https://books.google.com/books/about/Science_Without_Numbers.html?id=Exc1DQAAQBAJ

We know by logic the laws and axioms which are visible to thought itself - Frege's 'laws of thought' - and so requiring no empirical validation, on account of their being logically necessary; they're not 'out there' but are known true a priori. — Wayfarer

Interesting point of view as all the debate you opened here. But I am somehow disagree in Frege’s laws of thought explaining those axioms were supposedly we don’t need empirical validation because somehow is innate upon us.
Despite the concepts are clear to understand the perfect science and how physics works quoting John Locke’s primary and secondary attributes there is another philosopher which I guess is important here to disagree in these statements: George Berkeley.

George Berkeley said: if neither primary qualities nor secondary qualities are of the object, then how can we say that there is anything more than the qualities we observe? he established this question criticising John Locke’s one: If you put one hand in a bucket of cold water, and the other hand in a bucket of warm water, then put both hands in a bucket of lukewarm water, one of your hands is going to tell you that the water is cold and the other that the water is hot. Locke says that since two different objects (both your hands) perceive the water to be hot and cold, then the heat is not a quality of the water.
Then debating Plato Berkeley said: "an abstract object does not exist in space or time and which is therefore entirely non-physical and non-metal"

It is interesting because he tried to abolish all kind of platonic realism or classic empiricism. At least John Locke, as you pointed out, defended somehow primary attributes but Berkeley rejects it all saying about gravity (for example) gravity, as defined by Newton, constituted "occult qualities" that "expressed nothing distinctly. Berkeley thus concluded that forces lay beyond any kind of empirical observation and could not be a part of proper science.

A final statement of him was that the object of science should be purified the perceptions not explaining it.

Well this is why Berkeley is remembered as a extremist empiricist but I guess it is interesting bring his ideas in this debate.

Bertrand Russell said that 'physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.' — Wayfarer

Wise words there. I just realized that, although right now my mind draws a blank, there possibly are non-mathematical questions we can ask about the world or reality. For instance, off the top of my head, as a rocket blazes off in the direction of the red planet following Newton's equations of motion to a T, I could ask, "what does the rocket mean for humanity?" This is the best non-mathematical question I could think of at the moment, hopefully it'll do the job of illustrating the point that not everything about a rocket or anything else for that matter has to do with math. We're, as Bertrand Russell elucidates, perceiving only one facet of reality - there might be more interesting things going on in the non-mathematical domains of reality that we have absolutely no idea how to mine for valuable information. I could be wrong though as historians, anthropologists, sociologists, psychologists, fields as yet to undergo a mathematical revolution could very well be the ones that have their own unique answers to the question, "what does the rocket mean to humanity?" Of course all this assuming our thoughts and thus the answers to the question themselves are irreducible to some equation involving biochemical molecules.

I'm confident Plato himself could be as real as any of his neighbors. But the phrase Platonic Realism seems to me persistently oxymoronic. My bad no doubt. But can you help me understand a little better? Or by Platonic Realism do you mean the claim of a reality for his ideals? Along the lines of, though different from, Scholastic Realism's claim of the reality of universals?

These are designated the 'primary attributes' of objects, and distinguished, by both Galileo and Locke, from their 'secondary attributes', which are held to be in the mind of the observer.

...

And through the quantitative method of science, the ability to reduce an objective to its mathematical correlates, the certainty provided by logical prediction can be applied to phenomena of all kinds with mathematical certainty (which is, I think, the point of Kant's 'synthetic a priori). It's the universal applicability of these logical and mathematical procedures to practically any subject which opens access to domains of possibility which would be forever out of reach to a mind incapable of counting. — Wayfarer

If, the distinction between primary and secondary attributes is broken down in this way, so as to allow for the universality of mathematical applications, then why conclude that all is "of the object" rather than all is "of the mind". As javi2541997;511801 indicates, Berkeley demonstrated that all is "of the mind" is the more logical conclusion. The other conclusion, that all is "of the object", requires the unsubstantiated assumption made by Kant, of the thing-in-itself, noumena, an assumption rejected by skeptics.

Hence the necessity of Platonic realism to the natural sciences. — Wayfarer

I don't know how far this is relevant or true or reasonable but looking as math as "in the mind" as opposed to the world "out there" seems to be a misconception; after all to believe that would be to overlook a very conspicuous fact - the two seem to be "inexplicably" compatible with each other [ref: The unreasonable effectiveness of mathematics in the natural sciences]. This can't be a coincidence, right? If math works in describing reality once or twice, it can be a coincidence but ALL the time (till date of course)? Smells fishy! :lol: We have, it seeems, in this the seed of a conspiracy theory of cosmic proportions.

