That's contradiction, "first" means first, the possibility of infinite regress is therefore excluded. — Metaphysician Undercover

But how do you know it is truly "first"? You do not. So, you will keep trying to find the really "true" first that comes before the current first. It just keeps going on. Ad nauseam. That is why it does not work.

Unless you can justify this claim, it's nothing more than an opinion of an uneducated person. — Metaphysician Undercover

Knowledge is a gigantic database with lots and lots of theories and theorems.

I do not make any attempt whatsoever at memorizing that database.

So, if you mean that I have not read 99% of the database of existing knowledge, I totally agree. I even pride myself on not having done that. I only loosely remember, if even, the few things I accidentally have run into, usually for very arbitrary reasons.

I am more than happy with that, because my ambition is not to become some kind of redundant database of knowledge who in vain tries to be a very imperfect replacement for tools like Google Search or Wikipedia.

People really need to develop a purpose in life that is different from that, because their plan is otherwise bound to fail. So, are there a lot of things that I do not know? Yes, of course, and I am very proud of that.

I gave you the example, moral ethics ... I see, morality is nonsense to you. — Metaphysician Undercover

The most widespread and successful approach to morality is what the three offshoots of second-temple judaism propose, i.e. religious law.

As far as I am concerned, the epistemically soundest version of the religious-law morality method can be found in usul al fiqh, "Principles of Islamic jurisprudence". It is a gigantic library of innumerable publications.

Read up on it, and then you will understand that what you are doing in the realm of morality, i.e. "metaphysics", is just un-methodical bullshit. Seriously, that is why there has been no progress whatsoever in metaphysics for over 2500 years. That was to be expected, because there is simply no logic in that madness.

Yes, so there is but ontology; so long metaphysics;all is physical. — PoeticUniverse

My bold added, that portion being a metaphysical assertion.

But how do you know it is truly "first"? You do not. So, you will keep trying to find the really "true" first that comes before the current first. It just keeps going on. Ad nauseam. That is why it does not work. — alcontali

Of course, that's the nature of knowledge. Proceeding from the first principle has a similar problem,. There's no infinite regress, just some degree of uncertainty within knowledge, such that knowledge is forever evolving as we move forward.

The most widespread and successful approach to morality is what the three offshoots of second-temple judaism propose, i.e. religious law. — alcontali

OK, now the point is that someone must determine the rules, the law. It makes no sense, to argue as you do, that all respectable knowledge proceeds from first principles in an axiomatic way, because this neglects the fact that someone must determine the principles, in the first place, from which the axiomatic knowledge will proceed.

If you assume that all of the first principles for all divisions of knowledge have already been produced, this contradicts your original statement above, that we cannot know it's really "true", and therefore we must keep searching, in an endless way. You can't argue both sides of the contradiction. But this fact, the fact that we cannot know with absolute certainty that the accepted first principles are really true, is the reason why there is always a need for metaphysics. We cannot just accept as absolute truth, the first principles from which we proceed, in the other forms of axiomatic knowledge.

Read up on it, and then you will understand that what you are doing in the realm of morality, i.e. "metaphysics", is just un-methodical bullshit. Seriously, that is why there has been no progress whatsoever in metaphysics for over 2500 years. That was to be expected, because there is simply no logic in that madness. — alcontali

What is bullshit is your claim that there has been no progress in metaphysics in 2500 years. Do you think that human beings developed the current knowledge of the solar system, and the rest of the universe, by following the principles which were accepted 2500 years ago?

Of course, that's the nature of knowledge. Proceeding from the first principle has a similar problem,. There's no infinite regress, just some degree of uncertainty within knowledge, such that knowledge is forever evolving as we move forward. — Metaphysician Undercover

That is only the nature of falsificationist knowledge. That is absolutely not the nature of axiomatic knowledge. The Pythagorean theorem was provable 2500 years ago. It still is provable today. The same holds true for Thales' theorem. It is as provable today as 2500 years ago. Once provable, always provable. Hence, that particular view on the nature of knowledge is epistemically completely incorrect for axiomatic knowledge.

