Referring to Eugene Wigner's - The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Mathematical systems are invented and then discarded if discovered to be ineffective

(I hope @jgill agrees)

As Wigner wrote: "I would say that mathematics is the science of skilful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts".

I can invent the elementary mathematical system such that 1 + 1 = 3. Many mathematical systems can be invented. The mathematical system whereby 1 + 1 = 2 has also been invented.

As it has been discovered through observation of the external world that the mathematical system 1 + 1 = 2 is more useful than the mathematical system 1 + 1 = 3, the former has been kept and the latter discarded.

IE, Wigner was correct when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences", because any mathematics that has been shown not to be unreasonably effective has been discarded

Reason, logic and mathematics require regularities in the external world

Wigner wrote - The laws of invariance of physical theories.........regularities in the events in the world around us which can be formulated in terms of mathematical concepts with an uncanny accuracy"

If there were not inherent regularities in the world, we could not predict that two rocks dropped at the same time from the same height reach the ground at the same time, regardless on whether on the Earth or the far side of the Universe.

"Laws of nature" exist only in the mind and not the external world

Wigner wrote "It is not at all natural that "laws of nature" exist, much less that man is able to discover them"

As concepts such a tables, apples, governments, ethics, laws of nature, etc require relationships between their parts, and relations have no ontological existence in the external world (see FH Bradley) but only in the mind (see the Binding Problem and Kant's Apperception and its Unity), such concepts exist only in the mind and not the external world.

Our beliefs are always "unreasonably effective"

Wigner wrote: We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became sceptical concerning the uniqueness of the coordination between keys and doors".

In general, our beliefs in tables, apples, governments, ethics, laws of nature, mathematics, etc are always "unreasonably effective" and well suited to our understanding because beliefs are self-referential.

On the one hand, I have a concept of or a belief about a law of nature existing in the external world, and on the other hand, a law of nature is a concept or belief that only exists in the mind and not the external world.

IE, even if our belief is wrong, we still believe it.

Parts may exist in the world, but the whole only exists in the mind
The whole is a set of parts, but even a part is a set of parts. For the sake of argument, treat the parts as elementary and logical rather than real. As relations have no ontological existence in the world, but only in the mind, the parts may exist in the world, but the whole only exists in the mind.

From particular observations to general laws
From my particular observations in different locations over a period of time that the mere fact that my pen touches my pencil does not result in a change of velocity of either, I can make the general assumption that two objects in contact does not result in the change of velocity of either. I can also make the general assumption about the regularity of the laws of nature. This confirms Richard Hamming"s thought experiment that universally, heavy bodies fall at the same speed as lighter ones, contrary to Aristotle's teaching.

That I can predict a heavy object and a lighter one will fall at the same speed not only on Earth today but on the far side of the universe millions of years from now does initially seem to illustrate the unreasonable power of reason, and by extension logic and mathematics.

General laws only exist in the mind
As general laws, such as the law of nature that two objects when touching does not cause a change of velocity of either require relations between parts, a relation between object A and object B, then general laws can only exist in the mind and not the external world.

We have a whole concept of a universal table (apples, government, ethics, etc) in our minds, which is based on the observation of the relationship of particular parts in our external world. We have the whole concept of a universal law of nature in our minds, which is based on the observation of the relationship of particular parts in our external world. Both the concept of universal table and universal law of nature extend to the far side of the universe. Does our ability to extend the law of nature to the far side of the universe show the unreasonable power of reason ? No, no more than our extending the concept of a table to the far side of the universe shows the unreasonable power of reason.

Concepts such as tables and the law of nature remain in the mind. It does not follow that our projection of these concepts onto the external world makes them states of affairs that obtain in the external world. The fact that we can project our concept of tables and laws of nature onto the far side of the universe cannot be said to show the unreasonable power of reason, as neither of these concepts actually obtain as states of affairs.

As reason, logic and mathematics are self-referential, they cannot be said to be either reasonably or unreasonably effective
Our beliefs are self-referential, in that my concept of a table or a law of nature is of necessity well-suited to what I observe in the external world. IE, on the one hand I have a belief in my mind of a table or law of nature existing in the external world. On the other hand a table or law of nature is a belief that exists only in the mind and not the external world.

Thought experiments and the "unreasonable" nature of mathematics

Aristotle taught that heavy objects fall faster than lighter ones.

— RussellA

However, Richard Hamming's thought experiment gives a powerful reason why heavy objects should fall at the same speed as lighter ones. This thought experiment allows us to predict that universally a heavy object should fall at the same speed as a lighter one, not only on Earth today, but on the far side of the universe and millions of years from now. Such thought experiments can predict both what cannot be seen and what cannot be experimentally foreseen.

Personally, I have consistently observed across space and time that the mere fact of my pen touching my pencil does not result in a change of velocity of either of them, from which I may reasonably agree with Hamming that it follows that there is a universal law that heavy objects should fall at the same speed as lighter ones.

Does not such a prediction show the "unreasonable" power of reason, and by extension logic and mathematics ?

Beliefs are always self-referential, and therefore always well-suited to the world and always "unreasonably" effective

For example, a table is the relation between a table top and table legs. The same applies to apples, governments, unicorns, houses, ethics, etc. As relations don't ontologically exist in the world (FH Bradly) but only in the mind (the Binding Problem), tables don't ontologically exist in the world but only in the mind. As the concept of tables only exists in our thoughts and talk, it should be no surprise about the "unreasonable" effectiveness of our thoughts and talk about tables, as thoughts about tables and tables are one and the same thing.

The question is, are our laws of nature comparable with the situation as regarding the table? As tables only exist in the mind, perhaps our laws of nature only exist in our mind, and consequently, as both self-referential, obviously both well-suited to the world and "unreasonable" effective.

My deduction of the universal law that heavy objects should fall at the same speed as lighter ones is only valid as long as there is a condition of satisfaction between my beliefs and the state of affairs that obtains in the world. My belief clearly does not determine the state of affairs in the world, but as my belief is self-referential, my belief is both well-suited and "unreasonably" effective as to what I believe to be the state of affairs in the world.

Paradigm shifts in my beliefs does not alter the self-referential nature of belief

However, my belief in such a law of nature, my belief in how the world is structured, is no guarantee that what I observe will continue to comply with my present beliefs, in which case I may be forced through the same kind of paradigm shift as described by Thomas Kuhn and be forced to develop a new set of beliefs that correspond with my new experiences and observations.

The point remains that even this new set of beliefs will also be self-referential, in that even my new beliefs will be well-suited and "unreasonably" effective as to what I believe to be the state of affairs in the world.

Our self-referential belief in reason, logic and mathematics can only ever be well-suited to the world and "unreasonably" effective

IE, regardless of what beliefs I may have, what reasoning. logic or mathematics I use, my beliefs will always be well-suited and "unreasonably" effective to my understanding of the world around me because of the self-referential nature of belief.

I think all participants here know about the statement of the unreasonable effectiveness of mathematics. Shouldn't we, rather, speak of it's reasonable effectiveness? — Landoma1

The effectiveness of mathematics is neither reasonable nor unreasonable.

I observe the world. I observe that all things being equal, what happened in the past will happen in the future. This is neither reasonable nor unreasonable, it is just a fact about the world. I observe on the table in front of me my pen touching my pencil, and observe that the mere fact of touching does not cause a change of velocity of either my pen or my pencil. I discover facts about the world by observing the world. These facts are neither reasonable nor unreasonable, they are just how the world is.