Then debating Plato Berkeley said: "an abstract object does not exist in space or time and which is therefore entirely non-physical and non-metal" — javi2541997

Keep in mind, that at some point , the regressive description of existing things (atoms, protons, neutrons, electrons...) ultimately, right now, have no other explanation other than that of abstract mathematics (mathematical structures that are discovered) or a Platonic reality, of sorts.

However, to advance Berkley's idealism from modern day discoveries as you suggest, I think he provides for an nice backdrop or theory of metaphysical existence of consciousness. And that in turn squares with abstract qualities and structures existing in the universe, including our own conscious existence.

So you have consciousness itself and mathematical abstracts themselves, both existing without a so-called existential or complete material (or even logical) explanation. But instead, an abstract one.

Correct me if I'm wrong, but I don't think Berkeley actually resolved/reconciled consciousness requiring space and time to exist, or maybe he did... .

Hence the necessity of Platonic realism to the natural sciences. — Wayfarer

There are varieties of mathematical realism other than Platonism. The fact that certain relations among phenomena hold regardless of what anyone thinks about them does not entail that the corresponding mathematical objects metaphysically exist in a realm of concrete forms. As Charles Peirce maintained, echoing his father Benjamin, mathematics is the science of drawing necessary conclusions about hypothetical states of things. Abductive/retroductive explanations (theories/models) are fallible idealizations that require deductive explication (predictions) and inductive evaluation (experiments/observations) to ascertain whether and how well they match up with reality.

Correct me if I'm wrong, but I don't think Berkeley actually resolved consciousness requiring space and time to exist, or maybe he did... . — 3017amen

You are not wrong. Berkeley escalated a bigger step trying to emphasise what powerful the consciousness instead of trying to explain what is going on with primary/secondary stimulus. This is why authors say he is even more empirical than John Locke. At least this one explained how some attributes are needed to be explained/taught because without it we don’t really know what are we talking about.
For example, John Locke received this letter in his An Essay Concerning Human Understanding

If we block a child in a room all of his childhood teaching him the green colour while is actually yellow. Will he name all of his life “green” when he would actually see yellow? In this topic John Locke answered this is a perfect empirical experiment so he put the following sentence:
What you are trying to say is that complex terms like colours are not innate because we can teach children to misunderstand mixing them. I guess this is the same example of fearness. You can feel the fear because previously someone taught you what is darkness, witches, demons, etc...
Somehow John Locke understood there are some primar and secondary attributes but depends a lot how they are taught, thus experience

But Berkeley goes furthermore, he says that these are just flawed comments. We are wrong if we try to explain everything instead of purify it. The only truth is our perception doesn’t matter what we are taught.
Nevertheless, Berkeley is contradictory when he speaks about God defining him as perfect (idea)
Why did he do that? Why did not he defend exactly the same in Plato realism?

The question can't be answered without some kind of speculation, obviously. But we have to distinguish between tentative proposals about the nature of our mental experience and bold assertions. Such assertions have the right to exist, as all innate convictions, or persuasions, but we want to keep the discussion open and should treat all ideas as hypothetical.

I want to address a methodological question, if I may. Whether the speculation should be in sensory or extrasensory terms can turn into its own entire debate, but we have to articulate what constitutes an intuition. I have many times advocated on the forum, that ultimately, all of our epistemic efforts rest on preconceptions, persuasions, whatever we want to call them. That we don't access any self-evident facts, but only have attitudes that establish sustainable epistemic allostasis, guided towards epistemic homeostasis

In this regard, it serves well to divide our mental experiences into two aspects. Those that we consider to determine ourselves, and those that we recognize as extrinsically compelled. Essentially, we ascertain that there are boundaries on our personal freedom. The division, even if partly psychological, is not phenomenally inconsequential and it does maintain continuous character. From our point of view thus, some persuasions are self-regulated, consciously or subconsciously, while others are compelled from uncontrolled sources. Some of those which are privately controlled are sustained and some are contradicted by subsequent experience with the externally compelled ones.