OK, now the point is that someone must determine the rules, the law. It makes no sense, to argue as you do, that all respectable knowledge proceeds from first principles in an axiomatic way, because this neglects the fact that someone must determine the principles, in the first place, from which the axiomatic knowledge will proceed. — Metaphysician Undercover

For mathematics, these rules are arbitrarily chosen. You can find a good explanation of how it works in the Wiki page on the Brouwer-Hilbert controversy:

Hilbert's axiomatic system – his formalism – is different. At the outset it declares its axioms. But he doesn't require the selection of these axioms to be based upon either "common sense", a priori knowledge (intuitively derived understanding or awareness, innate knowledge seen as "truth without requiring any proof from experience"), or observational experience (empirical data). Rather, the mathematician in the same manner as the theoretical physicist is free to adopt any (arbitrary, abstract) collection of axioms that they so choose. Indeed, Weyl asserts that Hilbert had "formaliz[ed] it [classical mathematics], thus transforming it in principle from a system of intuitive results into a game with formulas that proceeds according to fixed rules". So, Weyl asks, what might guide the choice of these rules? "What impels us to take as a basis precisely the particular axiom system developed by Hilbert?". Weyl offers up "consistency is indeed a necessary but not sufficient condition" but he cannot answer more completely except to note that Hilbert's "construction" is "arbitrary and bold". Finally he notes, in italics, that the philosophical result of Hilbert's "construction" will be the following: "If Hilbert's view prevails over intuitionism, as appears to be the case, then I see in this a decisive defeat of the philosophical attitude of pure phenomenology, which thus proves to be insufficient for the understanding of creative science even in the area of cognition that is most primal and most readily open to evidence – mathematics."

If you assume that all of the first principles for all divisions of knowledge have already been produced, this contradicts your original statement above, that we cannot know it's really "true", and therefore we must keep searching, in an endless way. You can't argue both sides of the contradiction. — Metaphysician Undercover

What has gradually emerged are epistemic knowledge-justification methods, whereunder axiomatic, scientific-falsificationist, and historical. Each of these epistemic methods generates an epistemic domain around it, i.e. a database of knowledge that can be justified with it. I cannot see what else you could be looking for, because there is nothing else, and there hasn't been for 2500 years.

What is bullshit is your claim that there has been no progress in metaphysics in 2500 years. — Metaphysician Undercover

So, then where is that elusive progress visible? Any link?

Do you think that human beings developed the current knowledge of the solar system, and the rest of the universe, by following the principles which were accepted 2500 years ago? — Metaphysician Undercover

Science is falsificationist. It is an epistemic domain of knowledge justified by experimental observation/testing. The initially hypothetical knowledge was very often stumbled upon, through serendipity, trial and error, and sheer luck. Systematic testing obviously always follows much later. So, yes, a better understanding of the solar system and other parts of the visible universe took a lot of observation. In fact, it first took quite a bit of haphazard progress in optics and construction of telescopes just to be able to observe these things in sufficient detail. So, yes, if they had had proper telescopes 2500 years ago, they would obviously have seen it too. It wasn't a problem of following the wrong principles at all.

That is only the nature of falsificationist knowledge. That is absolutely not the nature of axiomatic knowledge. The Pythagorean theorem was provable 2500 years ago. It still is provable today. The same holds true for Thales' theorem. It is as provable today as 2500 years ago. Once provable, always provable. Hence, that particular view on the nature of knowledge is epistemically completely incorrect for axiomatic knowledge. — alcontali

When the two sides of a right angle are of equal length, the hypotenuse is irrational. Therefore the Pythagorean theorem as a first principle of geometry is deficient. Pythagoras himself grappled with this problem, and the fact that he could not resolve it bothered him. That the hypotenuse remains irrational indicates that the Pythagorean theorem remains unproven, just like the value of pi remains unproven.

For mathematics, these rules are arbitrarily chosen. — alcontali

If the rules are arbitrarily chosen then why choose a rule which results in the contradiction which is an irrational ratio? The fact is that the rules are not really chosen arbitrarily, they are chosen for purpose, pragmatics. The circle is useful, and pi is the result of the rule which creates the circle. The right angle is useful for making parallel lines, and the Pythagorean theorem is the result of the rule which creates the right angle. That each of these results in an irrational ratio indicates that they are lacking in truth and reality, despite the fact of being very useful.

So, then where is that elusive progress visible? Any link? — alcontali

I gave you the example, we now have a better understanding of the solar system. If you are unfamiliar with metaphysics behind this, you are not the only one. But that's because few people today study ancient metaphysics, they prefer modern metaphysics.

The initially hypothetical knowledge was very often stumbled upon, through serendipity, trial and error, and sheer luck. — alcontali

Actually, most of the initial hypotheses are sheer metaphysics. Take a look at Einstein's special theory of relativity for example. And today there is much metaphysical speculation into the nature of the universe, and the micro world of quantum mechanics.