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is a 1960 article by the physicist Eugene Wigner.

A biography by Galileo's pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones.

Richard Hamming reflected on and extended Wigner's Unreasonable Effectiveness in 1980. Hamming proposes that Galileo discovered the law of falling bodies not by experimenting, but by simple, though careful, thinking. Suppose that a falling body broke into two pieces. Of course the two pieces would immediately slow down to their appropriate speeds. But suppose further that one piece happened to touch the other one. Would they now be one piece and both speed up? Suppose I tie the two pieces together. How tightly must I do it to make them one piece? A light string? A rope? Glue? When are two pieces one?

Humans can invent many different mathematical systems. Those mathematical systems that are found to correspond with the world consistently through time are kept, otherwise they may be discarded. That some mathematical systems are discovered to be more effective that others is neither reasonable nor unreasonable, it is just what is.

Who is to say that the mere fact of my pen touching my pencil does not result in a change of velocity is a reasonable or unreasonable thing to happen ?

the game of the US constitution cannot continue if a small group of folk storm the Capitol Building — Banno

You do not have to worry about the rules of the game of chess yourself. It has been codified for you — Tobias

I feel like Daniel thrown into the lion's den.

There are different kinds of games
Within a particular game are duties and obligations. An institution has deontic powers in establishing duties and obligations on those who want to take part in that institution. The participant of the game must accept these duties and obligations. The game of the US Constitution cannot continue if the rules of the game are not followed by its citizens. The game of chess cannot continue if the rules of the game are not followed by its players.

However, the game of chess and the game of society are different. If I am not willing to accept the duties and obligations within chess, I am able to leave the table. However, society is different, in that if I am not willing to accept the duties and obligations within society I am not able to leave, as one of the rules of society is that everyone is a member.

Problems arise in obligatory games
Problems arise for those who disagree with the rules and obligations imposed by an institution that they are not able to leave. To illustrate the problems that arise when members of a society disagree with the rules and obligations imposed on them, one can look at a contemporary situation, the 6 January event, and a historical event, Galileo's championing the Copernican heliocentrism.

Galileo
At the time of Galileo's conflict with the Church, the majority subscribed to the Aristotelian geocentric view that the Earth is the centre of the Universe and the orbit of all heavenly bodies. Galileo championed Copernican heliocentrism - the Earth rotating daily and revolved around the sun. Galileo's position met with opposition from within the Catholic Church, the matter was investigated by the Roman Inquisition in 1615, which concluded that heliocentrism was foolish and absurd. For the next decade, Galileo stayed well away from the controversy. In 1632, Galileo published Dialogue Concerning the Two Chief World Systems, and was called to Rome the same year to defend it. He was brought to trial in 1633 before the Inquisitor. Throughout his trial, Galileo steadfastly maintained that since 1616 he had faithfully kept his promise not to hold any of the condemned opinions. However, in 1633 he was threatened with torture if he did not recant, ultimately being found "vehemently suspect of heresy", his Dialogue was banned, and he spent the rest of his life under house arrest.

Promise and obligation in games
Searle wrote: "How can my stating a fact about a man, such as the fact that he made me a promise, commit me to a view about what he ought to do ? In thinking about games, there are different situations:
1) There are voluntary games such as chess that the person neither needs to take part in nor wants to take part in, and as they make no promise to follow the rules, they are under no obligation to follow the rules, and therefore make committent as to what they ought to do
2) There are voluntary games such as chess where the person when promising to follow the rules is declaring that they will be playing the game of chess, not through obligation but through choice, and make no committent as to what they ought to do, only what they will do.
3) There are those obligatory games such as society where the person need make no promise to follow the rules are they are obliged to follow the rules and are committed to what they ought to do.

Unfortunately, I have to leave this game of philosophy, as we are about to get underway for Las Vegas to play a different kind of game.

With that very utterance, the promise is made, and the obligation created. — Banno

Searle says that within social institutions are duties and obligations

Within a social institution are duties and obligations. I sit down with someone for a game of chess, and we both agree that a particular piece is a bishop. For me, that the bishop moves diagonally is declarable even if I don't declare it. For the other person, that the bishop moves perpendicularly is declarable even if they don't declare it. We both promise to use the bishop correctly.

Searle in Ought and Is wrote: "With these conclusions we now return to the question with
which I began this section: How can my stating a fact about a man, such as the fact that he made a promise, commit me to a view about what he ought to do? One can begin to answer this question by saying that for me to state such an institutional fact is already to invoke the constitutive rules of the institution."

Who has the right to determine the duties and obligations within a society

As soon as the game starts I am annoyed that they have broken their promise to use the bishop correctly. The question is, why do I believe that the other person is under a duty and obligation to follow my understanding of the game. I could argue that the majority agree with me that the bishop moves diagonally and therefore the other person must have a duty and obligation to follow the majority.

But if the majority believe that the world is flat, why am I under a duty and obligation to also believe that the world is flat. Why does the minority have a duty and obligation to follow the majority ?

Edmund Burke - "The tyranny of a multitude is a multiplied tyranny."
Arthur Balfour - The tyranny of majorities may be as bad as the tyranny of kings.
Mark Twain - Whenever you find yourself on the side of the majority, it is time to pause and reflect.
Nietzsche in Beyond Good and Evil - The European herd man, on the other hand, puts on airs nowadays as if he were the only acceptable type of man, glorifying the characteristics that make him tame, docile, and useful to the herd as if they were the true human virtues: such as public spirit, benevolence, consideration, industriousness, moderation, modesty, concern, sympathy.

Summary

I am sure that Searle is correct when he says that the test of a social institution is whether it has deontic power in establishing duties and obligations on others. These deontic powers can only come from its own members, whether an elite minority or a heterogeneous majority. One further question to ask is how does one set of members gain deontic power over others of differing opinions. A further question is once having gained such deontic powers, how do they keep them.

Duty and obligation may be admirable, but surely not at the expense of the tyranny of a small elite or a heterogeneous majority.

If the other person is using the same words as I do, but defining them in different ways, I may be mistaken in thinking that they have made me a promise, and should not be surprised if they break what I think are their obligations.

The implications of the performative utterance are manyfold.

Private Facts and Public Facts

I see an object. There are brute facts that it is made of wood, has a weight and is larger at its base than its top.

I declare in a performatory act that "this piece is a bishop and can only move diagonally". The fact that this piece is a bishop and not a castle is a Private Fact for me. Someone else could equally have said "this piece is a castle and can only move perpendicularly". The fact that this piece is a castle and not a bishop is a Private Fact for the other person.

However, we could have both declared that this piece is a bishop, and the fact that this piece is a bishop for both of us becomes a Public Fact, ie, an Institutional Fact (assuming that we are both important figures in society).

But note that the piece becoming a bishop as a Public Fact, an Insitutional Fact, only happened after the declarations had been made

The apparent paradox "this statement is a lie"

Consider the paradox "this statement is a lie. We can then compare the statement "this piece is a bishop" with "this statement is a lie". The fact that this piece is a bishop only happened after the performative declaration, ie, the piece was not a bishop before the declaration. The fact that this statement is a lie only happened after the performative declaration, ie, the statement was not a lie before the declaration.

On the first reading, the statement "this statement is a lie" is a paradox of self-reference, in that the statement seems to have one meaning that is paradoxically self-contradictory. However, the statement "this statement is a lie" has in fact two different independent meanings. The first meaning is before he conclusion of the performatory act. The second meaning is after the conclusion of the performatory act.

