You have to account for the fact that our brain is capable of detecting isometries, similarities, etc, which is product of marriage between ourselves and our environment through long evolutionary process. In other words, there is apparent phase of alignment of the cognitive apparatus to some world qualities, which aren't purely analytic.

(We had an exchange with @Banno recently, where I presupposed observational capacity. To think of it, since I presupposed it before the conception of higher order abstractions, it may have appeared a moot point to insist that concepts in modern mathematics can be analytic, since the apparatus that performs the basic processing of the sensory information is developed in a clearly situated historical fashion.)

I will try to illustrate the empirical account of our ability to handle the aforementioned geometric mappings, from an evolutionary standpoint, by going back to the annoying umbrella analogy again.

I have never witnessed rain. I am basic reactive organism that doesn't employ universals yet, but is capable of situational memory through reproduction of rote learned responses to electromagnetic, mechanical and chemical stimuli from my surrounding environment. I have two choices for reactions. I am not very creative here. I either open my umbrella or not. My only job then is to arbitrate between those options at any time. I don't open my umbrella and it pours. I get cold, I may die. I used my umbrella, I am dry, and take no risk for my apparently fragile health. I open my umbrella when the weather is sunny, I get less sun. My vitamin D levels decrease, I may die. I close my umbrella after the rain stops, I get sunshine, good calcium absorption. Organisms that will always open their umbrella when it rains and close it when it doesn't will proliferate. The umbrella is a reaction, but in being correspondent to the elements, it also encodes the complex external phenomenon. I don't recognize this phenomenon because of its special character, but merely because I receive stimuli that map to prior experience in sustenance-positive fashion.

The concluding extrapolation is that basic cognitive faculties that allow us to ascertain certain repeating qualities of the environment from early organic history to modern day organisms can be traced back to basic reactive relations. But assuming that trial and error can explain our perceptual system, it would allows us to discover repeating features by their expression derived in our neurological structures.

Whether the material relation through chemical, electromagnetic and mechanical interaction isn't facilitated by underlying unifying causes that proliferate platonically is undecided. I don't think we could ascertain that much. For example, linearity might exist independently, in the sense that the laws in Newtonian physics are independent conceptual reality, but lines might be just token ideas that we have developed to express a set of conditions that govern the world as we see it, by whatever virtue our material sense relation happens to be, which requires speculations.

Benecerraf was probably concerned that even if we can achieve correspondence between our mental representations and the environment, which was rather glossed over, we couldn't argue the soundness of our abstractions from experience. I think that he makes the claim that belief is contingency that is formed from reasons not possible to define analytically, and abstractions cannot be given apriori empirical account. So, we believe numbers are a good model for physical aggregates. For example, counting discrete collections with numbers, every time we add one further object, we get a larger aggregate. But can we argue that this is a good argument to make use of them? I think that given the above basic cognitive capacity and some basic intuitions (rationality, induction, etc), we can. But Benecerraf would apparently disagree.

Edit: I may misunderstand the argument that he makes.

I have never witnessed rain. I am basic reactive organism that doesn't employ universals yet, but is capable of situational memory through reproduction of rote learned responses to electromagnetic, mechanical and chemical stimuli from my surrounding environment. I — simeonz

I'm afraid this is a very lame attempt. Remember Lucy, the Ramapithicus skeleton, integral to the whole story of hominid evolution, right? What was her timeframe, six million years ago, right? She would have no chance of grasping the 'concept of prime'. Fast forward 6.9 million years (and some), h. sapiens appears. H. sapiens has some ability to grasp the 'concept of prime'. H. Sapiens was the consequence of huge evolutionary leap, namely, the development of the huge hominid forebrain. But what about 'the concept of prime' has evolved or changed in those millions of years? Answer: nothing. The ability to calculate, to speak, count, imagine, and so on - these evolved, no doubt. But the subject matter of those abilities - how can that be 'explained' in terms of 'evolutionary development'? I think this is a very widespread myth concerning evolution. As if we can find some primitive antecedent of rationality, then we can see how it is made. I think that is nonsensical, I'm sorry. H. Sapiens breaks through to an ability to grasp ideas, but there is nothing in evolutionary theory to account for the nature of reason. This ability transcends the biological, which I know is a very non-PC thing to say.

Notice that excerpt from the article I quote above, which was on whether computers can be programmed to find mathematical proofs:

A [mathematical] proof is strange, though. It’s abstract and untethered to material experience. “They’re this crazy contact between an imaginary, nonphysical world and biologically evolved creatures,” said the cognitive scientist Simon DeDeo of Carnegie Mellon University, who studies mathematical certainty by analyzing the structure of proofs. “We did not evolve to do this.”

'We didn't evolve to do this'. And it's true. Mathematics has no evolutionary rationale. It's not a claw, tentacle, or a colorful feathered display to attract mates. It can't be 'explained' in terms of biological adaptation. Darwin was not a philosopher, but now, strangely, everything that goes under the name 'philosophy' is expected to be explicable in terms of evolutionary biology.

Please see Thomas Nagel's essay, Evolutionary Naturalism and the Fear of Religion.

On the contrary, within semeiotic the definitions of terms including "object" and "subject" are unambiguous and foster greater understanding. — aletheist

I made my decision through an assessment of the results of the semeiotic (Peircian) definition of "object". You have "objects" which violate the law of excluded middle, "objects" which violate the law of non-contradiction. And, vagueness, which ought to be represented as a feature of human deficiencies, inadequate principles, and inadequate application of principles, is seen as an objective part of the universe.

This is generally the most significant negative feature of Platonic realism. When mathematical principles, and other human creations like inductive generalizations, are apprehended as objective, unchanging aspects of the universe, we have no approach toward deficiencies, falsity or other defects within these principles. When mathematical principles are apprehended as the result of human activities then we view them as fallible.

Eh? What does that even mean? That the axioms "require" something to be axioms? Or that as axioms they mandate something? I'm not finding sense here. — tim wood

To be "true", an axiom must correspond with reality. We can make all sorts of useful axioms which do not correspond with reality. Usefulness does not entail truth because it is determined in relation to its purpose, as means to end. The reality of deception demonstrates very conclusively that usefulness does not entail truth. So usefulness, and pragmaticism in general, must be subservient to truthfulness, in a respectable metaphysics. This means that pragmatic principles cannot take top position in the hierarchy of decision making, because usefulness is determined relative to the end, so it does not necessarily provide us with truth. The further point which Plato himself indicated, is that the end is "the good", and Aristotle outlined the need to distinguish between "apparent good" and "real good".

What axioms, what objects? Just a simple example ought to suffice to demonstrate the necessity of Platonism. — tim wood

When an axiom, such as the axiom of extensionality, treats numbers as objects, then if this is true, the axiom will provide us with sound conclusions. If it is not true then the axiom will provide us with unsound conclusions. To be true, such axioms require that the ontology of Platonic realism is a true ontology.

treats numbers as objects, — Metaphysician Undercover

You mean like screws at the hardware store, or bricks? What do you mean when you say, "treat numbers as objects"?

to be true, such axioms require that the ontology of Platonic realism is a true ontology. — Metaphysician Undercover

Why? What does this even mean?

And it has to be said, from what you write, you apparently do not know what an axiom is. Nope. You apparently have no idea what an axiom is. Google "axiom."

She would have no chance of grasping the 'concept of prime'. Fast forward 6.9 million years (and some), h. sapiens appears. H. sapiens has some ability to grasp the 'concept of prime'. H. Sapiens was the consequence of huge evolutionary leap, namely, the development of the huge hominid forebrain. But what about 'the concept of prime' has evolved or changed in those millions of years? Answer: nothing. — Wayfarer

First, to talk about conceptualization, rather then instinct and notion, we need the development of language or some kind of signs. First, because otherwise we could not express definitions abstractly, and second because it appears that people started to conceptualize after they became capable of communicating their thoughts. So, assuming communication, abstract ideas are simply codification of experience attributes and behavior directives with appropriate linguistic structure. Prime numbers, specifically, are actually rather simple consequence of developing the concept of operations, which are quantity relations. They arrive at the scene when you ask, can I solve my linear equation in terms of integers. Algebraic necessity is sufficient for their introduction, but they can be observed in practice as the inability to achieve certain counts from subdivision of a rectangular area into congruent sub-rectangles. Equations themselves are regularities expressed through other regularities. They are predictive apparatus, for area estimation, for time keeping, for example. Solving equations attempts retrodiction - the estimation of conditions by their effects - which was frequently necessary. People conceptualized the problem, as something of a recurring event in their lives. It was both necessary to do so and apparent through self-reflection on their experiences.