Which leaves the question, how to preemptively outgrow your labile persuasions before their character is exposed by external forces. Or otherwise put, which persuasions are evidently bad. There isn't a single way to address the question. Maybe all persuasions eventually perish and are philosophically vacuous. (This is what I consider the argument for absurdism.) But lets limit the scope a bit. One way to thread towards persistence is to be open to experience. Your purview expands and hopefully your lability decreases. The second way to rectify defects is to reconcile contradicting persuasions. For example, I am persuaded to believe in reason. I am also persuaded to believe in sensory experience. But the overall picture of my sensory experience can contradict my reason, in which case I will have to rectify this incompatibility. You have to follow methodological balance that guarantees that you are open to knowledge, while maintaining and improving the quality of your knowledge.

Although this sounds simple, the problem is that you cannot directly infer fundamentals. You can rely on external cues for corrective, but not for synthetic guidance. We don't have some privileged capacity for inferring structure from experience, unless it subclasses the structure we already have. We start with blind assumptions and experiment. Those innate impulses to synthesize or reassign priorities work differently from sorting within the preestablished mental order. It relies on continuous trial and error. If a fundamental persuasion makes no positive difference to the individual, or even detracts from their experience, it should be consequently eliminated.

This does not always happen, however. If a systemic phenomenon, or fragment of the collective behavior contributes functionally, or catalythically, or becomes absorbed, it might not be removed. Objective truth can be overshadowed by group interdependencies. A persuasion may also be sustained overdue for its utility, such as the attainment of happiness. Happy persuasions might be deemed more important then the predictive ones. Such importance is not its own justification however, because in the long term, it vanishes if it is not provisioned by predictive sustenance.

But even stoic persuasions are not directed through a faultless process. As I said, the synthesis of fundamentals depends on trial and error. Sometimes we will spontaneously discover sustainable fundamental idea, such as rationality, the inductive method, statistical inference, objectivity, etc and maintain it henceforth. Or, we will spontaneously discover some unsustainable persuasion. In which case, assuming no group function to justify its existence, either the idea, the specimen or the species will be repressed from reproducing. But failing to affirm some belief also indirectly contributes to the reproduction of the emerging sustainable persuasions.

The point I am trying to make is, that persuasive impulses are not subject to reason at their prima-facie stage, because they represent openness to experience. Sometimes, they mask social signaling, but other means of social interaction eventually tend to displace them. Primitive intuitions are, in a sense, defended by their very existence, for however long it lasts. I don't propose that everyone should defend any spurred belief for the sake of the value of spontaneity. People who believe in the apparent primacy of empiricism and rationality should support the epistemics they choose, including through the politics of banishment of extrasensory claims in science. Active political position helps in the discovery of social value.

But the nature of the mind is a special subject of philosophy. It lacks determination. And I believe that we have to concede that if philosophy was always conservative, we wouldn't make the progress to our present day epistemic understanding. We should approach the question from a hypothetical point of view and debate the consistency of arguments, impartiality, interrelationships with other intuitions, and not treat our conjectures as privileged. Within reason...

I will try to come back for discussion of possible hypotheses. I have said before, I am not literate. But I can try to discuss a few ideas in broad strokes. Emphasizing the distinction between the interactionist and supervenience account of substance dualism would be useful, and how the former can be confirmed or refuted empirically. I think we should discuss some kind of empirically compatible hypothesis, such as property dualism, panpsychism, pantheism or emergent materialism. We should probably also discuss some type of idealistic existence monism (we are all fiction in the mind of the diety) and enactivism.

You say that you are not literate. I think that you are extremely literate, but just need to break up your great long paragraph. I found my eyes could not cope, but it seems well written and as if it is really worth reading.

I made some crude editing.
(I wrote the text in an external editor, then pasted it in a hurry. It was originally displayed on a wider content area.)

Yes, I think that makes it a lot better, and it was not a criticism, just a wish to be able to read what you had written.

But this also challenges the naturalist dichotomy of mathematics being 'in the mind' and the world being 'out there', which is how we are inclined to instinctively construe it. — Wayfarer

In a different thread, Metaphysician Undercover made a great point that an ideal object doesn't actually exist regardless of how well it approximates a real object. Reality is quantized, with a heterogeneously fractal geometry no matter the negligibility of this geometry to a perceptual frame of reference. Even a circle has microscopically fractal texture, so that the fact of a unit circle's area being pi, an infinite decimal, is only actually present in our thoughts. It seems impossible for an infinite geometrical quantity to exist on humanity's observational scale, at least from the vantage point of current science. This indicates a deep distinction between mathematical concept and mathematical object, mind and matter. An ideal shape is like a unicorn, a completely imaginary entity, but this discrepancy averages out to negligibility in many circumstances, allowing us to make the philosophically naive yet practical analogies of relativity so crucial to the logic of mathematical modeling. Math is a language describing fundamentally fictional entities.

