis to be studied by physics. I am not denying that math can be treated formally once we posit our axioms. I am discussing how we come to posit its axioms, and their epistemological status.

The problem is that a baseball being a baseball is not a relationship. It is intrinsic to what it is to be a baseball. — Fooloso4

Yes, still, the name is not intrinsic to it, but assigned in light of its relation to the game.

math is not logic. That was Hilbert's view — Dfpolis

That was not Hilbert's view. It seems you are confusing Hilbert with Russell. — GrandMinnow

Thank you. If you read the context, I was arguing against the position that math need only be logically self consistent, not Russell's more extreme position that math and logic were identical. In the SEP we read:

Hilbert believed that the proper way to develop any scientific subject rigorously required an axiomatic approach. In providing an axiomatic treatment, the theory would be developed independently of any need for intuition, and it would facilitate an analysis of the logical relationships between the basic concepts and the axioms. — Richard Zach

Godel's work shows more: it shows that there are truths that cannot be deduced from any knowable set of axioms. — Dfpolis

That is terribly incorrect. Godel's result is that, for any S that is a certain relevant kind of axiom system, there are true statements that cannot be deduced in S. However there are other systems, even of the relevant kind, in which the statement can be deduced. — GrandMinnow

One can always add a determinate and previously unprovable truth, or its equivalent (if one knows what it is and not merely that it is) to an axiom system and then "deduce" it. Still, the number of propositions we (all humans) can know is necessarily limited. So any knowable set of axioms is finite. No matter how large that finite set may be, there will be truths that cannot be deduced from it. Also, no computable procedure for generating new axioms will exhaust the possible axioms in a finite time. So, an exhaustive axiom set is unknowable. So there are truths we will never be able to deduce.

There is no axiom such that there is no system in which the axiom can be deduced. — GrandMinnow

That was not my claim. I do not deny that any particular truth is deducible from suitable axioms. Rather, I am saying we cannot generate actual axiomatic sets sufficient to deduce all truths in a finite time -- for any finite set of axioms will leave some truths undeducable.

'aleph_1' is not synonymous with 'uncountable' — GrandMinnow

Nor did I claim that it was. I was merely trying to provide a clue as to what was being discussed to those unfamiliar with aleph-1.

And showing that there are uncountable sets does not rely on proving the uncountability of the continuum — GrandMinnow

Did I say it was? I pointed to Cantor's 1874 proof as one way of knowing that the cardinality of the reals is not countable. The question asked was how can we come to concepts of countable and uncountable infinity from experience, not what are the principal findings of transfinite number theory.

comes even more simply from proving that the power set of any set has more members than the set, so if there is an infiinite set then there is an uncountable set. — GrandMinnow

And do you think that an explanation based on the concept of power sets is more comprehensible to a general philosophic audience than what I said?

And, just to be clear, Cantor didn't prove that the cardinality of the continuum is aleph_1. — GrandMinnow

I did not say that he did, but that he proved that the cardinality of the continuum was uncountable. You seem to think that I need to provide excruciating detail when that detail is not relevant to the point I'm making, namely that the foundations of mathematics have an adequate moderate realist interpretation.

The proposition that the cardinality of the continuum is alelph_1 is the continuum hypothesis, famously not proven by Cantor. — GrandMinnow

Again, I did not say that he did.

The cardinality of the set of real numbers (cardinality of the continuum) is 2^ℵo. It cannot be determined from ZFC (Zermelo–Fraenkel set theory with the axiom of choice) where this number fits exactly in the aleph number hierarchy, but it follows from ZFC that the continuum hypothesis, CH, is equivalent to the identity 2^ℵo = ℵ1. — Wikipedia

Perhaps I'm wrong on C being unfalsifiable. Perhaps some consequent of C can be falsified. — Dfpolis

If a consequence of C is falsified, then C is falsified. — GrandMinnow

Isn't that exactly what I said?

Hilbert didn't say that mathematics is only a language game. He regarded certain aspects of mathematics as a kind of language game. But he explicitly said that certain parts of mathematics are meaningful, and even that the ideal mathematics that he regarded as literally meaningless is still instrumental and crucial for the mathematics of the sciences. — GrandMinnow

If he was right, then the mathematical statements used by the natural science have to be instantiated in nature, and so are true in the sense of correspondence theory. That effectively vitiates formalism.

My question to you is, how do the details I have smoothed over serve to undermine my thesis? If they do not, then your criticisms are pedantic.

It those truths precede in time our experience of reality then they cannot be dependent on experience. — Fooloso4

It those truths precede in time our experience of reality then they cannot be dependent on experience. Such is the case with non-Euclidean geometries. — Fooloso4

Truth is not a value, but a relation between mental judgements and reality. Since it depends on judgements, it can't be prior in time to them. Only being can be.

As another example consider infinitesimal calculus. There is no experience of infinitesimals. — Fooloso4

There are no actual infinitesimals in calculus. There are limits as quantities tend to zero. That is the whole point of the epsilons and deltas in the formal definitions of calculus.

Do you imagine that neither Kant nor those who followed him were aware of this? — Fooloso4

Having read Kant's reasoning, he seems to have been unaware of the errors he was making.

Instantiation is not abstraction. — Fooloso4

I did not say it was. I said that non-euclidean geometries could be abstracted from models instantiating them.

The historical fact of the matter is that they weren't abstracted. Non-Euclidean geometries were first developed as purely formal systems. — Fooloso4

If so, that would mean they had a hypothetical status until it was realized that they could be instantiated. The notion that one could be shown to be the true geometry of the universe was explicitly stated by János Bolyai.

What is at issue is your claim regarding the intelligibility of an object. Whether or not human knowing exhausts something's essence, if intelligibility inheres in the object then a sufficiently advanced intelligence should be able to know what a baseball is without knowing what the game is, or, perhaps, would know from the ball what the game is. But there is nothing in the ball that would provide this information. — Fooloso4

According to the Wikipedia article: "Bolyai ends his work by mentioning that it is not possible to decide through mathematical reasoning alone if the geometry of the physical universe is Euclidean or non-Euclidean; this is a task for the physical sciences."

I have answered all this previously. Knowing an object's intrinsic nature need not entail knowing its relationships.

By your logic the intelligibility of a car does not include the potential to know that it is a means of transportation. — Fooloso4

One might figure it out, but only if one knew there were beings that could use it so.