The ability to calculate, to speak, count, imagine, and so on - these evolved, no doubt. — Wayfarer

So, we agree then that, without obvious internal contradiction, we could have developed innate biological capacity to discern objects in their environment, remember objects, ascertain relations, such as distances, congruence, similarity (using continuous integration of visual and auditory, and tactile cues, present and in memory), and detect simple patterns. So, at least, I hope that we can agree, that whether it is sufficiently elaborated by science or history, according to the empirical account, this is possible?

But the subject matter of those abilities - how can that be 'explained' in terms of 'evolutionary development'? — Wayfarer

I cannot fully explain how our brain functions, because we honestly don't have enough data, but it is considered to be broadly allocated for creative and quantitative tasks, so to speak. These features are apparently unevenly distributed between the hemispheres, as was established by tests performed on people where the brain was partially surgically separated to alleviate epilepsy symptoms. Both features are embodied in billions of nodes and trillions of connections. Assuming similar structure to A.I. that synthesizes images, the brain can constantly probe for proto-ideas, trying to make new ones from variations of old ones. Simultaneously, it tries to categorize sensory experience and decompose it into basic factors, which serve as seeding ground for those new concepts to emerge and be reincorporated into the neuronal structure themselves. In other words, the environment provides us with cues, which we then use to boot our own construction of new amalgemations of these features, but in abstract linguistic terms. I say, abstract terms, because even though language also breaks down to some experience or observation pattern, it can decode layers of meaning in stages, whereas literal form associations would limit us to hybridization of direct experience. Features that are more frequently encountered or more frequently used are more likely to be revisited. Therefore, we are bringing up many candidate concepts, which are extrapolations (I speculate, literally, as synaptic input extrapolations) of their linguistically expressed relation to observed patterns, and we either fit them in the scheme of things or discard them quickly from memory. Why do you perceive our ability to generate such candidate ideas of the type 'my experience or observation 1 and similar in structure, my experience or observation 2 and similar in structure, and so forth' as insufficient?

Note that even today's A.I. can generate images that amalgamate structure and detail from different training data. (Although I have to confess that it is both aided by us in its ability to discover isometry and similarity and is much simpler. But I assume that we have decided to admit the possibility that the discovery of isometry and similarity could have developed as evolutionary contingency.. Rightfully or not.)

P.S.:
Aside from synaptic extrapolations, such as linear extrapolation, another generalizing faculty that I presume the brain is capable of is induction through recursive feedbacks, which should be essential for some indefinite concepts that generalize from finite cases/experiences by some rule application ad-infinitum. For example, the abstract "for every" (for all). I envision as its precursor the cerebral expression of "everything" (e.g., in the universe), which could be encoded by applying "more", starting from something already big like "many". In other words, a feedback loop functions analogously to mathematical schema. Language allows unification of experiences in the brain by token signs or symbols, linear or ramped extrapolation allows generalization through simple trend reproduction, and feedback allows extrapolation through induction or recursion. I also said that some ideas are rejected from long term memory. I believe that the criteria for retention of any notion, abstract or otherwise, is its effectiveness, which has two components, compactness and generality or range of applicability. Compactness depends on its own complexity as neurological structure (how much space in terms of neurons and synapses it allocates) and it follows that ideas that mesh well with previous notions will be easier to retain, because they reuse a lot of the preexisting structure of other ideas. Generality or applicability not only reinforces the concept through recall, but it also serves compactness. It may have historically developed from the need for compactness, as innate biological trait that considers the relative ability of new information to displace old information in the long term. I think that today we favor generality and simplicity consciously, because through self-reflection, we have gradually come to explicate, articulate and appraise the notions evident value.

we agree then that, without obvious internal contradiction, we could have developed innate biological capacity to discern objects in their environment, remember objects, ascertain relations, such as distances, congruence, similarity (using continuous integration of visual and auditory, and tactile cues, present and in memory), and detect simple patterns. So, at least, I hope that we can agree, that whether it is sufficiently elaborated by science or history, according to the empirical account, this is possible? — simeonz

What I'm questioning is the degree to which the designation of these capacities as 'biological' is relevant. Certainly they're relevant or useful for the study of biology but the questions philosophers ask are existential and cannot necessarily be addressed in biological or biomechanical terms. Given all the facts of evolution, existence is still an existential predicament for human beings; that is what philosophy is concerned with.

Going back to the article on the indispensability of mathematics, and the problem of mathematical knowledge, why do you think the fact that we have an apparent innate ability to grasp mathematical proofs is said to be 'a challenge to our best epistemic theories'? Why do you think it was felt necessary to provide an alternative account of mathematical knowledge which sidesteps that challenge? What do you think the philosophical issue at stake is here? I'm not doubting the plausibility of the evolutionary accounts, but questioning their relevance to the philosophical issue at hand. I hope you can see that distinction.

So, assuming communication, abstract ideas are simply codification of experience attributes and behavior directives with appropriate linguistic structure. — simeonz

Consider the implication of the insertion of 'simply' in this sentence. Abstract ideas comprise practically the entire, vast, and diverse body of human culture, so that designation seems rather reductionist to me.

You mean like screws at the hardware store, or bricks? What do you mean when you say, "treat numbers as objects"? — tim wood

I mean to assume that a number is an object.

Why? What does this even mean? — tim wood

Do you know what "true" in the sense of correspondence means? It means to correspond with reality. So take the law of identity for example, it states that a thing is identical with itself,. And this corresponds with the reality of things, as we know them. A thing cannot be different from itself. And from this we also derive the law of non-contradiction. If a thing were other than itself, then the required description of it would be contradictory, because it would correspond to a specific description, and not correspond with that description, at the same time. We see that these principles correspond with reality, i.e. that they are true. Do you agree with me on this?

However, we can state principles, laws, or axioms which are not true. And it is not required that they be true, i.e. correspond with reality, in order for them to be useful. So we can state useful axioms which are not true.

And it has to be said, from what you write, you apparently do not know what an axiom is. Nope. You apparently have no idea what an axiom is. Google "axiom." — tim wood

There are two common senses of "axiom", the philosophical sense, and the mathematical sense. In philosophy an axiom is taken to be a self-evident truth, like the law of identity and the law of non-contradiction. In mathematics, an axiom is a starting point for a logical system, like a premise, but it is not necessary that the truth or falsity of the axiom (whether it corresponds with reality) be evident. I've taken this from the Wikipedia entry on "Axiom".

I mean to assume that a number is an object. — Metaphysician Undercover

Ok, what do you mean by object? I assume you do not mean like screws or brick at the hardware store.

Do you know what "true" in the sense of correspondence means? It means to correspond with reality. — Metaphysician Undercover

This strange from you. Because what true means in this sense is not-true, and I'd have thought you'd be all over that.

but it is not necessary that the truth or falsity of the axiom (whether it corresponds with reality) be evident. — Metaphysician Undercover

Not only is it not necessary, it is impossible, and it is irrelevant.

Admittedly very informally axioms are by default thought of as true, but we're looking more closely, or, I'm looking more closely because I think up above somewhere you got confused when you claimed that,

These mathematical axioms require that a term signifies an object. Only Platonism can support this prerequisite. — Metaphysician Undercover

My problem here is to try to find some starting point. You mentioned the axiom of extensionality. Apparently you claim this axiom requires that terms signify objects - I do no know what "signify" means in your usage - and that in turn requires Platonism.