So, yes, a better understanding of the solar system and other parts of the visible universe took a lot of observation. In fact, it first took quite a bit of haphazard progress in optics and construction of telescopes just to be able to observe these things in sufficient detail. So, yes, if they had had proper telescopes 2500 years ago, they would obviously have seen it too. It wasn't a problem of following the wrong principles at all. — alcontali

Actually, telescopes came after it was theorized that the earth revolved around the sun, and not vise versa, so understanding the heliocentric nature of the solar system was not the result of telescopes. The idea was floated around 2500 years ago, but the planets were given perfect circular orbits according to the principles of Aristotelian metaphysics. The assumption of perfect circles resulted in inconsistencies which could not be reconciled until Copernicus. The point though, is that metaphysical theory preceded the fine tuning observations which were required to adjust the theory.

Actually, telescopes came after it was theorized that the earth revolved around the sun, and not vise versa, so understanding the heliocentric nature of the solar system was not the result of telescopes. The idea was floated around 2500 years ago, but the planets were given perfect circular orbits according to the principles of Aristotelian metaphysics. The assumption of perfect circles resulted in inconsistencies which could not be reconciled until Copernicus. The point though, is that metaphysical theory preceded the fine tuning observations which were required to adjust the theory. — Metaphysician Undercover

What about, say, ten thousand years ago?

When the two sides of a right angle are of equal length, the hypotenuse is irrational. Therefore the Pythagorean theorem as a first principle of geometry is deficient. Pythagoras himself grappled with this problem, and the fact that he could not resolve it bothered him. That the hypotenuse remains irrational indicates that the Pythagorean theorem remains unproven, just like the value of pi remains unproven.

If the rules are arbitrarily chosen then why choose a rule which results in the contradiction which is an irrational ratio? The fact is that the rules are not really chosen arbitrarily, they are chosen for purpose, pragmatics. The circle is useful, and pi is the result of the rule which creates the circle. The right angle is useful for making parallel lines, and the Pythagorean theorem is the result of the rule which creates the right angle. That each of these results in an irrational ratio indicates that they are lacking in truth and reality, despite the fact of being very useful. — Metaphysician Undercover

Irrational just means that a number cannot be reached by merely applying the standard arithmetic operators (+ - x /) to integers. So, if Z are integer numbers ...,-3,-2,-1,0,1,2,3,4,5 ... then you can see that this domain is nicely closed under addition, substraction and multiplication, because all results are again members of that domain. Example, 3+5*2 = 13. So (Z, {+,-,*)} is closed.

This algebraic structure (Z, {+,-,*)} is called a "ring".

This structure is not closed under division. For example, 2/5 or 1/3, are not members of the domain. If we adjoin the inverses of these integers, ... -1/3, -1/2,1/2,1/3 ..., then it closed. We call that resulting domain in which the inverses are adjoined, the rationals Q, and the closed algebraic structure (Q, {+,-,*,/}) where division stays within the closure, a "field".

For the calculation of the hypothenuse, you can see that mere field operations ("arithmetic") are insufficient. If a and b are the sides of the right angle, then the hypothenuse c = √(a²+b²) is not necessarily a rational, even if a and b are rationals. Only numbers produced by field operations on Q are guaranteed to be rationals. In other words, Q is closed under arithmetic but not under square root computation. So, c is not necessarily a member of Q, the rationals. In general, you will need to adjoin a radical field extension to the rationals Q in order to compute c.

So, the Pythagorean solution is "irrational" in a sense that it lies in a radical field extension of the rationals Q. Such radical field extension is then again closed under arithmetic.

Algebraic numbers are the domain that contains the rationals and all possible such radical field extensions, and is therefore closed under the n-th root operation. The algebraics are also a "field" that is irrational (meaning: completely contains the rationals Q).

Still, the algebraics are not enough when you look, for example, at the roots of polynomials with rational coefficients. You will need to keep adjoining additional field extensions if you want to close the splitting field. For example, you will at the very least need to add i=√-1. From fifth-degree polynomials on, you are not even guaranteed to stay within the algebraics. That is the gist of the Abel-Ruffini theorem, which is an important result in Galois theory. Polynomial splitting can then result in roots being non-algebraic real numbers (or complex numbers).

So, in this context, "irrational" just means that the problem cannot necessarily be solved by using basic arithmetic, but that it may requiring adjoining to the rationals Q, other numbers produced with more complicated operations.

It took until the end of the 19th century before the dust more or less started settling on these things. Before that, they did not understand these algebraic structures particularly well.

Actually, telescopes came after it was theorized that the earth revolved around the sun, and not vise versa, so understanding the heliocentric nature of the solar system was not the result of telescopes. The idea was floated around 2500 years ago, but the planets were given perfect circular orbits according to the principles of Aristotelian metaphysics. The assumption of perfect circles resulted in inconsistencies which could not be reconciled until Copernicus. The point though, is that metaphysical theory preceded the fine tuning observations which were required to adjust the theory. — Metaphysician Undercover

There is indeed a massive and intractable issue with the issue of discovery of new knowledge.