IE, as these two independent meanings are not contradictory, there is no longer any paradox.

The direct realist argues that I'm looking at you and the indirect realist argues that I'm looking at your reflection. I don't see why we can't say both. — Michael

I don't think that we can say both.

I look at a rose and light of a wavelength of 700 nm travels from the rose to my eye. I look at a sunset and light of a wavelength of 700 nm travels from the sunset to my eye.

The Direct Realist would say that I have direct awareness of the external world.

If, as a Direct Realist would say, that I have a direct awareness of the external word, how does the Direct Realist know that the wavelength of 700nm entering the eye was caused by a rose or a sunset ?

If the ontology must be put in such terms, then Searle is pretty much a direct realist. Speech acts are very much public. — Banno

In JR Searle's lecture at the Czech Academy of Sciences 2011 on visual perception, he said "I think the rejection of naive realism was the single greatest disaster that happened in philosophy after Descartes"
See www.youtube.com/watch?v=7PfWedgBWag (terrible sound quality)

Indirect Realism may be unsatisfactory but must be better than Naive Realism

Although I say that I believe in Indirect Realism, it is in a sense an unsatisfactory position as it does fly in the face of common sense, and as Searle said: "But the idea that you can't ever perceive the real world but only a picture in your mind that creates a disaster, because the question that arises is what is the relationship between the idea you do perceive or the sense datum of the impression that you do perceive and the real world, and there is no answer to that which is satisfactory once you make once you make the decisive move of rejecting Naive Realism"

Searle supports Naive Realism

Searle points out the major argument against Naive Realism is that the naive realist cannot account for hallucinations: "And the rejection says what really all you can ever see is this thing here, because the naive realist cannot account for hallucinations"

However, for Searle, such an argument against Naive Realism is based on a single fallacy, an ambiguity in the use of such words such as be aware of, be conscious of, to perceive.

Searle says that opponents of Naive Realism use this ambiguity in the concept of awareness to attack Naive Realism by pointing out the indistinguishability between the perception of an hallucination and the perception of a veridical situation.

Searle argues that awareness has in fact two senses. The first sense is intentionalistic, about objects and states of affairs in the world, for example, being aware of a cup. The second sense is constitutive, such that an awareness of something is identical to the awareness itself, for example, being aware of a headache.

Searle's position may be put into a diagram.



Several things follow from the diagram.

In Searle's terms, Institutional Facts are hallucinations

I see an object on a table. As it is a Brute Fact that it is a piece of wood, I may put it on the fire for warmth. As it is a Brute Fact that it has a weight, I may put it on my papers to stop them blowing away.

However, I declare in a performative act that it is a bishop and can only move diagonally. However, someone else could just as well declare that it is a castle and can only move perpendicularly.

Institutional Fact means that the nature of the object is not mind-independent, but rather, the nature of the object is dependent on what is in the mind of the observer of the object. So, when I observe an object, the fact that it is a bishop that moves diagonally, is not in the object itself as a Brute Fact, but is in my mind as an Institutional Fact.

Thinking about the object as a bishop is the same situation as thinking about an object that does not exist in a mind-independent world. In Searle's terms, this is an hallucination. And also in Searle's terms, an hallucination is a synonym for an Institutional Fact. Searle said that he has never experienced an hallucination, yet every time Searle experiences marriage, money, chess, government, he is experiencing, in his own terms, an hallucination.

Searle's Intentional Awareness has the same problem of those who oppose naive realism

As seen in the diagram, Searle's Intentional Awareness appears similar to Kant's position as set out in Jäsche Logic 9:33 “consciousness is really the representation that another representation is in me”. However, both approaches push the problem further back, in that in Intentional Awareness I am not able to be conscious of a representation, but I can be conscious of a representation of a representation.

The question is, if I can be conscious of a representation of a representation, then why cannot I be conscious of a representation. Otherwise one is led into an infinite regress of being conscious of a representation of a representation of a representation, etc, forever.

The central problem with Searle's proposal remains is that how do I know that I am being conscious of the representation of a representation rather than being conscious of a representation, as both of these are indistinguishable. This is the same problem Searle attacks, in that opponents of Naive Realism also argue that a veridical situation and an hallucinatory situation are also indistinguishable.

Language requires both Brute Facts and Institutional Facts

I observe a physical cup in the world, which is a brute fact. Next to this object I see another physical object, the letters CUP, which is another brute fact.

In my mind, I associate these two Brute Facts using a relation. As relations only exist in the mind, as argued by FH Bradley (the nemesis of external relations), then such as relation is an Institutional Fact.

Language, therefore, requires both Brute Facts in a mind-independent world and Institutional Facts in the mind.

Summary

Searle supports Naive Realism. He proposes a mechanism of Intentional Awareness and Constitutive Awareness in order to counter attacks on Naive Realism by those who point out that veridical and hallucinatory situations are indistinguishable within one's conscious state.

Yet his proposal arrives at the same problem, in that an Intentional awareness of a representation of a representation and a Constitutive awareness of a representation are also indistinguishable within one's conscious state.

For the Indirect Realist, Institutional Facts must be metaphorical

From a position of Indirect Realism, in that I cannot perceive the external world as it really is and Husserl's phenomenology, where phenomena through the senses are the primary experience, I can write and think about Institutional facts - my driver's licence, the money in my account, the job I once had, the club I might have belonged to - but only metaphorically, as figures of speech that are not literally applicable.

Searle's intentionality refers to content in the mind not object in the external world

For Searle, the representational properties of a mental state are inherent in the nature of the mental state itself, whether or not it is actually related to some extra-mental object
or state of affairs. Intentionality of a mental state describes its content, not the object.

The consequence is that Speech Acts must be part of a private language

Wittgenstein in Philosophical Investigations argued that a language understandable by only a single individual is incoherent, yet, if my only certain knowledge is with these phenomena, whilst only having a belief in any external world the other side of them, then any speech act I take part in can only be directed at the phenomenal interface between what I know for certain and what I can only believe.

Promises are an example of a type of performative utterance that makes something the case. — Banno

An object becoming a bishop or a combination of letters becoming a word are historical events
A combination of letters or a piece on a chess board don't have intrinsic meaning, but have been given a meaning at some time in the past during a performative act.

The inventor of chess (simplifying history) in a performative act said that a piece having a rounded top with slit cut into it would be named a "bishop" and could only move diagonally. If, perchance, a piece on the chess board does not move diagonally, then it is not a bishop.

Language has developed in a series of performative acts, such that the combination of letters "p-r-o-m-i-s-e" means that that the person who has used it is obliged to carry out what they said they would do. If, perchance, the person does not carry out what they said they would do, then whatever word they used was not a promise - even if they had used the word "promise".


The situation for the subsequent user of language or player of chess is different.
The statement "the Bishop moves diagonally" is true, part of the "state of affairs" of the world, is an institutional fact, is part of a collective intentionality and is constative.

The statement "I ought to move the bishop diagonally" is incorrect use of language, as bishops must be moved diagonally.

As the statement "I promise to move the bishop diagonally" refers to a future event, it is nether true nor false and therefore performative.

However, that I made the statement ""I promise to move the bishop diagonally" is either true or false, and is therefore constative.

Summary
A word in language or a piece on a chess board have a meaning because they have been given a meaning in the past in a performative act. If a piece on a chess board does not move diagonally then it is not a Bishop. If a combination of letters does not result in what the speaker said they would do, then it is not a promise.