From online, the axion of extensionality:
"To understand this axiom, note that the clause in parentheses in the symbolic statement above simply states that A and B have precisely the same members. Thus, what the axiom is really saying is that two sets are equal if and only if they have precisely the same members. The essence of this is: A set is determined uniquely by its members."

What about this requires the treatment of anything as an object ("object" awaiting you definition), and what does it have to do with Platonism and why is Platonism "required"?

Ok, what do you mean by object? — tim wood

Worth noting here - this is something I’m saying, I don’t know if the poster you asked will agree - that a number or geometric form is a noumenal object, that being an object of ‘nous’, mind or intellect.

So it’s not an object of sense, which is what is presumably implied by many of the question about what ‘object’ means in this context. It’s not a phenomenal or corporeal object, like a hammer, nail, star, or tree. You could even argue that the word ‘object’ is a bit misleading in this context, but if it’s understood in the above sense - as something like ‘the object of an enquiry’ or ‘the object of the debate’ - then it is quite intelligible nonetheless. (See Augustine on Intelligible Objects).

Worth noting here - this is something I’m saying, I don’t know if the poster you asked will agree - that a number or geometric form is a noumenal object, that being an object of ‘nous’, mind or intellect. — Wayfarer

May I call it an idea? The point being that the world of ideas is different from the world of worldly objects. And that failing to keep the distinction in mind leads some minds astray. But let's see what he says.

What I'm questioning is the degree to which the designation of these capacities as 'biological' is relevant. Certainly they're relevant or useful for the study of biology but the questions philosophers ask are existential and cannot necessarily be addressed in biological or biomechanical terms. Given all the facts of evolution, existence is still an existential predicament for human beings; that is what philosophy is concerned with. — Wayfarer

The laws of biological and chemical order, may or may not have unifying underlying platonic causes. I honestly could not conjecture either way. Alternatively, nature might just have possible state configurations, with restricted transitions, or predetermined timeline of states, or even (more in tact with relativistic physics) collection of timelines for state components whose spatial ordering arises effectively by virtue of the patterns expressed in the otherwise unordered configuration components. The point is, that configurations don't need relatable logic. Aside from their combinatorial essense, which exposes codetermination in the state configuration, the relationships between the state components don't require abstract meaning. For a system inside this state to actually establish homeostasis or allostasis with the environment, the prerequisites are reproduction of the local transition patterns according to a spatial state ordering that could explain causally the chronology of each component, symmetry of the component transitions (low entropy) and change (abundant energy). Neurological, physical and physiological state can be formed by obeying correspondence with the environment into the predefined constraints on the evolution of the state space.

We could also ask about mental experience after that. As I have answered before, this could be explained in many ways, but only as speculation. I do favor the idea of emergence or compartmentalization of some innate reflection potential that applies universally to the state, by combining granular experience potentials from each component in increasing capacity for self-determination when they operate in some coherent fashion (such as in our brain), or by subdivision of the overall experience potential of the universe into smaller identities that maintain particular object constancy around components that operate coherently (such as in our brain), etc.

This departure aside. I am pushing the idea, if you will, that nothing works for simply fundamental reasons, and without elaboration of the particular context and history, there are layers on top of layers, where the puzzle is bewildering to investigate. How we expose the fundementals will depend on what we can work out about the details that were produced situationally and in consequence. Only then we can remove them from the picture and discover what is left.

For example, if the human cognitive apparatus was indeed produced in stages of increasing sophistication and it is still organized in hierarchical manner that is pivotal to efficient feature extraction and denoising of raw sensory input, we didn't simply happen to grasp our circumstances overnight, because of secretion of knowledge into us, but there was gradual accumulation of faculties in our design (whether inspired by natural forces or not) and those faculties, and not platonic forms, serve as landing pad for the knowledge that sits on top of them.

That is why I asked if you would agree that our basic cognitive functions, to pick up symmetries, patterns, etc, are articulated in our brain, i.e. visual, auditory, somatosensory cortex, and whether you allow that we may have derived those faculties from evolution. This is complex area beyond my competence that I won't fully explain, science cannot explain it exhaustively either, so if you would agree, it advances the question on faith. The same applies to stages of evolution in general. Even an unicellular organism, such as choanoflagellates, is a rather complicated biological system. It is possible to envision chemistry evolving to bacterial and later protist lifeform, but this includes many difficult stages. Self-replicating polymers, chemical encapsulation in micelle, metabolism (homeostasis by staged reactions, separation of exothermic and endothermic reactions, separation of decomposition and synthesis reactions, production of organic catalysts) for which we don't have much in the way of historical account, aside from stromatolite fossils, and which we are attempting to reenact by guessing the conditions. Or multicellular life that may have began as slime molds, and the nervous system that may have appeared as nerve nets. We discover this by phylogenetic analysis to some degree, but process of elimination that you can contest is also involved, because we lack fossils. Because lifeforms were soft tissue, depriving us from the crucial account of early morphogensis and cell differentiation, including cephalization, we cannot account for those confidently. In fact, cell and tissue differentiation is still actively studied. Language, which is crucial in my account, seems to have been driven by signalling advances, when our predecessors were forced by ecosystemic changes to move from the tree branches to the tall grass-ridden ground and to start to communicate opportunities or threats.

Going back to the article on the indispensability of mathematics, and the problem of mathematical knowledge, why do you think the fact that we have an apparent innate ability to grasp mathematical proofs is said to be 'a challenge to our best epistemic theories'? Why do you think it was felt necessary to provide an alternative account of mathematical knowledge which sidesteps that challenge? What do you think the philosophical issue at stake is here? — Wayfarer

I am reading Benecerraf's Mathematical Truth, which was referred to by the Wikipedia article you quoted. I still cannot grasp the entire argument, and the author quotes another paper that pertains to the incompatibility between platonism and rationality specifically, but to the best of my understanding, knowledge according to the text is a synthetic condition, i.e. provoked, and abstractions are analytic, i.e. applied as template. The claim is that the theory cannot be married to our knowledge in some apparent and explained sense, because their character is incompatible.

Consider the implication of the insertion of 'simply' in this sentence. Abstract ideas comprise practically the entire, vast, and diverse body of human culture. — Wayfarer

The designation of some amalgamation of diverse kinds of experience and extrapolations is not that surprisingly complex in principle. The appearance of such faculty is astounding, but its operation seems to rely on crudeness itself. The brain is very ample structure, and any token word is probably encoded in a redundant fashion. Thousands of neurons and millions of synapses may be employed for a single concept (or a notion), for making associations with multitudes of sensory experiences and linguistic terms, creating significant semantic backup. So, when I said simply, I meant that the mechanism is simple. Involving human culture concerns being extended and situated in your ecological and social environment. Here, from empiricist perspective, I would consider the idea of social evolution, where experience aggregates collectively and the social dynamics evolve in parallel to the individual. The personal and the social organisms evolve together and interdependently.

P.S.; Benacerraf: Mathematical Truth

Worth noting here - this is something I’m saying, I don’t know if the poster you asked will agree - that a number or geometric form is a noumenal object, that being an object of ‘nous’, mind or intellect.
— Wayfarer
May I call it an idea? — tim wood

Yes, with the qualification that 'idea' in this context has determinate meaning, i.e. a real number or mathematical proof is an idea. Not simply an idea in the general sense of mental activity 'hey I've got an idea, let's go to the pub.' (Not that it's a bad idea.)

The laws of biological and chemical order, may or may not have unifying underlying platonic causes. I honestly could not conjecture either way. Alternatively, nature might just have possible state configurations, with restricted transitions, or predetermined timeline of states, or even (more in tact with relativistic physics) collection of timelines for state components whose spatial ordering arises effectively by virtue of the patterns expressed in the otherwise unordered configuration components. The point is, that configurations don't need relatable logic — simeonz

But whether they are ‘possible state configurations’, or not, science still presumes an order. F doesn't equal MA only on certain occasions; ‘hey, that cannonball missed, the law wasn’t working today’. And if their 'configurations' couldn't be expressed in maths, then likewise, hard to see how science could get a foothold. (Your posts are hard work, although they’re worth the effort - but it’s intriguing to see how you interpret these questions, as your attitude is so different to my own. The question that occurs to me, is whether you see yourself as pursuing philosophy as distinct from science, or whether you think there is no difference and that one subsumes the other.)