I think that the reason I was interested in your discussion is the way you spoke of the philosophy of mind. I have been reading this thread today, finding it fascinating, more on the level of consideration of mind, because I am most certainly not a mathematician. I am interested in your view of mind lacking determination. The angle I am coming from is one arising in the thread I made on pessimism and optimism, and realising that in the discussions which I am having, I am coming from the angle of believing that our consciousness, perhaps as part a larger consciousness may have a determining factor in our lives, and realising that others don't necessarily have that view at all.

However, I am not sure whether this is relevant
what you are querying, but I am probably responding to yours because it is a more general one within the thread.

Hence the necessity of Platonic realism to the natural sciences. — Wayfarer

Science and mathematics knows how to measure quantity and often defines reality by quantity. However we have our subjective definitions of quality but unable to define objective quality. We don't know how to measure objective values so unable to feel "meaning" such knowledge offers. A may equal B in quantity but not in objective quality. Simone Weil wrote:

Now, ordinary language and algebraic language are not subject to the same logical requirement; relations between ideas are not fully represented by relations between letters; and, in particular, incompatible assertions may have equational equivalents which are by no means incompatible. When some relations between ideas have been translated into algebra and the formulae have been manipulated solely according to the numerical data of the experiment and the laws proper to algebra, results may be obtained which, when retranslated into spoken language, are a violent contradiction of common sense.

If the algebra of physicists gives the impression of profundity it is because it is entirely flat; the third dimension of thought is missing.

A person understands in the complete meaning of the term when they can experience the external world with the third dimension of thought as opposed to the usual duality which limits us to measures of quantity and subjective values.

Hence the necessity of Platonic realism to the natural sciences. — Wayfarer

Necessity? Or rather contingency?

I made an assumption that mathematical truths cannot be irreducibly complex, which holds for mathematical proof design or quantification of mathematical proofs. Meaning that mathematics seems to be invented rather than discovered.

Hartry Field is often mentioned by one of the mathematical philosophers on this site, his name escapes me at the moment, but thanks for the reference. I don't know if I would understand his work at all, it is grounded in mathematics and symbolic logic, neither of which I am adept in.

I am somehow disagree in Frege’s laws of thought explaining those axioms were supposedly we don’t need empirical validation because somehow is innate upon us.
Despite the concepts are clear to understand the perfect science and how physics works quoting John Locke’s primary and secondary attributes there is another philosopher which I guess is important here to disagree in these statements: George Berkeley. — javi2541997

I agree Berkeley is an important philosopher and that his arguments are ingenious but I don't know if I would want to reference him, at least not without doing a lot more reading.

As for Frege, from that essay I linked:

Frege believed that number is real in the sense that it is quite independent of thought: 'thought content exists independently of thinking "in the same way", he says "that a pencil exists independently of grasping it. Thought contents are true and bear their relations to one another (and presumably to what they are about) independently of anyone's thinking these thought contents - "just as a planet, even before anyone saw it, was in interaction with other planets." '

Furthermore in The Basic Laws of Arithmetic he says that 'the laws of truth are authoritative because of their timelessness: "[the laws of truth] are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this, that they authority for our thought if it would attain to truth." — Tyler Burge, Frege on Knowing the Third Realm

The key point is that 'number is real in the sense that it is independent of thought' - but at the same time, it can only be grasped by a rational intellect. This is the key point in my view.

The fact that certain relations among phenomena hold regardless of what anyone thinks about them does not entail that the corresponding mathematical objects metaphysically exist in a realm of concrete forms. — aletheist

No, they're abstracts, by definition. It is the nature of the reality of number that is the point at issue.

There's another recent essay, What is Math? from the Smithsonian Institute, which notes:

scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.

I think this brief paragraph speaks volumes. At issue is the sense in which numbers can be said to exist. They don't exist as phenomena - unlike phenomena, they don't come into or go out of existence, and are not composed of anything (save other numbers) - so they're of a different order to phenomenal existents. And it seems to me that this is what is being furiously resisted by current orthodoxy. As the SEP article on Platonism in Philosophy of Maths says:

Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences.[1] Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate. 1

I think the statement that this 'would be' an important discovery is unintentionally ironic, as if it's something which has never been considered.

