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
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.”
On the contrary, within semeiotic the definitions of terms including "object" and "subject" are unambiguous and foster greater understanding. — aletheist
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
What axioms, what objects? Just a simple example ought to suffice to demonstrate the necessity of Platonism. — tim wood
You mean like screws at the hardware store, or bricks? What do you mean when you say, "treat numbers as objects"?treats numbers as objects, — Metaphysician Undercover
Why? What does this even mean?to be true, such axioms require that the ontology of Platonic realism is a true ontology. — Metaphysician Undercover
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
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?The ability to calculate, to speak, count, imagine, and so on - these evolved, no doubt. — 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?But the subject matter of those abilities - how can that be 'explained' in terms of 'evolutionary development'? — Wayfarer
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
So, assuming communication, abstract ideas are simply codification of experience attributes and behavior directives with appropriate linguistic structure. — simeonz
You mean like screws at the hardware store, or bricks? What do you mean when you say, "treat numbers as objects"? — tim wood
Why? What does this even mean? — tim wood
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
Ok, what do you mean by object? I assume you do not mean like screws or brick at the hardware store.I mean to assume that a number is an object. — 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.Do you know what "true" in the sense of correspondence means? It means to correspond with reality. — Metaphysician Undercover
Not only is it not necessary, it is impossible, and it is irrelevant.but it is not necessary that the truth or falsity of the axiom (whether it corresponds with reality) be evident. — 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.These mathematical axioms require that a term signifies an object. Only Platonism can support this prerequisite. — Metaphysician Undercover
Ok, what do you mean by object? — tim wood
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.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
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.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
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.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
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.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
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
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
So, when I said ‘simply’, I meant that the mechanism is simple. — simeonz
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.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
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.Your posts are hard work, although they’re worth the effort — 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.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
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.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
Ok, what do you mean by object? I assume you do not mean like screws or brick at the hardware store. — tim wood
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
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
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 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
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
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
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?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
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
Doesn't the distinction between a Platonic object, as eternal truth, and a human idea which may be mistaken, seem somewhat arbitrary? — Metaphysician Undercover
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
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.
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
We both have an idea of seven. I buy the notion that our several sevens are identical - and must be. — 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. — Wayfarer
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
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.In this matter the proposition ‘results from chance’ is itself self-contradictory. — Wayfarer
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.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
And see if you can find one, any one, off by itself where no mind is to have it.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
Great, and where do those come from? Mind, now, nothing human here.Idealism might propose independent "Ideas", as Ideals, which are independent from any human ideas. — 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. — tim wood
Great, and where do those come from? Mind, now, nothing human here. — tim wood
And see if you can find one, any one, off by itself where no mind is to have it. — tim wood
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
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.Proofs in mathematics are said to be discovered, as they are logical possibilities that arguably would exist even if no one discovered them. — Janus
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
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
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
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
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
Maybe the current crises in cosmology and physics vindicate Plato's original contention that matter itself is unintelligible. — Wayfarer
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