So, when I said ‘simply’, I meant that the mechanism is simple. — simeonz

The ‘mechanism’ is not simple at all. The process by which DNA replicates, and the operation of the human brain, are two of the most complex processes known to science. The idea is simple, but I don’t think that supports your point!

But whether they are ‘possible state configurations’, or not, science still presumes an order. F doesn't equal MA only on certain occasions; ‘hey, that cannonball missed, the law wasn’t working today’. And if their 'configurations' couldn't be expressed in maths, then likewise, hard to see how science could get a foothold. — Wayfarer

The local factors of two spatio-temporal regions may be symmetric or asymmetric. By extrapolation of those conditions to the state of the entire universe, we construct the notions of complete chaos (no redundancies), or complete order (uniform, or vacant state). We ask what demands our case to be situated so particularly between them. It is epistemically reasonable to investigate, but it may be ontologically unintelligible question to ask. There is no guarantee that our understanding, from our limited experience, can be made compatible with the actual ontological perspective. It may be incommensurate with it, so to speak. We could be witnessing all the necessary phenomena that provide the meaning, but since the very meaning is unrelatable to the view and objectives that we have, our human ethics, etc, we may not appreciate it. Even if we were conveyed this meaning in explicit terms that we can interpret, we may still not appreciate it. Hence, complete disorder or order may be extrapolation that we just investigate by epistemic habit and compulsion.

Both nominalists and platonists should however agree that homomorphic and amorphic micro-state dynamics exist. I believe that their disagreement is about phenomenology, and about the implications on phenomenology on epistemic issues. That is why I turned to the philosophy of the mind initially. Because I felt that the merger of phenomenology and epistemics here is unclear. The contention seems to be between conjecture for direct disclosure of underlying design through mental experience and conjecture for representational comprehension of regularities through situated interactions. If we assume no causality from our mental state to its material vessel, or no distinction between substances of mind and matter, the same combinatorial account should be epistemically compliant with both views.

Your posts are hard work, although they’re worth the effort — Wayfarer

I was too verbose and conflated when it came to the requirement for "reproduction of the local transition patterns ". I meant that symmetries of the micro-state transitions are necessary for the emergence of predictive systems. Representational morphisms demand it. I wanted to be relativistic as well, so I proposed that spatial structure was causally inferred by independently specified micro-state timeline dynamics. The truth is, that the state should be described in some structure, manifold, such as Minkowski space, whose symmetries have different criteria, but unfortunately, I am not qualified to elaborate them.

The ‘mechanism’ is not simple at all. The process by which DNA replicates, and the operation of the human brain, are two of the most complex processes known to science. The idea is simple, but I don’t think that supports your point! — Wayfarer

I treated the problem in two parts, but I aimed to argue that abstract conceptual cognition, at least hypothetically, could occur without the presence of some binding agent that conveys the essence of patterns in nature directly to us, making them self-evident. First, I argued that the sophistication of our cerebral structure is sufficient for neurological processes to emergently develop conceptualization. That through the presence of linguistic skill, acquired through genetic propensity for vocal semiotics and learned behavior, along with our complex perceptual system and vast neurological capacity for processing and storage, we can encode associations, such that we can hypothetically account for abstract cognition at the level of synaptic activations.

On the other hand, the arrival of such complex nervous system naturally is much more complicated. Not just because of DNA. Self-replicating polymers are conjectured to have appeared, because organics are demonstrably chemically active and polymerize easily, and although labile in unprotected environment, the presence of solid catalytic surfaces where the matter is deposited or rock pores, could have retained them for longer durations. The process of self-replication is possible with short chained RNAs or RNA-DNA hybrids (chimeric polymer). They can form double stranded structure. The strands would then have been disassociated during particular phases of naturally occurring energy cycles in the environment (hot and cold conditions of hydrothermal vents, or high and low tides). Cellularization is a problem, but early emphaphilic compounds may have served the role of today's lipids. But how we have arrived at a metabolic cycle in the first prokaryotic cell, is a difficult question. Even if we can design metabolism that boots from prebiotic chemistry, all the fantastical stories would depend on our assumptions about special conditions and events that we can never verify. It is too complicated to arbitrate if locales of primordial earth were so very different from today's world. And we cannot magically circumvent the erosion of evidence produced from the action of entropy, that leaves us with stretches in our imagination. My objections to the hypothesis of supernatural events are, first, that they are too narrowly specified (theistically determined, etc), to the point where the details are frequently not essential for the required effect, and second, if they were indeed produced by intervention of omnipotent agency, I fail to conceive why the omnipotent agent couldn't make the regularities in nature more coercive to evolution, instead of making impromptu changes after the fact. In any case, we cannot give confident account scientifically for many stages of evolution, such as the first appearance of metabolism. morphogenesis, and partially, about language and its effects. So, any hypothesis is possible, as long as its elaboration of detail is relevant to the question being answered and is otherwise conservative (Occam's razor), and its presuppositions are also articulated.

The question that occurs to me, is whether you see yourself as pursuing philosophy as distinct from science, or whether you think there is no difference and that one subsumes the other. — Wayfarer

Human experience is integral part of knowledge and should not be neglected. I don't propose that there is universal formula for being correct. But people should not forego their experience. Science and philosophy need to attempt to reconcile, bilaterally.. With justified skepticism on both sides.


Edit:

I took the liberty of doing some very serious editing. So, for anyone who has read the content, if you decide, you may want to reread it, or at least I hope should not be surprised. Mostly it was for stylistic reasons - decided to rephrase some sentences, add clarifications, removed one clarification that didn't make sense.

Ok, what do you mean by object? I assume you do not mean like screws or brick at the hardware store. — tim wood

Of course screws and bricks are objects. Why not? I take for the defining of "object", individuality, particularity, and this is described as a unique identity by the law of identity. So the conditions for being an object is to be a unique individual, and this means having an identity proper to itself.

This strange from you. Because what true means in this sense is not-true, and I'd have thought you'd be all over that. — tim wood

That's how my dictionary defines "true" and it seems to be how it is most commonly used. If you want to propose something different, I could look at that and we might hash it out, but I think you'd have a hard time changing my mind after I've spent so many years studying this.

The only other option I see as viable is to define "true" in relation to honest. Is that what you would prefer "truth" is a form of honesty or authenticity?

Not only is it not necessary, it is impossible, and it is irrelevant.

Admittedly very informally axioms are by default thought of as true, but we're looking more closely, or, I'm looking more closely because I think up above somewhere you got confused when you claimed that, — tim wood

How is it, that determining the truth or falsity of a mathematical axiom is not necessary, it is impossible, and irrelevant, yet axioms are "by default thought of as true". There is no honesty here. This is clearly self-deception, to think of a proposition as "true", when truth or falsity plays no role in its formulation.

From online, the axion of extensionality:
"To understand this axiom, note that the clause in parentheses in the symbolic statement above simply states that A and B have precisely the same members. Thus, what the axiom is really saying is that two sets are equal if and only if they have precisely the same members. The essence of this is: A set is determined uniquely by its members."

What about this requires the treatment of anything as an object ("object" awaiting you definition), and what does it have to do with Platonism and why is Platonism "required"? — tim wood

The word "members" signifies distinct and unique individuals, "objects" as per my definition. Since numbers are commonly said to be the members of sets, then numbers are objects with identity. Notice that the identity of a set is dependent on the assumption that a number, as a member, is an object with an identity.

The reason why Platonism is required is that this is the ontology which supports the assumption that numbers are objects, by designating this as true, i.e. in correspondence with reality. Here's a brief explanation. Let's assume we use the symbol "2" to refer to a group of two things, as the quantity of things there. Do you agree that this is a true description of how one would use the symbol?