I just realized that, although right now my mind draws a blank, there possibly are non-mathematical questions we can ask about the world or reality. — TheMadFool

Of course, no disputing that.

I watched that Penrose interview shortly after it was published. Those Closer to Truth interviews are a goldmine. I commented on that video:

'[Maths being] always out there, somewhere' [1:29] is a misleading analogy, because numbers are not 'in' time and space, so, not 'out there' anywhere. They're not located. The problem is, we instinctively seek explanations in terms of what is 'out there' - it's the habitual extroversion of Western culture. Otherwise known as 'naturalism'.

I have many times advocated on the forum, that ultimately, all of our epistemic efforts rest on preconceptions, persuasions, whatever we want to call them. That we don't access any self-evident facts, but only have attitudes that establish sustainable epistemic allostasis, guided towards epistemic homeostasis — simeonz

Isn't this 'biological reductionism'? That being the effort to 'explain' reasoning and mathematical capacity in terms of purported underlying regulative biological systems? The conceptual difficulty here is that science itself relies on the cogency of rational argument to establish any kind of explanatory framework. You can't examine the nature of rational thought from some point outside of it, treating it as an external or objective phenomenon, because any such explanation is already an exercise in rational thought. This point is discussed in some detail in Thomas Nagel's Evolutionary Naturalism & the Fear of Religion.

I believe that we have to concede that if philosophy was always conservative, we wouldn't make the progress to our present day epistemic understanding. — simeonz

I don't think present day philosophy of mind has much going for it, really. It places severe a priori limits on the nature of knowledge. Sure we have much better science and technology but are we superior in wisdom to the ancients?

Even a circle has microscopically fractal texture — Enrique

I'm not sure how the technical definition of a fractal applies here. Explain what you mean, please.

if you can represent something mathematically, that you can use mathematical logic to make predictions about it. The greater the amenability of an object to mathematical description, the more accurate the prediction can be — Wayfarer

Doesn't quite sound right from a philosophical perspective. Realism is about things and objects, but science is not. Both math and science are primarily about relations where point objects only serve as instances to an equation or to a law. 'Platonic' realism in science only acts as mental scaffolding to assist in visual modelling of possible worlds of whatever specialty is under examination. Thus the 'reality' of a mathematician might be in the world of tessellations or knots, that of a chemist in spatial orientation and partial charges of molecules in interactions. Plato himself of course had nothing to do with any of these 'realities', numbers were copies or combinations of Ideal metaphysical objects.

No, they're abstracts, by definition. — Wayfarer

You are right, my bad--but that is precisely why I maintain that mathematical objects cannot exist in the strict sense of reacting with other like things in the environment. In accordance with that metaphysical definition, anything that exists is concrete.

It is the nature of the reality of number that is the point at issue. — Wayfarer

I agree, and I maintain that reality is being such as it is regardless of what anyone thinks about it. In accordance with that metaphysical definition, the mistake that Platonism has in common with nominalism is treating reality as synonymous with existence. On the contrary, although whatever exists is real, there are realities that do not exist--including numbers and other mathematical objects.

the mistake that Platonism has in common with nominalism is treating reality as synonymous with existence. On the contrary, although whatever exists is real, there are realities that do not exist--including numbers and other mathematical objects. — aletheist

Wasn't the whole issue of scholastic realism versus nominalism is that the former accepted the reality of universals (in Aristotelian form, as mediated by Aquinas), while the nominalists did not? It was, i believe, Duns Scotus who introduced the idea of the 'univocity of being', which denies that there are different modes of being, although I admit this is a very thorny issue and I need to read a lot more about it.

I'm not sure how the technical definition of a fractal applies here. Explain what you mean, please. — jgill

My technical rigor is surely not spot on, but what I mean is if you draw or construct a precise circle out of actual materials, the circumference's surface contains imperfections, no matter how slight (depending on the technique: pencil, machinery or whatever), and these average out to a fractal-like structure of negligible nesting proportions. This differs from a quintessential fractal in that the compositional detail is less homogeneous and prominent, but is still structures nestled within structures, so basically analogous.

Current physics instructs us that any geometrical object instantiated in the real world will be quantized at the most basic level and is thus fundamentally angular, so an area of pi for example is probably impossible in matter, as the Hilbert program intuited at a relatively early stage of scientific math (I'm getting that information secondhand, you're welcome to correct me).