Existing knowledge cannot possibly be the main ingredient in the discovery of new knowledge, because in that case humanity would never have discovered any knowledge at all, or else, discovered all possible knowledge already.

Hence, the discovery process of new knowledge cannot possibly be justifiable as knowledge. We simply do not know how to discover new knowledge, and we can certainly not justify how we managed to do it anyway. It is to an important extent the result of non-knowledge mental faculties and possibly also fundamentally unknown environmental inputs.

Gödel's first incompleteness theorem also provably dismisses the idea of running through all possible well-formed formulas as to question a knowledge machine whether the formula is provable or not. For example, in the language required to axiomatize the existence of numbers, it is possible to produce formulas that are logically true but impossibly provable by the knowledge machine. So, if you enumerate the well-formed formulas in that language (which happens to be first-order logic), from first to last, the knowledge machine will run into examples of formulas of which the provability is simply undecidable.

So, it is just not possible to run new candidate knowledge claims through a knowledge machine filled with existing knowledge to check if these new claims happen to be justifiable. Gödel proved that this is not a legitimate knowledge discovery procedure. We will undoubtedly have to keep doing it with leaps and bounds, through serendipity, trial and error, and what have you, to slowly, gradually, and painstakingly, but surely, acquire new justifiable knowledge claims.

Irrational just means that a number cannot be reached by merely applying the standard arithmetic operators (+ - x /) to integers. — alcontali

"Irrational" refers to an incommensurable ratio. This means that the two things being related to each other cannot be measured by the same system of measurement, such as the examples I gave you, the circumference and diameter of a circle, as well as the sides of a square and it's hypotenuse. What this indicates is that there is incommensurability between one spatial dimension and another.

Still, the algebraics are not enough when you look, for example, at the roots of polynomials with rational coefficients. You will need to keep adjoining additional field extensions if you want to close the splitting field — alcontali

And you claim that the efforts of the metaphysician are pointless due to infinite regress. It appears like in reality the efforts of the mathematician are pointless due to infinite regress.

So, in this context, "irrational" just means that the problem cannot necessarily be solved by using basic arithmetic, but that it may requiring adjoining to the rationals Q, other numbers produced with more complicated operations. — alcontali

You mean the problem can be solved by hiding the infinite regress behind "complicated operations". A good metaphysician is trained to recognize such sophistry.

Existing knowledge cannot possibly be the main ingredient in the discovery of new knowledge, because in that case humanity would never have discovered any knowledge at all, or else, discovered all possible knowledge already. — alcontali

I see we agree on something anyway.

We simply do not know how to discover new knowledge, and we can certainly not justify how we managed to do it anyway. — alcontali

But we do know how to discover new knowledge. It is basically a process of trial and error. It requires an assumption, a presupposition, which is not taken as true or false (knowledge), but is taken as a principle to be tried, like an hypothesis. You explained this above, in your explanation of what science is.

The issue here, between us, is where do these principles to be tried come from. We cannot just choose them randomly because there would be an infinity of possibilities. Therefore we must proceed with some guidance in choosing the principles to be tried, this is metaphysics. The metaphysician recognizes the failures, errors of others, and narrows the pathway with this form of trial and error.

Gödel's first incompleteness theorem also provably dismisses the idea of running through all possible well-formed formulas as to question a knowledge machine whether the formula is provable or not. For example, in the language required to axiomatize the existence of numbers, it is possible to produce formulas that are logically true but impossibly provable by the knowledge machine. So, if you enumerate the well-formed formulas in that language (which happens to be first-order logic), from first to last, the knowledge machine will run into examples of formulas of which the provability is simply undecidable.

So, it is just not possible to run new candidate knowledge claims through a knowledge machine filled with existing knowledge to check if these new claims happen to be justifiable. Gödel proved that this is not a legitimate knowledge discovery procedure. We will undoubtedly have to keep doing it with leaps and bounds, through serendipity, trial and error, and what have you, to slowly, gradually, and painstakingly, but surely, acquire new justifiable knowledge claims. — alcontali

This is exactly why we cannot choose the principles to be tried, arbitrarily, as you seem to think that we do. We need some intuition as to which of the proposable principles are credible. This comes from a thorough examination of the existing knowledge, the flaws within reveal the errors, and therefore where new proposals are required. So your "knowledge machine" requires a method of analysis of the already existing knowledge to determines errors. This is where new knowledge comes from, determining errors in the old knowledge, not from introducing new proposals and checking for consistency with the old. A new proposal which is inconsistent with the old knowledge is not necessarily wrong, it could be that the old knowledge is wrong.