In this case, "two" is what is said about the group of things, it is a predication, and the subject is the group. The group is a quantity of two. Here, it is impossible that "two" refers to an object, because it necessarily refers to a group of two objects. However, if we employ a Platonist premise, we can assume that this Idea, the quantity of two, is itself an object being referred to by the numeral "2", independently of any group of two things. Then we might use the symbol "2" to refer to this object, the quantity of two, independently of any existing groups of two. So when 2 is the member of a set, that is what the symbol "2" represents, an object, the number 2, which is independent of any group of two.

That's why Platonism is required for set theory because it provides the premise whereby the number 2, or any other number, exists independently of any quantity of things. By this ontology it is true that the symbol"2" refers to an object, the number 2. Without this premise, when "2" is used it would necessarily refer to two objects, not one object.

The point being that the world of ideas is different from the world of worldly objects. And that failing to keep the distinction in mind leads some minds astray. But let's see what he says. — tim wood

That's exactly the point I was arguing when you interjected. Altheist was offering a definition of "object" from semeiotics which would dissolve the distinction between ideas and physical things, making them both "objects" as what is denoted by a symbol, under that proposed definition.

Worth noting here - this is something I’m saying, I don’t know if the poster you asked will agree - that a number or geometric form is a noumenal object, that being an object of ‘nous’, mind or intellect.

So it’s not an object of sense, which is what is presumably implied by many of the question about what ‘object’ means in this context. It’s not a phenomenal or corporeal object, like a hammer, nail, star, or tree. You could even argue that the word ‘object’ is a bit misleading in this context, but if it’s understood in the above sense - as something like ‘the object of an enquiry’ or ‘the object of the debate’ - then it is quite intelligible nonetheless. — Wayfarer

I don't mind using the same word "object" to refer to a sensible object, and also an intelligible object, as an approach to these categories, so long as we maintain the separation between what it means to be an intelligible object and what it means to be sensible object. What I objected to was altheist's proposed definition of "object" which would dissolve this distinction, making sensible objects and intelligible objects all the same type of "object" under one definition of "object".

However, I find that when I employ adherence to the law of identity as the defining feature of an object, then it's difficult to maintain the status of intelligible objects as true "objects" under this principle. This presents the difference between the phenomenal and the noumenal. The human intellect apprehends the phenomenal, but we assume a perfection, or Ideal, which is beyond the grasp of the human intellect, like God is. This is where we derive the idea of the individual unity, and why it is impossible for the human intellect to grasp the completeness, or perfection, of the unique individual. And "object" is generally used to refer to a unique individual.

Yes, with the qualification that 'idea' in this context has determinate meaning, i.e. a real number or mathematical proof is an idea. Not simply an idea in the general sense of mental activity 'hey I've got an idea, let's go to the pub.' (Not that it's a bad idea.) — Wayfarer

Here's a problem to think about. At what point does an idea manifest as a full fledged "intelligible object"? What would be the criteria to distinguish a simple idea in the general sense, from an "Idea" or "Form" in the sense of a mathematical object?

Let's say there are two extremes, the bad idea and the good idea, with countless cases in between. The good ideas, like mathematical objects get designated as "Ideas", or "Forms", Platonic objects of eternal truth. The bad ideas are human mistakes. But what about all the things in between which are not so easy to judge? What about a human idea which gets accepted and becomes an object, like Euclid's postulates? Or on the other hand a proposed mathematical axiom which gets rejected as insufficient? Doesn't the distinction between a Platonic object, as eternal truth, and a human idea which may be mistaken, seem somewhat arbitrary?

The point being that the world of ideas is different from the world of worldly objects. And that failing to keep the distinction in mind leads some minds astray. But let's see what he says.
— tim wood
That's exactly the point I was arguing — Metaphysician Undercover

We agree, then, that screws and bricks as objects, are objects in a sense that numbers taken as objects can never be? We seem to be. @Wayfarer says I can call them ideas. Do you agree?

I think too you'll agree that no two screws or bricks, or any two objects, can be identical, except in some abstract sense. That is, as screws or bricks, but not as objects. Do you?

Next the axiom of extensionality, as referenced above, if applied to objects like screws and bricks allows only for objects being identical to themselves. Whether the axiom allows screws and bricks to be identical with each other in the abstract sense of their being as screws and bricks is more than I know, and anyway I'm assuming subject to correction that it's an axiom for mathematics. Same page so far?

We both have an idea of seven. I buy the notion that our several sevens are identical - and must be. This just a matter understanding what ideas are in use - maybe this is what the axiom formalizes. And seven is just an idea.

If you wish to grant seven or any of its kin near or far some kind of extra-mental reality whether called Platonism or even universals of some kind you're free to do so. But if you wish to argue it, then yours the difficult path. My impression is that you claim it. I challenge you to exhibit the work that demonstrates it. Which of course I hold impossible.

I think too you'll agree that no two screws or bricks, or any two objects, can be identical, except in some abstract sense. That is, as screws or bricks, but not as objects. — tim wood

The whole point of what was to become form-matter dualism, is that the forms of things can be identical, or rather, particular things can ‘participate’ in a form. So the ‘idea of a screw’ or ‘the idea of a brick’ can be turned out in many individual shapes and sizes, but the form is the same for each - a screw is a screw, not a nail. So the identity, the what-it-is-ness, is imparted by the form it embodies (‘I asked for a screw not a nail!’) And also by the function it is intended to perform (form follows function.)

Doesn't the distinction between a Platonic object, as eternal truth, and a human idea which may be mistaken, seem somewhat arbitrary? — Metaphysician Undercover

Sure. The difference seems much more obvious to us moderns, though. I can imagine in the classical period, that the concept of the form was much crisper and easier to imagine.

The human intellect apprehends the phenomenal, but we assume a perfection, or Ideal, which is beyond the grasp of the human intellect, like God is. — Metaphysician Undercover

Now wait just a minute. Isn’t the idea, in form-matter dualism, that ‘the mind perceives the Form, and the eye the Shape?’ Go back to the original metaphor of hylomorphism - a wax seal. The wax is the matter - it could be any wax, or another kind of matter, provided it can receive an impression. The seal itself is the form - when you look at the seal, you can tell whose seal it is (that being the purpose of a seal). That is the original metaphor for hylomorphism.

So this principle was extended and elaborated in later hylomorphic dualism - the intellect, nous, ‘receives’ the form, the eye ‘perceives’ it. That is explicated at length in this passage from a text on Thomistic psychology:

if the proper knowledge of the senses is of accidents, through forms that are individualized, the proper knowledge of intellect is of essences, through forms that are universalized. Intellectual knowledge is analogous to sense knowledge inasmuch as it demands the reception of the form of the thing which is known. But it differs from sense knowledge so far forth as it consists in the apprehension of things, not in their individuality, but in their universality.

Hence the relationship between ‘forms’ and ‘universals’. It seems clear as crystal to me, but apparently not to everyone.

Self-replicating polymers are conjectured to have appeared, because organics are demonstrably chemically active and polymerize easily, and although labile in unprotected environment, the presence of solid catalytic surfaces where the matter is deposited or rock pores, could have retained them for longer durations. — simeonz

In this matter the proposition ‘results from chance’ is itself self-contradictory. That something ‘just happens’ is not an explanation. Why is it that in every branch of science, causal relations are sought, but in respect of the formation of life, the absence of a causal explanation is the desired outcome? I don’t think the answer to that question lies within science.

We both have an idea of seven. I buy the notion that our several sevens are identical - and must be. — tim wood

I don't buy this, because you and I are different, just like two bricks are different. If two bricks are different why would you think that any one property that one brick has would be identical to the property of another brick. And if ideas are properties of human beings, why would you think that an idea which I have would be identical to your idea?

Do you know what identity is, according to the law of identity? It means the very same as, one and the same. Identity is proper to the thing itself, and it is shared with nothing else, because if something else had the same identity it would not be something else, but the same thing. So I don't buy the idea that the very same idea could be in your mind, and my mind. I think the evidence indicates that this is not true.