Motion of course takes effect at a very essentialized level, and this is the source of both the existence and perception of continuity. Whether motion is more like pixels synchronized on a computer monitor or the wild gyrations of a seismograph seems uncertain, but I intuitively lean towards the chaos theory seismograph picture. I think quanta are extremely disequilibrated due to the complexity of their emergent relations while in motion.

Wasn't the whole issue of scholastic realism versus nominalism is that the former accepted the reality of universals (in Aristotelian form, as mediated by Aquinas), while the nominalists did not? — Wayfarer

That was indeed the medieval debate, but its modern manifestation is affirming the reality of generals in addition to the existence of individuals. Peirce described himself as an extreme scholastic realist in this sense, maintaining that reality includes some possibilities and some conditional necessities, rather than consisting only of actualities.

Of course, no disputing that — Wayfarer

The Unreasonable Effectiveness of Mathematics in the Natural Sciences' — Wayfarer

Well, for what it's worth, turbulence

The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping in a fluid flow. However, turbulence has long resisted detailed physical analysis, and the interactions within turbulence create a very complex phenomenon. Richard Feynman has described turbulence as the most important unsolved problem in classical physics. — Wikipedia

Math, not as effective as Eugene Wigner thought, eh?

The Unreasonable Ineffectiveness Of Math

Math, not as effective as Eugene Wigner thought, eh? — TheMadFool

The device you're communicating with depends on the unreasonable effectiveness of maths. Interesting article, but the sense in which I'm arguing for Wigner's view, is certainly not that maths or the mathematical sciences are in any sense omniscient in principle or practice. Very well aware of that.

That was indeed the medieval debate, but its modern manifestation is affirming the reality of generals in addition to the existence of individuals. — aletheist

I think that since the success of the nominalist attitude, which was one of the main forerunners of empiricism generally, that scholastic realism has been forgotten to such an extent that there is barely any awareness of what it meant.

...[C]ritics of Ockham have tended to present traditional [i.e. scholastic] realism, with its forms or natures, as the solution to the modern problem of knowledge. It seems to me that it does not quite get to the heart of the matter. A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.

In short, the appeal to forms or natures does not just help account for the possibility of trustworthy access to facts, it makes possible a notion of wisdom, traditionally conceived as an ordering grasp of reality. — Joshua Hochschild, What's Wrong with Ockham

Furthermore in The Basic Laws of Arithmetic he says that 'the laws of truth are authoritative because of their timelessness: "[the laws of truth] are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this, that they authority for our thought if it would attain to truth — Tyler Burge, Frege on Knowing the Third Realm

@Wayfarer

This point is interesting. I understand now what Frege is trying to tell us. I like that characteristic of “timelessness” and so he is somehow right too despite Berkeley theories.
If some statements made by the humankind understanding or investigating the nature or reality are so efficient that literally are passing through the centuries without doubt of their existence probably is due to they are true.

For example: 1 + 1 = 2. Why? Because I count it as an act with my fingers. We can argue here if 1 + 1 equals to zero or infinite. But the law of truth or primary attribute that equals to 2 doesn’t need to drive to error. Despite of Berkeley criticism about not purifying at all the nature around us.

Isn't this 'biological reductionism'? That being the effort to 'explain' reasoning and mathematical capacity in terms of purported underlying regulative biological systems? — Wayfarer

I wasn't trying to be ambivalent towards people's preconceptions, or indifferent towards my own preconceptions. I elaborated my rational and empirical, but possibilian persuasions. I explained how I reconcile those qualities of attitude. Such as, why a rational empiricist can be possibilian, which could then allow this discussion to progress further, without being divided between people of different persuasions. I made a case, hopefully epistemically justified, that possibilianism is natural consequence of rational empiricism, for philosophical subjects which lack clear determination. And I challenge you to make a case on your end for epistemic justification of empiricism, if you felt it was necessary or you felt that my claims were inherently condescending towards yours.

First, my persuasions demand to be recognized and reconciled. I cannot become irrational, simply because I see chance to be in this forum. I can not become rejecting of my sensory experience, simply because I have the opportunity to do so now. This is not how I have structured my personality. If I were to switch mine with yours, I would be just Wayfarer's doppelganger, and we would agree on more subjects, but this is not how my nature works. And believe me, whether rational empiricism is right or not, this is not how my nature works.