As Searle said "One can begin to answer this question by saying that for me to state such an institutional fact is already to invoke the constitutive rules of the institution".

Interpreting Searle, we naturally assume that we live in a social group that shares fundamental beliefs. In such a social institution, if someone has made a promise then this commits me to a view about what they ought to do, because if I had no committent to a view about what they ought to do, then that person had not made a promise - even if they had used the word "promise".

At weekly meetings, refugees from reason gather and reaffirm their reason-denying beliefs. — Art48

You are defining "reason" and "truth" in a limited way, as being dependent upon what is on the other side of the "wall". You say that reason is the attempt to look past the "wall" at what may be uncomfortable truths.

But why cannot reason also be remaining this side of the "wall" and accepting beliefs that not only do we believe to be true but also are comfortable with, and which, when all said and done, do pragmatically work ?

Only one impossible answer: we do in fact experience the (noumenal) world; and our experience is not localized to this grey physical mass. Consciousness is, after all, noumena. Nothing escapes this. Certainly not phenomena. — Constance

Interpreting what you wrote in my own terms.

You wrote: I am far less interested in objects than I am in the self.

We begin with the self, the "I" that is conscious, the "I" that has thoughts. The "I" has thoughts about things external to the thoughts themselves, things that change with time, and these things are called phenomena. All the "I" knows for certain are phenomena - the colour red, a sharp pain, an acrid smell, a sour taste, a crackling noise. The "I" has thoughts about these individual phenomena, but more than that, the "I" combines these individual phenomena in various ways. The "I's" thoughts are about phenomena and various combinations of phenomena.

A whole is only conceivable in relation to a part, just as up is only conceivable relative to down. Meanings are generated in opposition.

The nature of relations is critical. My belief is that relations do ontologically exist in the mind (the Binding Problem). We call these combinations of phenomena "noumena". We think about particular combinations of phenomena and sometimes we give them a name. The combination of phenomena, the colour red, an acrid smell, a crackling noise we can name "fire", and this "fire" is a noumena. We can say that combinations of phenomena exist in a logical reality, in that noumena exist in a logical reality. A logical reality that exists in the mind.

I don't think of noumena as objects at all. I think of noumena as the indeterminacy inherent in all that is.

Noumena are combinations of phenomena. But a combination is a relation. As relations only ontological exist in the mind, noumena only ontologically exist in the mind. We can think about the noumena occupying a space, but such a space is only a logical space, nothing more than that. When thinking about space, as we are thinking about the relation between phenomena, we are thinking about a logical space.

On the other hand, there we are observing the world and it is intuitively powerful, this presence of things and our engagement. It is not possible that I am not experiencing "reality" for what is real can only be a measure of the way reality is presented.

Our thoughts about these combinations of phenomena, these noumena, are intuitively powerful because they ontologically exist within our mind, within a logical space and a logical reality.

Nothing at all can escape the what we see as eternal, noumenal, infinite.

There is almost no limit to the number of possible combinations of phenomena, in a mereological sense, meaning that there is almost no limit to the potential number of noumena existing in a logical reality

Space and time, when pressed for basic meanings, are apodictically eternal.

In experiencing phenomena, I have freedom to combine them in an almost unlimited number of spatial and temporal ways, a logical space and time unbounded and eternal.

I am surely receiving the (noumenal) world indirectly. But one can never get around, in an empirical way, that the thick membrane of brain tissue simply has no epistemic access to the "outside"

The mind needs no epistemic access to the external world in order to perceive noumena. The mind perceives the noumena directly as combinations of phenomena in a logical space existing within the mind.

Only one impossible answer: we do in fact experience the (noumenal) world; and our experience is not localized to this grey physical mass. Consciousness is, after all, noumena. Nothing escapes this. Certainly not phenomena.

Our consciousness is of phenomena and combinations of phenomena , both having an ontological existence within the mind. These combinations of phenomena, which we know as noumena, exist in a logical world that exists within the mind.

Kant's a priori pure intuition

Kant's a priori pure intuitions of time and space may be explained as being a logical time and space created by ontological relationships between phenomena, ie, noumena, within the mind.

Logic and the world

a perverse belief in a logically structured world can generate a false sense of paradox

Relations are an ontological part of the logical world we perceive in our minds. The world we imagine outside of the phenomena we perceive is a world that we cannot imagine to have relations (FH Bradley's Regress argument). It is inevitable that the application of relational logic onto a world without relational logic will inevitable lead to paradox.

But that is not Kant. We do not become aware of noumena indirectly. We do not become aware of this at all. This is the trouble with analytic philosophy and the attempt to tall about Kant and transcendental idealism.It does not have any thematic development for this. And I will say this with emphasis: If you are looking for some way to make sense out of Kant's idealism, and to build on this, elaborate on what Kant laid out there, then talk about direct and indirect realism is not a viable alternative as it insists that empirical observation, somewhere in the discoveries through microscopes and telescopes, is going to be relevant. — Constance

A question
Kant said that a priori knowledge is "knowledge that is absolutely independent of all experience". I propose that such priori knowledge is innate within the brain, a product of over 4 billion years of evolution and is part of the physical "hardware" of the brain.

I am curious as to your belief as to the source of this a priori knowledge, this pure intuition of time and space intrinsic in our minds?

What are "noumena"

Kant wrote in Prolegomena to any Future Metaphysics 1783: "And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something."

Kant included causation within the category of pure understanding, an a priori pure intuition, where an effect requires a cause. Given causation as an a priori pure intuition, it follows that the observer must know without doubt that there has been a cause to the phenomenon, and this cause may be called a "noumenon".

In my terms, a belief in causation is a Kantian a priori pure intuition because it has been wired into the brain through evolutionary processes,

The problem remains that although such an a priori belief may be pragmatically useful, there is no guarantee that it corresponds with the reality of the external world.

IE, I am not aware of any justification by Kant as to why a priori pure intuitions should of necessity correspond with the reality of the external world. This is the same problem found in Indirect Realism, in discovering the reality of the external world through internal representations.

Concepts

There must be a distinction between the whole and its parts. When we observe something, we are observing a whole made up from a relationship between parts. As relations don't ontologically exist in the external world, as illustrated by FH Bradley, and relations do ontologically exist in the mind, as illustrated by the Binding problem, we can say that the parts of the object do exist in the external world, but the whole object, as a relation between its parts, can only exist in the mind as a concept.

The parts we observe are assembled in the mind into concepts - a table is a table top plus table legs, a house is a roof plus walls plus windows, etc. But many mereological permutations are possible of the parts we observe within the external world - a table top plus table legs, my pen and the Eiffel Tower, etc. We sensibly choose and name those particular combinations that are beneficial to our evolutionary well-being and survival.

It follows that if we think of noumena as objects in the external world consisting of a relationship between a set of parts, then it is true that noumena don't ontologically exist in the world, as relations don't ontologically exist in the external world, but only in the mind of the observer as a concept.

You wrote "If you are going to take seriously some impossible interface with noumena, it is not going to happen through a discursive reasoning process of what is "out there" because what is out there will always be conditioned evidence and noumena are not conditioned"

IE, in my terms, it follows that our understanding of noumena as defined as objects in the external world must be transcendental in that objects in the external world don't ontologically exist.