Idealism might propose independent "Ideas", as Ideals, which are independent from any human ideas. These Ideals are supposed to be the true immaterial objects. This is what Plato describes in The Republic. There is the divine Idea of a bed, the perfect bed. The carpenter attempts to replicate this Ideal with one's own idea of a bed, then builds a replication of that idea. Notice the two layers of representation between the artificial material object and the independent "Idea", as an object. The human idea does not obtain to the level of "object" with independent existence, because it is only a representation of that supposed independent, divine Ideal.

The whole point of what was to become form-matter dualism, is that the forms of things can be identical, or rather, particular things can ‘participate’ in a form. — Wayfarer

The theory of participation comes from Pythagorean Idealism. It can be argued that Plato actually refuted this theory. Through his analysis of this type of Idealism, he actually exposed its weaknesses. Although Aristotle is given credit for the actual refutation, he simply synthesized, in a more formal argument, the information provided by Plato's analysis.

A very good example of the theory of participation is fount in The Symposium. Beautiful things obtain their beauty by partaking in the Idea of beauty. What is evident here is that there is an independent Idea, also sensible things which partake in that Idea, and then human ideas which are produced from observation of the sensible things. Notice how the sensible world is a medium between the independent Ideas, and human ideas, because it is the sensible things which partake of the independent Idea, not the human ideas themselves. The human ideas are derived from the sensible things

Plato wanted to understand how the sensible particulars partake in the separate Ideas. The issue is that the Ideas must be prior to the sensible particulars in order to account for numerous particulars being part of the same Idea. This means the Ideas must be in some sense a cause. But from the human perspective, we get our ideas from the sensible things, so we see them as the cause of ideas. So from our perspective we see sensible things as active, and the ancient view was that sensible things actively participated in the separate Ideas. This makes the separate Ideas appear as passive (eternal, unchanging), and denies them causal capacity.

The key to turning this around is revealed in The Republic, as "the good". The good is the motivation for action, as the ground for intent. When we assign causal capacity to intent then we see the reality of human actions, and the fact that the sensible objects follow from the human ideas, necessitating that the idea of the artificial thing is prior to its sensible existence. Both Plato and Aristotle assign this order to natural things as well, making the independent or separate "Forms" the cause of natural sensible objects.

In The Republic, Plato removes the sensible object as necessarily the medium between the human idea and the divine Ideas. This is contrary to Kant, who makes all human ideas dependent on sensation. But for Plato, it appears like the good, in the sense of what is morally proper, cannot be derived from sensible existence, it is only apprehended by the mind. Therefore the human mind must have the capacity to be guided directly toward the divine Ideas, without the intervention of sensation.

Now wait just a minute. Isn’t the idea, in form-matter dualism, that ‘the mind perceives the Form, and the eye the Shape?’ Go back to the original metaphor of hylomorphism - a wax seal. The wax is the matter - it could be any wax, or another kind of matter, provided it can receive an impression. The seal itself is the form - when you look at the seal, you can tell whose seal it is (that being the purpose of a seal). That is the original metaphor for hylomorphism. — Wayfarer

I don't see the point in distinguishing shape from form. The shape is a part of the form, the part perceived by the eyes. But the eye cannot interpret the meaning in the shape.

Remember, in Aristotelean hylomorphism there is two distinct senses of "form". There is the form of the object which inheres within the object itself, combined with its matter, constituting its identity as the thing which it is, and there is the form which the human mind abstracts. These two are not the same, as the abstraction does not contain the accidents.

In this matter the proposition ‘results from chance’ is itself self-contradictory. — Wayfarer

If by chance, you mean, improbable event, then this is not what is involved. The hypotheses are not presupposing extraordinary occurrences. That wouldn't methodologically agree with conventional empiricism. If you mean that the we rely on ideas whose historical accuracy cannot be firmly supported, then you are correct. We cannot fight the effects of irreversible erosion of remnant evidence for proto-organics whose active proliferation would not have survived the climactic and ecosystemic changes that have transpired henceforth. Science is forced to speculate, and appeal to reason. There is no internal contradiction in doing that, just methodological hermeticism. The same applies to conjectures in morphogenesis, because soft tissue organism do not fossilize in a manner that confers their organ structure. Some ideas can only be hypothesized. Not because science is in contradiction, but because the effects of time and entropy preclude us from recovering the historical account necessary for inspection of scientific consistency. This forces abiogensis to rely on scientific retrodiction (since this is the only form of prediction we have), fossils, sediments, phylogenetic analysis of organisms, and as a last resort, conclusions by elimination. We also need time. Not to create fiction, but to figure out arguments for or against claims. On the other hand, you might mean that the conditions, as hypothesized, even if true, are very particular to earth. That is arguably true. While this may support a theistic argument, it does not necessarily contradict science and support revelation in the sense of incident miracle. I will explain this as it ties into a discussion trend on this forum.

When I am discussing physics and natural sciences, I am not intently contrasting them with theism, just with scientifically incompatible theism. Science is not an overall world view for me, but just a fraction of my world view. Namely, faith in the virtue of experience and its reconciliation with reason. Physics is not in a privileged position over experience and reason to establish rules and maintain them, because it favors a particular mindset. This is what mainstream religion used to do, and this is why I am not instituionally religious. The laws of science evolve constantly. What it tries to do is very narrowly defined and has comparatively little bearing on the condition of the universe. Physics tries to infer from experience predictive ways to reason about state patterns which appear to reproducibly apply to all spatio-temporal vicinities. In other words, it deals with universal constraints that can be observed anywhere, in close proximity around a location. It does not account for the global affairs altogether, aside from those local constraints that apply everywhere.

There are caveats, naturally. Since the universe, by scientific retrodiction is conjectured to have been concentrated, it is pertinent to ask, how the known limitations of local state dynamics would transitively confine, through their consistent following application, the development of matter after it dispersed. This will either confirm or refine our conception of the natural law. The second issue is, that since we know that we cant make the laws fully predictive, at least locally (QM asserts it), the question is whether the present day celestial variety lies within the realm of that cognitive gap we can account for, or are there initial varieties that have spawned it. Without any physically contradicting explanation, we could concur that they were present, either as a starting feature, or because time may protrude back beyond the concentrated stage in additional historical cycles. Another caveat is that laws are now mostly probabilistic, which makes them implicitly global in some sense. The second law of thermodynamics applies to all vicinities, but its strength depends on the size and the volume under consideration. And even then, the result is inclined, not strict, so the pattern that the law postulates makes local sense, but from a global vantage point. The same is true for QM, which applies rather weakly for singular events, but matches much more strongly for spans of time and at greater scales.

From this, I think it is apparent that whether something is a miracle is not dependent on being in agreement with a known physical law, but whether it is in agreement with reproducible pattern of sensory experience. If newly uncovered state dynamic is consistent, the situation would provoke amendment of the scientific expressions that convey the predictive implications. On the other hand, claims for hypothetical material events whose probability for occurring is extraordinarily small according to our prior experience, and whose sensory realization (such as described) cannot be demonstrated, are unlikely to be treated in agreement with science. As I have mentioned before, persuasion in the effectiveness of the scientific methodology is ultimately spontaneous, but I agree much of it. I agree that minimalism when conjecturing from evidence is warranted. That patterns of experience should be interpreted as simply as we can (by cognitive ability) without rendering the power of the interpretation too limited to be useful. The only vindication for detail is how it extrapolates to generalization. This is the methodological convention for science, and I agree with it.

We claim that certain studies are natural, because they investigate the relationship between events using physical law. They trace the connection between initial conditions and particular outcome, trying to establish how the constraints we know derive the typical result with reasonable certainty. Science does not explain how the particular global context was formed. It does not therefore explain the root cause of the initial conditions. Even when sciences seek deeply rooted causes, they only end up in other apriori features. The present day state of affairs may easily fall within the predictive gap of our physical law. Either way, there is scientific contradiction to admit that the initial state of the universe can be supreme design, but any conjecture about the quality and nature of the designer is opposed to scientific minimalism.