"Irrational" refers to an incommensurable ratio. This means that the two things being related to each other cannot be measured by the same system of measurement, such as the examples I gave you, the circumference and diameter of a circle, as well as the sides of a square and it's hypotenuse. What this indicates is that there is incommensurability between one spatial dimension and another. — Metaphysician Undercover

Well, the link with classical, Euclidean geometry has long ago been abandoned in contemporary number theory. I suspect that it was completely gone by the end of the 19th century, at the same time as they dumped Euclid's Elements. I have never had to carry out arithmetic using a straightedge and compass, like the Greek in antiquity apparently did.

You mean the problem can be solved by hiding the infinite regress behind "complicated operations". A good metaphysician is trained to recognize such sophistry. — Metaphysician Undercover

Well, taking a square root is no longer basic arithmetic, and therefore considered "more complicated". It is not that even a simple calculator cannot do it. These operations got historically, gradually introduced in order to solve problems. Actually, Pythagoras already needed square roots.

We need some intuition as to which of the proposable principles are credible. — Metaphysician Undercover

Yes, I did refer to non-knowledge mental faculties. Intuition is clearly one.

This is where new knowledge comes from, determining errors in the old knowledge, not from introducing new proposals and checking for consistency with the old. A new proposal which is inconsistent with the old knowledge is not necessarily wrong, it could be that the old knowledge is wrong. — Metaphysician Undercover

I believe that there must be ingredients in the process of knowledge discovery that are fundamentally unknowable, because if we could know them, then we could even systematize the discovery of new knowledge, while this is fundamentally not possible. Therefore, every attempt at trying to harness the process is bound to fail. Hence, determining errors in the old knowledge cannot possibly be the main ingredient in the knowledge-discovery process either. For example, they did not start building the first computers because there were errors in the old mechanical calculators that preceded them.

Well, the link with classical, Euclidean geometry has long ago been abandoned in contemporary number theory. I suspect that it was completely gone by the end of the 19th century, at the same time as they dumped Euclid's Elements. I have never had to carry out arithmetic using a straightedge and compass, like the Greek in antiquity apparently did. — alcontali

And what do you think lead to that move? Metaphysics.

I believe that there must be ingredients in the process of knowledge discovery that are fundamentally unknowable, because if we could know them, then we could even systematize the discovery of new knowledge, while this is fundamentally not possible. — alcontali

This would only be the case if you restrict the act of knowing, in the manner that you have proposed. Let's say that there is a system or method for producing knowledge, the axiomatic system you described. The system cannot know itself, so the "ingredients" of knowledge which are unknowable, as you say are those things which comprise the system. A logician cannot know what makes the logic employed, work, without going outside of the logic. So this is why metaphysics is important, it employs a completely different method, to evaluate the axiomatic systems. If it were a specific system which metaphysicians employed, then metaphysics would run into the same problem. Metaphysicians do not use any specific system, it is more like intuition, so metaphysics appears to be random nonsense to the uninitiated.

Yes, I did refer to non-knowledge mental faculties. Intuition is clearly one. — alcontali

It is necessary to distinguish between knowledge, as an object desired or possessed, and the activities which bring knowledge into existence. When we allow for the existence of non-knowledge based mental activities, we allow for a process which could bring knowledge into existence. If, for simplicity sake, we generalize and call this intuition, then we have something named, which we can discuss, and analyze toward understanding it. We can say now, that principles, axioms, are not chosen arbitrarily, but they are chosen by intuition. Intuition would assess the applicability of various possible principles, in relation to various goals, ends. Now we have separated the means from the ends, and this produces the necessity of assessing the ends themselves. That's the endeavour which pragmatism forces onto the metaphysician. Pragmatism brings light to the fact that axioms are chosen for a purpose, now the metaphysician must identify and evaluate the purpose.

For example, they did not start building the first computers because there were errors in the old mechanical calculators that preceded them. — alcontali

Since a machine is designed to give the human being what one wants, the inability of a machine to give the human being what the person wants, is an error in the machine. It is not an error in the machine's processing activity, but an error in the design. You might say, that an error in design is a human error, but all errors are human errors, and if the machine's processing activity screws up, it is just an error in design.

Metaphysicians do not use any specific system, it is more like intuition, so metaphysics appears to be random nonsense to the uninitiated. — Metaphysician Undercover

I am heavily "epistemized" and deeply invested in the idea of the existence of various knowledge-justification methods. Without such method, it is not knowledge.