Meaning

Meaning in language is in the relationship between parts. "Apple" has no meaning in itself. "The apple is green" has meaning because of the relationship between its parts, "apple" and "green". As relations have no ontological existence in the external world, but only in the mind, and as meaning is a relationship between parts, meaning cannot exist in the external world, but only in the mind

You wrote: "This is why hermeneutics is so important, for it sees this and therefore puts interpretation first, and it is not physicality that takes priority, but meaning, and this goes to language and logic."

IE, in my terms, any meaning discovered in the external world must be transcendental, as meaning has no ontological existence in the external world but only in the mind.

One arrives at the proposition that only what is said empirically and analytically can make sense via his apriori arguments. — Constance

Kant's a priori pure intuitions

I agree with you that Kant in Critique of Pure Reason argued that we can only understand the truth of the noumena in the world by applying a priori pure intuition to the phenomena we receive from these noumena.

Kant wrote: "Space and time are its pure forms, sensation in general its matter. We can cognize only the former a priori, i.e., prior to all actual perception, and they are therefore called pure intuition; the latter, however, is that in our cognition that is responsible for it being called a posteriori cognition, i.e., empirical intuition." (B60)

He also wrote: I call all representations pure (in the transcendental sense) in which nothing is to be encountered that belongs to sensation. Accordingly the pure form of sensible intuitions in general is to be encountered in the mind a priori, wherein all of the manifold of appearances is intuited in certain relations. This pure form of sensibility itself is also called pure intuition. (B35)

However, Kant does not explain the source of these a priori pure intuitions. He does not explain how we are able have these a priori pure intuitions.

Indirect and Direct Realism

Today, there are those who believe in Indirect Realism and those who believe in Direct Realism.

Direct Realism is the common sense view within the philosophy of mind which states that objects are as they appear to be. All objects are made of matter and that our perceptions are entirely correct, in which case noumena correspond with phenomena.

Indirect Realism is the view that there is an external world that exists independently of the mind, but we can only perceive that world indirectly through sense data. Sense data can only represent the mind-independent world, meaning that we can only ever know a representation of the external world, in which case phenomena can never allow us to know noumena directly.

I personally believe in Indirect Realism. I understand Kant's position as also being similar to that of the Indirect Realist, even though he did not use this terminology

What is the source of a priori pure intuitions

Where do our a priori pure intuitions come from? Some would say from a metaphysical god, others would say that there is a physical explanation.

It follows from my belief in Physicalism, where everything in the world is physical, a world of matter and forces, and my belief that we are not born as "blank slates", in that all our behaviour is learned, that we are in fact born with innate a priori pure intuitions. These innate a priori pure intuitions are part of the structure of the brain, part of the hardware of the brain, part of the physical arrangement of neurons within the brain.

It seems clear that the brain has the physical structure it has as a consequence of an evolutionary process lasting over 4 billion years. A process where organisms change and evolve over time, along the lines of the natural selection as set out in Darwin's On The Origin of Species.

IE, our a priori pure intuitions are a direct consequence of a physical evolutionary process.

A future question

Kant assumed that our a priori pure intuitions are true to the reality of the world. However, would this be the case if as a result of a physical evolutionary process?

A modern interpretation of Kant's Transcendental Idealism

To date
I am using the analogy that our a priori knowledge is the hardware of the brain, and our a posteriori knowledge is the software of the brain. The hardware of the brain has evolved over more than 4.5 billion years of evolution in synergy with the world enabling us to conceptualise time and space. The software of the brain enables us to observe apples falling off tables.

My belief is that the world can be described within the matter and forces of Physicalism rather than any supernatural intervention.

It follows that we should aim to discover knowledge empirically rather than metaphysically. However, there is a limit to human intelligence, and for knowledge beyond the limits of human intelligence we have no alternative but to use speculative conjecture. We have no alternative but to resort to metaphysical explanations (one could also say, metaphorical explanations)

All empirical theory is suspended, following Kant — Constance

Not true, it seems to me. For Kant, knowledge needs both empirical observation and rationalism. Kant is not saying that we don't observe the world, but he is saying that what we think we observe is determined by the innate nature of our brain. Innate are the pure intuitions of time and space, a prioiri knowledge that we know independent of experience. He wrote in Prolegomena to any Future Metaphysics 1783 - "And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something." Kant postulated that the mind intuits sensory experience, which it then processes in the faculty of the understanding to produce an ordered predictable world.

IE, Kant believed intuition of objects in the external world is the primary source for our understanding.

Apriority is transcendental. a presupposition to all empirical thinking — Constance

In understanding the external world, we try to make sense of empirical observations using innate, a priori knowledge. Our understanding of necessity transcends the reality the of the things as they are in themselves. As Kant wrote in the Fourth Paralogism: " I understand by the transcendental idealism of all appearances the doctrine that they are all together to be regarded as mere representations and not as things in themselves, and accordingly that space and time are only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves.

My reading of transcendental is not that of the supernatural, but rather that that there are many aspects of the world that we cannot explain using current scientific knowledge, such as the mind-body problem. This is not to say that such problems cannot be explained by future empirical science.

The transcendental paradox of self-awareness
1) As "I" subjectively know the colour red, "I" subjectively know time and space.
2) But the "I" is no more nor less than the physical structure of the brain, where the brain may be considered to be neurons in a particular arrangement.
3) Given an identity between 1) and 2), then the physical structure of the brain knows time and space.
4) But time and space are expressed within the physical structure of the brain
5) Given an identity between 3) and 4), the physical structure of the brain knows the physical structure of the brain, ie self-awareness.

IE, the paradoxical consequence of a priori knowledge is the brain's self-awareness.

Summary
IE, For Kant, knowledge requires both empirical observation and metaphysical interpretation. As a believer in the metaphysics of god and morality, it is not that he considered the metaphysical of more primary importance than the empirical, rather he strived to put the metaphysical on a more scientific basis, which must remain an ongoing process.

Can’t critique the philosophy not given to us, using conditions not known to the author of the one that was. — Mww

I'm not trying to critique Kant's Transcendental Idealism, rather, I'm trying to interpret it in today's terms.

There is NOTHING that can be said that explains apriority — Constance

Kant's Transcendental Idealism

Determinism
My belief is that every thought or feeling we have is expressed within the physical structure of the brain. I accept that others may believe that we may have thoughts and feelings beyond that which is determined by the physical structure of the brain, such as a god, but I personally don't.

Transcendental Idealism
The brain can get information about the external world through the senses - sight, sound, touch, hearing, smell. Kant is making the point in his theory of transcendental idealism that we know things about the external world such as causation, time and space that we could not have discovered by observing phenomena through our senses, as illustrated by Hume. He calls this knowledge a priori knowledge.

A priori knowledge
As our knowledge about causation, time and space is not discoverable through our senses alone, and yet as all knowledge is expressed within the physical structure of the brain, then this knowledge must be a pre-existing part of the brain. A priori knowledge is part of the built-in hardware of the brain, where empirical a posteriori observation is part of the software. We know a priori the nature of causation, time and space as much as we know the colour red when observing the wavelength 700nm.

Evolution
A priori knowledge cannot be explained from an empiricist viewpoint, where the human mind is a "blank slate" at birth and develops its thoughts only through experience. A priori knowledge can be explained as the product of an evolutionary process that began on Earth over 4.5 billion years ago, a continuous process of synergy within the world from unicellular organisms to human brains of up to 100 billion neurons. Darwin was the first person to develop the theory of evolution by natural selection. As Kant died before Darwin was born, Kant was not able to benefit from Darwin's insights.