Some examples of natural sciences that we talked about. Neurology tries to figure out how the admissible transitions postulated by physics conclude at the biological outcomes that we typically observe with reasonable certainty. (It is far from succeeding.) Morphogenetic studies try to establish how the physical law traces the path of development of life from fertilized egg cell to a developed human being. Abiogenetic studies try to explain the arrival of contemporary organisms from early prebiotic chemistry. In contrast, revelation theism attacks the lack of evidence and criticizes the use of conjectural latitude to reaffirm naturalism and conventional science. The fact is that the early factors and events are obscured. Abiogenesis therefore has to rely on plausibility as argument, of events that are admissible considering the evidence present, but unpoven. Theism considers lack of hard evidence and confident reason scientific impotence, but does not require it of itself, because proof and reason are inessential to its central faith. They even consider its lack vindication of their ontology. In other words, theists start epistemically satisfied without reliance on detailed knowledge of the world and consider themselves in a better position, because their opponents are obviously challenged by their harder epistemic requirements.

I am tentatively theistic, possibilian, misotheistic. I conjecture things like telepathy, or zodiac influences, good and bad energies in the world, etc. But my ideas are tentative, reevaluated, doubted, and if they survive the test of experience and contemplation, increase in detail and confidence. My conjectures aim to become more articulate from detail that I accumulate. I am not looking to gain fundamental wisdom that refrains from elaboration of my world view by facts. I call this epistemically positive attitude. I employ fixed set of persuasions, indeed, but all my ideas are under constant attack, and my experiences are given time to convince me or dissuade me. In contrast, conventional mainstream theism can argue in a manner that appears epistemically satisfied, prior to experience, and experience appears to be gained mostly introspectively. The knowledge of material relations is considered antithetic to the ideal proposed. I consider this attitude epistemically negative. I am sorry if I come off antagonistic, but this is how I see things about most theistic proposals.

I will again try to articulate, to the best of my knowledge (which is not very ample), why RNA may have formed naturally over time. Its arrival is currently conjectured to have happened in stages. Such stages of increasing complexity can be synthesized in laboratory conditions, but one problem that exists is that the chemical concentrations supplied, the thermal and mechanical conditions are not naturally present today. The hypothesis is, that because the intense geothermal activity, the frequent moon cycles, the carbon dioxide concentration in the air and water, and the stronger sun radiation, those conditions may have existed for a while. Linking the stages is another challenge, as the retention of the intermediates, i.e. nucleobases, nucleotides, pre-RNA compounds, short RNA or RNA-DNA hybrid chains, is not natural in unprotected aqueous environment. Several hypotheses exist. My understanding here is shallow, and I will advise you to double check, but apparently the properties of certain solids, particularly clays or crystals, identify them as bonding agents of carbon compounds, which become retained on such surfaces, a sort of locale for the emergence of organic film. Those newly formed prebiotic organic substances, being protected from dissolution in the surrounding water by their solid host, are compelled to react with each other and polymerize over time. It was a staged process of attainment of structure. While chance was involved at each stage individually, those surfaces show in laboratories that they are sufficiently conducive to polymerization, thus would be able to effect a starting point for primitive self-replicating compounds over time. Another not so different hypothesis is that the pores of rocks served as areas, which concentrated and retained intermediate organic substances together, prevented them from diluting in the surrounding environment, and partially protected them from reacting with other proliferate chemical agents. This may have provided early substitute for cellularization, and hence fostered the appearance of longer polymers (which are less stable) and eventually metabolic cycles (which is indeed thornier topic). And a hypothesis exists that isolation was provided by same phase separation. This is possible in emulsions, or coacervates, which are substances that form droplets in other liquids. Those droplets might have recombined through fussion and fission, which would allow them to exchange reactants over time, allowing for early form of natural selection. It is also possible that cellularization existed before self-replicating polymers, offered by simple organic amphiphilic compounds. This could have provided a stage for the arrival of RNA-like polymers later, either distributed by vesicle or possibly as a kind of viroid.

I am not the person to answer questions about this topic. But to me, it appears that there are semi-plausible conjectures. As I explained, they depend on the hypothetical initial conditions. If I wanted to emphasize a weakness, I would attack the appearance of enzymic metabolism. Even though, as I said, any attack without a known historical account is proof by your opponent's ignorance, which I do not condone. But, still, it appears to be a weak link, or at least I haven't encountered plausible natural explanations. Attacking morphogensis is similar, but even if the detail is not clear, there is reasonable expectation of growth in complexity under the proliferation of forms during the Cambrian era. Language is maybe insufficiently explained, as a phenomenon that evolved quickly, under presumed environmental stress, but in just single species.

If two bricks are different why would you think that any one property that one brick has would be identical to the property of another brick. — Metaphysician Undercover

Any property? They're called bricks. Can you think of any reason why? And if your and my sevens are not the same, then I have some ones and fives I'll trade for your tens and twenties.

This is what Plato describes in The Republic. There is the divine Idea of a bed, the perfect bed. The carpenter attempts to replicate this Ideal with one's own idea of a bed, then builds a replication of that idea. — Metaphysician Undercover

And see if you can find one, any one, off by itself where no mind is to have it.

Idealism might propose independent "Ideas", as Ideals, which are independent from any human ideas. — Metaphysician Undercover

Great, and where do those come from? Mind, now, nothing human here.

And how does "Idealism" propose? I buy the poetry of Plato's attempt to solve what was for him a problem. But we're 2400 or so years beyond that. We don't have his problems, nor live in his world. His work a matter of fact the proper subject for the history of philosophy. Like many old things still of some use in some areas, but applicable itself in no sense except by people resolved to living by understandings long, long obsolete.

And you're the guy who goes to the building supply store to purchase bricks. You're handed two bricks, one in each hand. You look at the one in your left hand and say, "That is one great brick!" And you look at the one in your right hand and say, "What the hell is that?!" There may be strange things in your philosophy - clearly there are - but nothing stranger than your philosophy. You can buy a brick, but not bricks. And I'm thinking that's a problem Plato would not have had.

Any property? They're called bricks. Can you think of any reason why? And if your and my sevens are not the same, then I have some ones and fives I'll trade for your tens and twenties. — tim wood

I don't see your point. Your ones and fives, and my tens and twenties are physical objects like bricks. And each one of your ones is different from every other one of your ones, just like each brick is a different brick, despite the fact that they may all look the same to you. So why would you assume that there is some type of a one, which is the very same one as every other one, despite occurring in distinct situations?

Great, and where do those come from? Mind, now, nothing human here. — tim wood

They are proposed as Divine, therefore not from human minds.

And see if you can find one, any one, off by itself where no mind is to have it. — tim wood

If you read what I said, you'd understand it as saying that the separate Ideals, which are the property of a Divine Mind, are not found by human minds. Human minds are lacking in the perfection required for such Ideals.

And you're the guy who goes to the building supply store to purchase bricks. You're handed two bricks, one in each hand. You look at the one in your left hand and say, "That is one great brick!" And you look at the one in your right hand and say, "What the hell is that?!" There may be strange things in your philosophy - clearly there are - but nothing stranger than your philosophy. You can buy a brick, but not bricks. And I'm thinking that's a problem Plato would not have had. — tim wood

Clearly, despite the fact that I have two things both of which I call a brick, and I have a similar brick in my right hand to the one in my left hand, they are not both the same thing. The fact that the two things, called bricks, each have a different identity, is what the law of identity is meant to express. Do you agree with this?

Proofs in mathematics are said to be discovered, as they are logical possibilities that arguably would exist even if no one discovered them. — Janus

I take your general point about a distinction between some things being invented and discovered. Nice.

Curious how modality seems to be the big background issue on the forums at present - it comes up repeatedly in various discussions, and now shows itself here. That logical possibilities exist is just to say that there are patterns in logical space, that there are patterns in the way we can string symbols together. We might indeed describe the process of identifying these patterns as making a discovery. That's not strong enough to support the contention of platonic realism in the OP.