Still, I completely acknowledge that non-knowledge mental faculties are key, not just for the discovery of new knowledge, but in general. But then again, systematization means converting things into knowledge. If it is not knowledge, but rather intuition, this is guaranteed to be a failing strategy.

f, for simplicity sake, we generalize and call this intuition, then we have something named, which we can discuss, and analyze toward understanding it. — Metaphysician Undercover

There cannot be knowledge, i.e. a justified (true) belief, about intuition, because in that case it would be knowledge and not intuition.

We can say now, that principles, axioms, are not chosen arbitrarily, but they are chosen by intuition. Intuition would assess the applicability of various possible principles, in relation to various goals, ends. — Metaphysician Undercover

I have run into at least two research fields where the goal was to redo a particular axiomatic system with arbitrarily-chosen subsets of its axioms.

Hilbert calculi are like that. You cripple first-order logic by removing some of its construction logic, and then you check what's left. It is very interesting. The point is to show that it is perfectly legitimate to leave out whatever you want, and go with the remainder, and see where you get.

Second-order arithmetic (Z2) is a similar research topic. Cripple arithmetic by adding/removing rules, operators, and so on, and see where you get

In the end, this kind of research rather amounts to playing with "cool toys". But then again, it is not possible to know what people will find unless they actually try. Furthermore, this type of research nicely emphasizes the true nature of axioms as fundamentally arbitrary starting points.

am heavily "epistemized" and deeply invested in the idea of the existence of various knowledge-justification methods. — alcontali

What do you mean by "deeply invested"?

Still, I completely acknowledge that non-knowledge mental faculties are key, not just for the discovery of new knowledge, but in general. But then again, systematization means converting things into knowledge. If it is not knowledge, but rather intuition, this is guaranteed to be a failing strategy. — alcontali

Again, I think I need to stress the difference between knowledge, and mental activity. Do you agree that mental activity is not knowledge, but it uses knowledge? Furthermore, there must be mental activity which does not even use knowledge, as this would be required to account for the coming into existence of knowledge, unless you place knowledge as prior to mental activity (but this could only be intuition, which you deny as knowledge).

So we must respect the fact that if we exclude intuition as knowledge, then we necessarily have mental activity which does not use knowledge, but can itself bring knowledge into existence. The strategy by which this mental activity proceeds cannot be "guaranteed to be a failing strategy", because it is responsible for the existence of knowledge. Therefore, the mental process which proceeds without the use of knowledge ought not be denigrated as a guaranteed failure.

In the end, this kind of research rather amounts to playing with "cool toys". But then again, it is not possible to know what people will find unless they actually try. Furthermore, this type of research nicely emphasizes the true nature of axioms as fundamentally arbitrary starting points. — alcontali

I do not believe that this does show that axioms are arbitrary. This is because there is a difference between playing with toys, and working with tools. Playing with toys is random and arbitrary, but working with tools is purpose driven. Axioms are tools, they are not toys.

Suppose we create an analogy in this way. Knowledge is a tool, and the thinking mind uses knowledge in its purposes driven activities as a tool. But the mind engages in other activities as well, more like playing with toys. The "toys" here are not knowledge, but in a way they are still tools, because the playing is in some ways purpose driven and it's just the case that toys are used by the mind instead of knowledge. The toys are the arbitrary axioms which you refer to, axioms which are not adopted for the purpose of doing any particular sort of work, which would make them tools. But they are used for the purpose curiosity and wonder, for play, like an artist playing with different colours, or a composer playing with different notes. So new axioms are discovered through this activity of creative playfulness, which because it is not putting tools to work it is not an act of using knowledge in thinking, it's more like thinking for the purpose of finding interesting things, playing. .

What do you mean by "deeply invested"? — Metaphysician Undercover

Well, I actively seek to disagree with people who defend the idea of "subject matters", because in my opinion, "subject matters" do not matter much. What really matters, are epistemic domains. So, I am actively in opposition to subject-matterism which is the core of contemporary curriculum design, which is by the way utterly misguided.

The verbatim transmission of knowledge databases to be memorized by students is such an incredibly bad approach to what education is supposed to be. We simply do not need people to act as living, imperfect copies of Google Search or Wikipedia, or other knowledge accumulation engines. I am staunchly against all of that.

We have not properly digested the advent of computers. People need to finally come to the understanding that you either use the machine, or else you build or program the machine, because in all other cases, it is you the machine.

Do you agree that mental activity is not knowledge, but it uses knowledge? — Metaphysician Undercover

Yes, agreed, rationality/knowledge is merely a tool.