Knowledge
We know causation, time and space in two distinct ways, as a priori knowledge built into the physical structure of our brain by evolution, and as a posteriori knowledge discovered through empirical observation.

IE, we experience the empirical world (the software) through a "meta-empirical" world (the hardware). Our a posteriori knowledge (the software) is transcended by our a priori knowledge (the hardware).

I’ll grant innate abilities, which is just a euphemism for instinct. — Mww

So far we have three words: instinct, ability and knowledge. Instinct is an innate fixed pattern of behaviour. Ability is the possession of the skill to do something. Knowledge is the intellectual understanding about something.

Your son showed great intelligence in successfully combining instinct, ability and knowledge. He instinctively knew it was necessary to eat. He was able to move the watch from one position to another. He knew that food comes in watch-sized objects.

IE, instinct, ability and knowledge are all distinct aspects of human intelligence.

Does the theory of evolution distinguish between innate knowledge and mere instinct? — Mww

As regards instinct, babies have an innate instinct to move away from heat.

However, I am sure that babies also have certain innate knowledge.

Babies don't know how to talk and walk, but they have the innate knowledge of how to learn how to talk and walk. It would be wrong to say that babies have the innate instinct of how to learn how to talk and walk.

Similarly, babies have an innate knowledge of time and space. It would be wrong to say that babies have an innate instinct of time and space.

IE, babies are born with both innate instinct and knowledge.

lifespan..............just wondering. — Mww

The dates were intended to reinforce the idea that Kant was not able to benefit from Darwin's later work on the theory of evolution, in that today we can explain Kant's "a priori" knowledge as innate knowledge, a product of billions of years of evolution.

So, if indeed it is the case that our perceptions and conceptions are solely the product of evolution, then why should there be any basis for trust in the independent capacity of reason to arrive at truth? — Wayfarer

At the very least we need to be able to reason in order to survive. As Hoffman argued, reason allows us to navigate the world around us and has evolved to what it is today through natural selection.

I believe that in order to survive, I should not walk off a cliff. I can justify this by noticing that others who have done this have not survived. It is true that if I walk off a cliff I will not survive. Therefore, I have knowledge that in order to survive I should not walk off a cliff, where knowledge is justified true belief. My reasoning has led me to a truth.

Reasoning to survive exists outside language, in that the Neanderthals were able to successfully survive for almost 400,000 years without language. The Neanderthal reasoned and knew without language the truth of the danger of walking off a cliff.

IE, visceral reasoning arrives at truths.

Isn't confidence in reason justifiable because it is not solely dependent on biological evolution? — Wayfarer

We know that reason may lead to truths in knowing how to survive, but where is the truth beyond that which is necessary to survive. Where is the truth in a Derain. Where is the truth in an aesthetic experience.

I agree that once the ability to reason has evolved through the biological necessity of survival, then we can use our ability to reason about other things not to do with survival, such as trying to understand why a Derain is aesthetically more successful than a Hockney.

Although reason was born out of the necessity to survive, reason can now stand on its own two feet and go out into the world and reason about a whole range of different things.

It is true that when I look at a Derain I experience an aesthetic form. But what exactly is true. It cannot be the form that is true. It cannot be my response that is true. It cannot be the interaction between the form and my mind that is true. It is the proposition "when I look at a Derain I experience an aesthetic form" that is true. Truth also exists in language.

IE, linguistic reasoning also arrives at truths

In other words, to rationalise what we take to be true in terms of what is advantageous to survival, sells reason short - a very common tendency in modern philosophy. — Wayfarer

There are two types of truth - a visceral truth known outside of language and a linguistic truth known within language. There are also two types of reasoning - a visceral reasoning outside of language and a linguistic reasoning within language.

IE, as of necessity Philosophy uses language, Philosophy is also concerned with using reason as a means of discovering truth within language.

Your accounting, or sourced from secondary literature? — Mww

I had been reading The Critique of the Power of Judgement because of my interest in aesthetics. The title stuck in my mind and I mistakenly wrote in my post Critique of the Power of Judgement rather than Critique of Reason.

Many people are far more knowledgeable about Kant than me, so I think it only wise to also refer to secondary sources, such as the Stanford Encyclopedia of Philosophy. Don't you agree ?

If language is self referential, the there are two ways to think about this. ..................................One way says the world as the world is bound up with the ways we know it; ontology and epistemology cannot be separated and my coffee cup IS a coffee cup AS a bundled phenomenon. The idea of the cup is literally the cup-thing itself. So, I point to my cat, and the pointing, the concept, the predelineation of the past informing the present occasion as well as the anticipation of what the "future cat" will be, do, all of this is constitutive of the occurrent apperception of my cat. All of a piece. Any separation of parts would be an abstraction, which is fine because this is what analysis is, as long as we don't think analytically determined entities ae entities in their own right............................................. Another way is to understand that the knowledge that brings the palpable thing into understanding and familiarity is qualitatively distinct from the palpable thing. To me, this is a very strong and even profound claim. It is not about some noumena that is postulated but beyond sight and sound; it's about the palpable presence of the thing, and its being alien to the understanding, so their you are, confronting metaphysics directly. This is called mysticism. — Constance

I agree that there there are two distinct ways in which we understand the external world, and these may be described in various ways.

1) Metaphysics, our past history, Sartrian existence and Kantian a priori knowledge are all aspects of the same thing. This is, as you say, about "confronting metaphysics directly".
2) Physics, our present situation, Sartrian essence and Kantian a posteriori knowledge are also all aspects of the same thing. This is, as you say, "apperception".
Each is distinct, as hardware is distinct from software, yet both are mutually dependent, and both are required for the proper functioning of the whole human organism.

The colour red is experienced both physically and metaphysically

Consider our experience of the colour red. From physics, I know that the wavelength of red light is 700nm. But I also have a private subjective experience of the colour red, an experience that can never be described to another person. At the moment of having the subjective experience of the colour red, it is not the case that I am observing the colour red, rather, it is the case that I am the experience of the colour red. An experience transcending any physical knowledge into an immediate and visceral metaphysical knowledge.

IE, our knowledge of, for example, the colour red, is both physical and metaphysical

Evolution explains Kant's a priori

We are observers of the external world, yet we are also part of the world. We have an existence upon which we build an essence. This existence did not arise yesterday, or the day we were born, but has been underway for billions of years. We have evolved in synergy with the world. Humans are born with certain innate abilities, in that the brain is not a blank slate, as described by both post-Darwinian "evolutionary aesthetics" and "evolutionary ethics". In the 3.7 billion years of life on earth, complex life forms have evolved to have certain innate intuitions necessary for continued survival. It is not the case that we have certain intuitions and they happen to correspond with the world, rather, our intuitions were created by the world and therefore of necessity correspond with the world. Through the process of evolution the mind gradually models the world around it. If the model had not been correct, then the mind and body would not have survived. Therefore, the sensible intuitions innate within the mind have been created by the world in which the brain has survived.

IE, it is not the case that the mind has an intuition of the world that it exists within, rather, the intuitions of the mind necessarily correspond with the world it exists within, otherwise it would not have been able to successfully survive and evolve.

We understand the world both in a Kantian a priori and a posteriori way

The two distinct ways we relate to the world can be further understood within Kant's theory of the "synthetic a priori". Kant combined the ideas of the Empiricists and the Rationalists. For the Empiricists, such as Hume, only what can be observed has meaning, where a posteriori knowledge is "as mere representations and not as things in themselves"
For the Rationalists, such as Leibniz, understanding is in the mind, where a priori knowledge is "only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves".