@Wayfarer - not sure where we were up to. How did the self-training course go?

Proofs in mathematics are said to be discovered, as they are logical possibilities that arguably would exist even if no one discovered them. — Janus

@Banno drew my attention to your response, so I would like to suggest that while we discover separate instances of logical relations in objects and situations, and in us, through the intellectual predisposition to operate our decisions effectively under logical premises, this doesn't seem to change the fact that we are persuaded by instinct to extrapolate those cases to universal laws, without some reliable providential certainty. So, instances of logic are evident (empirically or introspectively, which is still a form of observation of nature), and logical laws are taken on faith. I support reason and science, because I believe in them, having observed their predictions so far, but the emphasis here remains on believe.

P.S.: I also believe in the scientific methodology, as I have previously stated. That is, to learn from experience and to rectify beliefs when confronted with reproducible and reliable contradicting evidence.

Physics is not in a privileged position over experience and reason to establish rules and maintain them, because it favors a particular mindset. This is what mainstream religion used to do, and this is why I am not instituionally religious. The laws of science evolve constantly. What it tries to do is very narrowly defined and has comparatively little bearing on the condition of the universe. Physics tries to infer from experience predictive ways to reason about state patterns which appear to reproducibly apply to all spatio-temporal vicinities. In other words, it deals with universal constraints that can be observed anywhere, in close proximity around a location. It does not account for the global affairs altogether, aside from those local constraints that apply everywhere. — simeonz

Well said, and quite to the point. (I'm not institutionally Christian but have attended Buddhist services so I guess that makes me 'religious' in some sense.) But the point here is philosophical rather than religious. As you observe, physics proceeds by strictly excluding anything which cannot be accounted for in physical theory. In the context of modern science, this manifests as the consideration of only that which can be made the object of quantitative analysis, and represented and expressed in mathematics (which a point made in the OP.) But as you're no doubt aware, physics has become paradigmatic for science generally, and is associated with the philosophical outlook of physicalism and, more broadly, naturalism. That's what is at issue as far as I'm concerned. And my contention is that the nature of life and mind cannot be reduced to, or explained solely in terms of, physics or physical laws. If that make me a dualist, so be it, I'm quite happy to wear that moniker.

The skeptical challenge to the dualist position is: well, you say there is this 'spooky mind-stuff', so where is it? This is where the limitations of the method of objectification need to be made clear. The attributes of the intellect (nous) appear by way of what the mind is able to grasp, in other words, in the operations of reason. They are themselves not an object of scientific analysis, although without the use of reason, scientific analysis could not even start. But as the empiricist instinct is always to proceed in terms of what can be objectively grasped and quantified, then the operations of reason, although assumed by it, are not visible to it.

what the Empiricist speaks of and describes as sense-knowledge is not exactly sense-knowledge, but sense-knowledge plus unconsciously-introduced intellective ingredients, -- sense-knowledge in which he has made room for reason without recognizing it. 1 — Jacques Maritain

How did the self-training course go? — Banno

Ongoing. I'm learning SalesForce. They have an entire training environment online. The training is free, but it costs US$200.00 to sit the certification exam. There's a lot of demand for SalesForce administrators, I'm hoping to add it as a string to the bow (as technical writer). That's what I'm supposedly working towards, but I'm endlessly distractable, especially by this forum. There's a lot of detail, much of it tedious. Anyway, today's Sunday (although that said at this minute I supposed to be vacuuming the swimming pool.)

Like many old things still of some use in some areas, but applicable itself in no sense except by people resolved to living by understandings long, long obsolete. — tim wood

I contend that it is because of Platonism that the West was able to realise the scientific revolution, where the Orient was not. The separation of form and substance, the analysis of the relationship of ideas and matter - all of these were essential to the formation of science. The fact that science has now forgotten its own origins is symptom of degeneration, not of progress. Maybe the current crises in cosmology and physics vindicate Plato's original contention that matter itself is unintelligible.

The skeptical challenge to the dualist position is: well, you say there is this 'spooky mind-stuff', so where is it? This is where the limitations of the method of objectification need to be made clear. The attributes of the intellect (nous) appear by way of what the mind is able to grasp, in other words, in the operations of reason. They are themselves not an object of scientific analysis, although without the use of reason, scientific analysis could not even start. But as the empiricist instinct is always to proceed in terms of what can be objectively grasped and quantified, then the operations of reason, although assumed by it, are not visible to it. — Wayfarer

I'm in broad agreement with this. I just don't think it entails platonic realism, nor that The Unreasonable Effectiveness of Mathematics in the Natural Sciences helps the case much.

I still think that's because of the difficulty of conceiving of the sense in which numbers, forms, ideas, and so on, exist. In this post I frame the issue with reference to the 'instinctive naturalism' that we are born into (Magee on Schopenhauer.) We naturally divide experience in terms of the objective ('out there', separately existing, the world) and subjective ('in here', mental, internal). That is something which we learn in infancy. But the subtle point is that this is also a 'construction' (in Schopehauer's sense of vorstellung, representation). It is, in Buddhist terminology, 'mind-made' (vijnana).

Now the realist will object - wait a minute, you're saying the whole world exists inside the mind? (which is just what @Janus asked.) When you ask that question, you're projecting a perspective from outside the mind; you're imagining a universe with no-one in it, which was, of course, empirically the case prior to the evolution of h.sapiens ¹. But the point is, scientific realism tries always to assume 'the view from nowhere', a perspective which brackets out the subjective elements of judgement altogether, to arrive at a rigorously objective understanding which is the same for all observers. Within that framework, humanity is one amongst all other phenomena. But that 'construction' of a world devoid of any subject, is a methodological step, it's not a metaphysical truth. It too is a construction, albeit not something in the individual mind, but a collective construct. But what happens in modern thinking is that the methodological step is interpreted as a metaphysical truth, which overlooks or forgets what the human mind brings to this whole picture, the sense in which the mind 'holds it together'. Again that is the argument of the article on the blind spot of science.

But even within this framework, mathematical proofs are valid because they are indeed 'common to all who think'. They're part of the structure of reason - which is Frege's view. But because they're not an aspect of empirical reality (out there somewhere) then they can't be regarded as empirically real - which is Benacareff's view. And if they're not empirically real, they're not real, because there ain't no other kind of 'real'.

That's where I've gotten so far. Now, back to the swimming pool.


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1. This point is why Kant said he was 'an empirical realist but a transcendental idealist'. Things can be true from an empirical perspective, but that doesn't mean the empirical perspective is the final truth about things. This also has parallels in Buddhist philosophy as the 'doctrine of two truths, conventional and ultimate'.

So when 2 is the member of a set, that is what the symbol "2" represents, an object, the number 2, which is independent of any group of two — Metaphysician Undercover

2={0,{0}} , 3={2,0,{0}}={0,{0},{0,{0}}} , etc. from the Peano Axioms through set theory. But there are other ways. Just a passing comment.

Maybe the current crises in cosmology and physics vindicate Plato's original contention that matter itself is unintelligible. — Wayfarer

That's the way Aristotle designed his system of logic, from the premise that matter is unintelligible. Part of the physical reality is intelligible, form, and part is unintelligible, matter. It was evident that there are aspects of reality which cannot be understood because they appear to defy the three fundamental laws of logic. What Aristotle did was insist that we uphold the law of identity, and insist that we uphold the law of non-contradiction, but for that aspect of reality which appears unintelligible he allowed that the law of excluded middle to be violated under certain circumstance. So for example, in the case of future occurrences which have not yet been determined (the sea battle tomorrow for example), propositions concerning them are neither true nor false. And even after the event occurs, if it does, it is deemed incorrect to think that the proposition stating that it would occur was true prior to it occurring. In his Physics and Metaphysics, "matter" is assigned to this position of accounting for the real ontological existence of potential, that which may or may not be.

Thanks for the example --- not that I understand it.