Furthermore, there must be mental activity which does not even use knowledge, as this would be required to account for the coming into existence of knowledge, unless you place knowledge as prior to mental activity (but this could only be intuition, which you deny as knowledge). — Metaphysician Undercover

Yes, agreed, the discovery of new knowledge is mostly carried out with other, non-knowledge, tools/mental faculties.

The strategy by which this mental activity proceeds cannot be "guaranteed to be a failing strategy", because it is responsible for the existence of knowledge. Therefore, the mental process which proceeds without the use of knowledge ought not be denigrated as a guaranteed failure. — Metaphysician Undercover

Ha, but if we could "know" the nitty-gritty of these other, non-knowledge mental tools, then they are actually knowledge, and that would be contradictory. Therefore, I am opposed to any strategy that consists in trying to systematize these other mental tools, because in order to do that, we would need to thoroughly "know" them, which is is not possible, because they are not knowledge.

Hence, I believe that most corporate R&D budgets are fundamentally mismanaged. The worst case of mismanagement, however, are undoubtedly government-funded budgets for scientific research. They usually seek to somehow know and systematize the unknown and even the unknowable, which is something for which you would need to know the search result already, but in that case you do not need to search for it in the first place.

But they are used for the purpose curiosity and wonder, for play, like an artist playing with different colours, or a composer playing with different notes. So new axioms are discovered through this activity of creative playfulness, which because it is not putting tools to work it is not an act of using knowledge in thinking, it's more like thinking for the purpose of finding interesting things, playing. — Metaphysician Undercover

Yes, probably something like that or similar. Still, I admit that I do not really "know".

Yes, agreed, the discovery of new knowledge is mostly carried out with other, non-knowledge, tools/mental faculties. — alcontali

Good, but you're still not making the distinction which I asked you to make, between the thing, the tool, (knowledge in this case), and the activity which uses the thing. A tool is not the same as the activity which uses the tool. Knowledge is not the same as the mental activity which uses knowledge. If you make this distinction, then the same thing, an axiom for example, may be considered to be knowledge when it is used as a tool, put to work toward some goals, or it may be consider to be not-knowledge, not a tool, when it is considered to be arbitrary, and used as a toy in play like you described. The same thing is apprehended in a different way, depending on the activity which is using it.

Likewise, if we take one specific type of activity, using knowledge as a tool toward a goal for example, we could potentially use many different tools toward reaching the same goal. Each tool (axiom, or piece of knowledge) selected to be used would be useful, but some would be better than others, specifically the tools designed for that particular type of task. And, no matter how good the tool appears to be, we ought to respect the fact that a metaphysician might find a better tool. However, more likely than not, this would involve changing the task (the activity). An activity is a means to an end, and analysis of the end might determine that the end itself is slightly misguided, or that the activity is not the most efficient way of reaching that end, so a change to the activity would be required, also requiring a change to the tool.

Ha, but if we could "know" the nitty-gritty of these other, non-knowledge mental tools, then they are actually knowledge, and that would be contradictory. Therefore, I am opposed to any strategy that consists in trying to systematize these other mental tools, because in order to do that, we would need to thoroughly "know" them, which is is not possible, because they are not knowledge. — alcontali

I see that, but I wasn't talking about tools (knowledge) at that point, I was talking about the mental activity which uses the tools. So let's say that some mental activity employs "strategy", that's a word you've introduced. Strategy is a tool which is often comprised to a large degree, of intuition. So we cannot say that all strategy is knowledge. Strategy is a tool which is applicable toward bringing about a desired end. It dictates the way we act, in the sense that it is used to determine the way that the mental activity uses the tools, knowledge, and how the tools are chosen. So strategy is more closely aligned to the end (the goal) than it is to the activity (the means to the end), because it is used to determine the activity.

Notice, I am not trying to "systemize" these mental tools, only to understand them. They are already systemized by the mental activity which uses them, and that's what makes them understandable, they are systemized. Therefore you've made an important error in the passage above. You have stated that it is not possible to know these tools because they are not knowledge. But there is an activity which brings knowledge into existence, so just because something is not knowledge doesn't mean that it is impossible to know it. A particular strategy for example may begin as not-knowledge (being based in intuition), but after being tried and tested it becomes knowledge. What this indicates is that there are mental activities which are not understood, because the tools employed are not knowledge, but these tools are not unknowable, our knowledge just has not progressed to the extent of knowing them.