Empiricism claims that our ideas are fashioned out of experience between an observer and an external world and the ideas thus formed if they have any bearing on external reality then elementary sensations are bound together by some principle of association. Kant argued that on this reading, science could not have developed, yet, as science is successful, the principles of association must have been provided by the observer such that "nothing in a priori knowledge can be ascribed to objects save what the thinking subject derives from itself".

The observer can only understand what they observe if they have a prior ability to experience what they observe, in that we are able to see the colour red but not the infra-red because of our innate abilities. Kant wrote in his Critique of the Power of Judgement : "We can only cognize objects that we can, in principle, intuit. Consequently, we can only cognize objects in space and time, appearances. We cannot cognize things in themselves". (A239). Foundational to all our understanding of what we observe is our innate understanding of space and time: "Space and time are merely the forms of our sensible intuition of objects. They are not beings that exist independently of our intuition (things in themselves), nor are they properties of, nor relations among, such beings". (A26, A33)

It is true that Kant (1724 to 1804) did not propose an evolutionary mechanism for a priori pure intuitions, as he was not able to benefit from Darwin's (1809 to 1882) theory of evolution, Kant's principle of "synthetic a priori judgements" remains valid.

IE, We are born with certain innate abilities that have taken billions of years to evolve, and based on these innate abilities we can observe the external world, but we can only observe in the world what our innate abilities allow us to observe. Our understanding of the world is from observed phenomenon which are given meaning by a pre-existing and innate understanding of them. The physics of the world is understood through an innate knowledge that transcends experience, ie, a metaphysics.

Our understanding of the world must always be limited

FH Bradley's regression argument illustrates the that relations have no ontological existence in the external world. The Binding Problem, that we experience a subjective whole rather than a set of disparate parts, illustrates that relations do have an ontological existence in the mind. As Kant argued that we make sense of the world by imposing our a priori knowledge onto our a posteriori observations in the external world, similarly we can also make sense of the world by imposing a reasoned relational logic onto a relation-free external world.

IE, both these show the inherent limits to our understanding of the world, in that we will only ever be able to understand those aspects of the world for which we have an a priori ability to understand. This means that there are things about the world that will forever be beyond our imagination, as a horse's understanding of the allegories in The Old Man and the Sea will forever be beyond the horse's imagination.

Language is more than self-referential

As language is, taking one example, the observed a posteriori linkage between a name "red" and a known a priori part (red), rather than being said to be self-referential in the sense of the Coherence Theory of Language, language is still able to refer to the world in the sense of the Correspondence Theory of Language.

Summary

We know the world in two distinct ways - i) metaphysically, rationally, as an evolutionary memory, as a Sartrian existence, a Kantian a priori ii) physically, empirically, as a present experience, as a Sartrian essence and a Kantian a posteriori.

Ohfercrisakes.....that he wanted to deny it is every bit as false as he did deny it. He equally never did either. — Mww

True, but that is not what was written.

You are ignoring the qualifier "as much as" which is qualifying the clause that follows it - "Kant wanted to deny metaphysics".

"as much as Kant wanted to deny metaphysics"....................This is catastrophically false, but none of your co-respondents noticed nor cared — Mww

Speaking as a co-respondent, the phrase used was not "Kant denied metaphysics", which may well be "catastrophically false". The phrase was "as much as Kant wanted to deny metaphysics", which has a completely different meaning and is not "catastrophically false".

Paradoxes like Zeno's should be telling us that geometry and reality are very different..................but the world altogether is not logical; it is alogical, apart from logic, qualitatively different................language is mostly self referential....................We live in epistemology. The world before us apart from this is utterly metaphysical. — Constance

I agree with what you have written.

The question is why are geometry and reality very different

For me, the reason is that relations are foundational to our logic, yet relations have no ontological existence in the external world.

This explains why geometry and reality are very different, the world is alogical, language is self-referential, we live in epistemology and the world is utterly metaphysical.

If there was a more persuasive explanation why logic and reality are very different than because of the the nature of relations, then this would be of interest.

The next question is why we need to know why geometry and reality are very different

Perhaps it is sufficient to know what pragmatically works. I turn the ignition key on my car and the engine starts. I don't need to know why the engine starts, all I need to know is that turning the key starts the car. Why not treat the external world as an empirical experience and not search for any sense beyond this.

My justified belief that relations within logic are fundamentally different to relations within reality can never be knowledge

My belief is that logic and reality are very different because of the nature of their relations, and this I can justify. However, my justified belief that logic and reality are very different because of the nature of their relations can never be knowledge, as I can never have a true understanding of a reality that is relation-free using reasoning where relations are fundamental.

In this respect, my justified belief remains a working hypothesis, and will remain so
until presented with a more persuasive explanation as to the nature of logic and reality. My belief must always remain an invention rather than a discovery, as my belief transcends what I can ever discover.

Summary

The nature of relations is the fundamental barrier between our understanding of the external world and the external world itself.

The Democratic President specifically asked for a woman rather than a man, and yet the nominee cannot explain the difference between a woman and a man.

If the nominee does not know whether they are a woman or a man, then perhaps they should recuse themselves from the nomination, as the President specifically asked for a woman.

If logic qua logic can produce nonsense like this, then as a system of understanding the world, it is more than suspect. It is "wrong". — Constance

Language is more metaphor than logic

I have always been mystified that adding one-half plus one-quarter plus one-eighth plus one-sixteenth etc adds up to one, in that adding together an infinite number of things results in a finite thing.

I can explain this paradox by understanding that relations are foundational to the logic we use, in that 5 plus 8 equals 13, etc, yet relations, as illustrated by FH Bradley, have no ontological existence in the world.

It is therefore hardly surprising then that paradoxes will arrive when comparing two things that are fundamentally different, ie, our logic and the world.

But I do not at present see any way around any of these — Constance

We must be remember that when paradoxes do arrive, that this will be an inevitable consequence of the nature of logic, rather than indicative of anything strange happening in the world.

The fact that logic will inevitably lead to paradox explains why metaphor is such an important part of language, so much so, that a case may be made that "language is metaphor".

Here's a paper by Lakoff and Johnson (PDF): Conceptual Metaphor in Everyday Language. It gives an idea of how deeply metaphorical our language (and our thinking) is. — jamalrob

I see where you are coming from.

Language as metaphor
Nietzsche wrote “We believe that when we speak of trees, colours, snows, and flowers, we have knowledge of the things themselves, and yet we possess only metaphors of things which in no way correspond to the original entities.”

Metaphor is language’s most powerful weapon.

Consider "I can see the solution" and "I can see the apple". We commonly assume that "I see" is used metaphorically in the first instance and literally in the second instance, however language is more complex than this.

We talk all the time with metaphors but do not notice this because we use them naturally, both in daily life and in science - Maxwell’s demon, Schrödinger's cat, Einstein’s twins, the Greenhouse Effect, natural selection, dendritic branches. Metaphors are not paraphrases for other literal expressions, but are how ideas are expressed. Metaphors describe the world and are not explanations.

Metaphors and Indirect Realism
The conceptual metaphor, understanding one idea in terms of another, is foundational to the meaning of Indirect Realism.