But, as a rational, empirically trusting (to a point) person, I do realize that my knowledge has limits, and those limits lie in my own intuitions. That is, I realize that I have attitudes without justification, but hold to them until proven wrong. Then, it seems to me that it would be hypocritical to deny any explanation for philosophically indeterminate subjects, whether it would be theistic or not, dualistic or not, even if it is a creative conjecture. My only conditions were, that we keep the discussion hypothetical, to keep it open to everyone, out of political necessity this time. I also proposed that we try to explain how our hypotheses contrast with each other, their compatibility and incompatibility, their similarity and dissimilarity, consider any possible internal inconsistencies, internal redundancies, or internal sources of incompleteness and vagueness, where by internal, I mean self-exposed or self-confessed.

The conceptual difficulty here is that science itself relies on the cogency of rational argument to establish any kind of explanatory framework. You can't examine the nature of rational thought from some point outside of it, treating it as an external or objective phenomenon, because any such explanation is already an exercise in rational thought. This point is discussed in some detail in Thomas Nagel's Evolutionary Naturalism & the Fear of Religion. — Wayfarer

As I have stated in our previous discussions, while there might be a different point of view from the outside, of which I confess, I am not aware, I don't feel that I am compelled by this hypothesis or by epistemic necessity to explain my knowledge. I am not denying that the universe is partially intellectually cognizable, thanks to the fact that it is inherently orderly. Paraphrasing what you stated in some earlier conversation, in rational empiricist terms order is that which explains. But my cognition is just reproduction of order within order, which captures a measure of what the explanation is. The full explanation rests on its own existence, not mine. I don't require that I can explain orderliness through my cognition, because that suggests that my cognition, which is just homomorphic fragment of order within order, is central to the nature of order, and not contingent to the complete picture of orderliness. Orderliness is its own nature. It doesn't require to be explained by me. It justifies itself, however it does. I could synthesize such a construction, where order has underlying explanation, from a greater vantage point, which I somehow antropomorphize. Meaning, it becomes explained in terms that reduce in complexity to my own complexity. Sure. But that just embeds our universe in a super-universe. If I could hypothesize a final antropomorphically cognizable universe, what would distinguish it from ours? Do I do that, just because I cannot fully grasp my own? What I am getting at, is that nature explains itself to itself, but no to me.

I don't think present day philosophy of mind has much going for it, really. It places severe a priori limits on the nature of knowledge. Sure we have much better science and technology but are we superior in wisdom to the ancients? — Wayfarer

This gets us to the fundamental distinction between my point of view and yours, which ties beautifully with @Jack Cummings 's question about optimism and pessimism. I see a board of chess on which human beings serve purpose. In the game, they receive the gift of overtaking other pieces, which is just the virtue of their function, but at their level of abstraction or sense of meaning, it appears the logical conclusion of the game. But it is completely unrelated to the game's objective, which wouldn't translate to them at all, and never will, because a pawn has a different sense of purpose. The game has its own unrelated purpose. The game will find its objective, but the pawn will not appreciate it. You see a classroom, where human beings are challenged by lessons, aimed to teach them fundamental truths of a greater vantage point. From my purview, there is no greater wisdom then getting a sense of your identity in the moment, while appreciating your limitations, continuously adapting, hoping that the game is not over for you. To you, there is no greater error then the assumption than the lesson is understood, before reaching a self-evident self-explanatory conclusion. You are ontological optimist and I am ontological pessimist. You believe in benevolent antropocentric antropomorphic universe, I believe in every men as its own universe, clashing against the tides of the exterior motives, trying to adapt without losing its dignity and personally established purpose.


Edit: As I said, I do intend to come back and try to outline my take on a some hypothetical propositions in broad strokes. It might take a day or two. Not that I am that knowledgeable, but we need some kind of enumeration of major ideas.

The device you're communicating with depends on the unreasonable effectiveness of maths. Interesting article, but the sense in which I'm arguing for Wigner's view, is certainly not that maths or the mathematical sciences are in any sense omniscient in principle or practice. Very well aware of that. — Wayfarer

I didn't mean to say you didn't know this stuff but what I want to bring up is there are certain areas in physics where math, as they claim, "breaks down" e.g. black holes, the Big Bang singularity, to name a few. I wonder if this means anything? Does it shake scientists' faith in math as a complete, self-contained, tool for studying the world at large?