Indirect Realism is the belief that our conscious experience is not of the real world itself but of an internal representation of the real world

As "the solution" is not an object in the world but a concept in the mind - "the apple" is also not an object in the world but a concept in the mind. Therefore, as we treat "I see the solution" as a metaphor, we should also treat "I see the apple" as a metaphor rather than literally.

A belief in Indirect Realism leads to a belief that not just is metaphor important in language, but "language is metaphor".

However, even the insight that our language is deeply metaphorical will not lead, as Lakoff and Johnson write, to any new perspective about "the truth", as "understanding one kind of experience in terms of another kind of experience" will always lead to an infinite regression, where "the truth" will always remain, as I see it, out of reach.

If we would consider the omnipresent virtual particle fields residing in the vacuum of nature the eternal unmoved prime mover, we would still be left with the question where that came from. — EugeneW

Aristotle
Aristotle's answer would be that the universe is eternal having never come into existence. His is not the God of Genesis who created the world out of nothing.

But the universe is in eternal motion, and for Aristotle the universe needs a cause for its continuing existence and motion, and that cause is a God, outside the world, changeless and immaterial.

Aristotle's theology is set out in books VII and VIII of Physics and book XII of Metaphysics

Such a God is an "unmoved mover", not responsible not for the creation of the universe, as for Aristotle the universe is eternal, but responsible in a non-physical way for the continuing motion within the universe.

Modern interpretation
Aristotle's belief that the universe is eternal seems reasonable. If a thing exists, as it is almost unimaginable that at a later moment in time it could disappear into absolute nothingness, it is also almost unimaginable then at an earlier moment in time it could have appeared from absolute nothingness.

Gravity may also be considered an "unmoved mover", whether considered as a force or curvature in space-time. A "mover" with infinite range where all things are attracted to one another, and "unmoved" in that whether a force or a curvature in space-time can cause motion without being in motion itself.

I see the answer as being "metaphor".

But what brought space and time into being? — EugeneW

Aristotle in Physics Book 8 claims that motion is everlasting, has no beginning and will have no end.

And yet he discusses the "unmoved mover", where "the first movement is moved but not by anything else, it must be moved by itself"

Although his "unmoved mover" has been identified with a spiritual explanation, Aristotle in Physics Book 8 doesn't explain its nature.

Today, this "unmoved mover" can be explained in more scientific terms, without the need to address what brought space and time into existence.

Aristotle is arguing first that motion in the universe is everlasting and second that the motion we observe in the world must have its primary cause in something that cannot be in motion, a first immaterial "unmoving mover".

He writes at the end of section 5 of Physics Book 8 - "From what has been said, then, it is evident that that which primarily imparts motion is unmoved: for, whether the series is closed at once by that which is in motion but moved by something else deriving its motion directly from the first unmoved, or whether the motion is derived from what is in motion but moves itself and stops its own motion, on both suppositions we have the result that in all cases of things being in motion that which primarily imparts motion is unmoved."

The question is, are his premises sound and his his argument valid ?

As @Metaphysician Undercover pointed out, the paragraph in the OP has been taken out of context.

Aristotle's inference of a spiritual rather than physical explanation for an "unmoving mover" may be brought down to earth.

1) Imagine a rock travelling through space at 10,000 km/hour. In Aristotle's terms, where is the unmoving mover that keeps the rock travelling forwards at a constant speed ? How to explain the Law of Conservation of Energy, whereby the kinetic energy of the rock is maintained ?
However, motion is relative, and we may consider the rock as stationary within a moving environment. In this case, the rock being stationary, no unmoving mover is needed, and the existence of an unmoving mover is not required.

2) Imagine the same rock in distant space. Movement is not a property of a single body, but is a property that emerges when more than one body are in near location, whether the gravitational force between the moon and the Earth or the magnetic attraction between two magnets. If another body approaches this particular rock, the paths of the bodies will be changed by a gravitational attraction.
In this case, the primary mover is gravity, which may be understood as a curve in space, and in Aristotle's terms, an unmoving mover

In summary, in both cases, it is not necessary to consider a mysterious entity outside the known universe, in that the "mover" can be explained as a physical state of affairs within current time and space.

I know certain things by acquaintance - a headache, an acrid smell, the colour red, a sweet taste, a screeching noise. I know other things by description - Aristotle, Sherlock Holmes, a unicorn.

I cannot know time by acquaintance, as "We can only experience the moment we are in. We cannot experience at this moment either the moment before this moment or the moment after this moment. Therefore, we can never directly experience either the past or the future."

I can only know time by description.

As Aristotle, as well as everyone else, only knows time by description and not acquaintance, his conclusion that time is eternal and without beginning must remain a hypothesis, interesting, but still an unprovable hypothesis.

Do you think Aristotle's argument is sound or valid? — Kuro

The phrase "Aristotle's argument is correct" is incorrect.

A sound argument has a different meaning to a valid argument.

There should be four questions within the poll:
Aristotle's argument is sound
Aristotle's argument is not sound
Aristotle's argument is valid
Aristotle's argument is not valid

Aristotle's argument is valid but not sound.

His premise is false - "Now since time cannot exist and is unthinkable apart from the moment, and the moment a kind of middle-point, uniting as it does in itself both a beginning and an end, a beginning of future time and an end of past time"

His reasoning is correct

His conclusion is false - "it follows that there must always be time"

There is a problem with Aristotle's premise

We can only experience the moment we are in. We cannot experience at this moment either the moment before this moment or the moment after this moment. Therefore, we can never directly experience either the past or the future.

Therefore, as we can never directly experience either the past or the future, we can never have first hand knowledge of the meaning of the terms time, past, present, eternal, creation or motion.

Therefore, Aristotle's conclusion that time and motion are eternal can only ever be an interesting hypothesis.

I'd like to think that natural selection is not random. — Cidat

If a drop of rain falls downwards, the path of the raindrop is not random, in that the new position of the raindrop depends on its previous position. The path of the raindrop is also logical, in that it is following a set of rules, in this case, the laws of nature. Therefore the path of the raindrop is both logical and not random.

Extrapolating, natural selection is both logical and not random, meaning that the fact that one species dominates is both logical and not random. However, any final situation, regardless of what it had turned out to be, would be both logical and not random. Two species dominating would have been both logical and not random. No species dominating would have been both logical and not random.

It does not follow that because the final situation is both logical and not random, the final situation has been teleologically pre-determined. Even though the final situation is both logical and not random, it does not follow that the final situation has any special meaning.

The fact that a sequence of events is both logical and non random is insufficient to give meaning to any subsequent state of affairs.

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I regret to inform that the Eiffel Tower does not exist, although on the left bank in Paris there's a bunch of iron atoms shaped in the form of the Eiffel Tower. — Olivier5

Depends what one means by exist.
We seem to agree that the Eiffel Tower does not exist in Platonic Form, in that it seems a strange idea that prior to 1889 the Eiffel Tower existed below the ground in Algeria in the form of iron.
But your previous comment "As long as I can eat and work on it, and occasionally climb on it, the table is real enough for me" suggests that we agree the Eiffel Tower exists in Aristotelian form, in that we can both eat in the Jules Verne Restaurant and visit the Observation Platform.

If the world offers no information regarding the independent existence of apples and tables, then I cannot discover whether I just ate an apple or a table — Cuthbert

Because there is no information in the Eiffel Tower that the Andromeda Galaxy exists, it does not follow that we have not been able to discover the existence of either the Eiffel Tower or Andromeda Galaxy.