But how do you know it is truly "first"? You do not. So, you will keep trying to find the really "true" first that comes before the current first. It just keeps going on. Ad nauseam. That is why it does not work. — alcontali

In ancient philosophy, the only knowledge worthy of that name rested on what is truly first, the ground of being, the origin of the manifold, the un-created. In the millenia since, this has become associated with religious doctrines, and rejected on those grounds. But within the ancient ruins lie a deep truth. 'A wise person must have a true conception of unproven first principles and also know the conclusions that follow from them. “Hence Wisdom must be a combination of Intelligence [Intellect; νοῦς] and Scientific Knowledge [ἐπιστήμη]: it must be a consummated knowledge of the most exalted objects.” Contemplation is that activity in which the nous intuits and delights in first principles.' ¹

You yourself have written eloquent polemics against 'scientism'. Perhaps the understanding represented by classical metaphysics is what has been lost, thereby allowing 'scientism' to fill the void that was left behind; the illusion that all could be subjected to our measure.

I agree that we ought not to idolize metaphysics, but I think the essential attribute of metaphysics is that, whereas what we conceive of as 'natural science' comprises what we think we can explain by way of natural principles, metaphysics is concerned in some sense with what explains us, and also what gives rise to those natural principles in the first place. It is, as it were, prior to any of the specific arts and sciences, and for that very reason, resists elaboration and explication, as it can only ever be intuited by the discursive intellect. That is why all of Plato's metaphysical passages were allegorical, puzzles, aporia, and suggestions; he did not pretend to have charted it.

Most modern philosophy complains about metaphysics, calls it obscure, best abandoned, not useful. Aristotle himself said somewhere (I can never find this passage again) that metaphysics is 'sublimely useless'. It serves no purpose; the best thing, and the only thing, that the human intellect can do is contemplate it; if we are able to do that, then just that is true happiness and virtue.

A sentiment long consigned to history, I'm afraid.

the essential attribute of metaphysics is that, whereas what we conceive of as 'natural science' comprises what we think we can explain by way of natural principles, metaphysics is concerned in some sense with what explains us, and also what gives rise to those natural principles in the first place. It is, as it were, prior to any of the specific arts and sciences, and for that very reason, resists elaboration and explication, as it can only ever be intuited by the discursive intellect. — Wayfarer

If there ever was a dialectical nutshell, that would certainly be a worthy contender.

found this snippet on a blog site re Heidegger's commentary on metaphysics:

It is entirely correct and completely in order to say, "You can't do anything with philosophy." The only mistake is to believe that with this, the judgment concerning philosophy is at an end. For a little epilogue arises in the form of a counter-question: even if we can't do anything with it, may not philosophy in the end do something with us, provided that we engage ourselves with it?

Introduction to Metaphysics, 13 (H9-10).

(I think I need to read this text in full.)

Right on. Philosophy does something with us. Or to us. Makes us think.

Instead of looking at the real, physical world, he looks at the abstract, Platonic world of knowledge and tries to discern if particular patterns emerge. The scientist does that with the real, physical world, . . . — alcontali

Until the 20th century, scientists did indeed examine the real, physical world. But since the advent of Relativity and Quantum Theory, physicists have been discovering that the fundamentals of reality are more theoretical & metaphysical than empirical & physical. Quantum Fields and Virtual Particles are far from the physics of Isaac Newton. Matter is now known to be composed of Energy, but what is energy made of? Nobody knows, so the essence of energy is undefined. Massless photons are described as "waves" without a medium. Gravity is no longer an attractive force, causing "spooky action at a distance", but merely the curved "fabric" of matterless space.

So, it seems to me that Natural Philosophy evolved into Modern Science around the time of Newton. But after Einstein, the cutting edge of Science has been moving deeper into the abstract realm of theory and metaphysics. So Philosophy is becoming relevant again for understanding the real world.

Metaphysics : http://blog-glossary.enformationism.info/page14.html

Matter is now known to be composed of Energy, but what is energy made of? Nobody knows, so the essence of energy is undefined. — Gnomon

Energy is defined as the capacity to do work. Energy is not what matter is composed of, it is a property of moving objects.

So Philosophy is becoming relevant again for understanding the real world. — Gnomon

Yes, philosophy is relevant, as necessary to avoid misunderstanding, like above.

Not surprisingly, your question has elicited a variety of responses, most of which, it seems to me, are just a bit off the mark. Personally, I'm comfortable with A. W. Moore's take on it, from his book, The Evolution of Modern Metaphysics: "Metaphysics is the most general attempt to make sense of things."

How does one (categorically) predicate that which necessarily precedes, and thereby exceeds, all predicates?

Scholatics (or neo-platonists) defined G (in contrast to g) by negating all traditional dogmatic predicates for G, in effect, asserting G by 'what G is not'.

Suppose we adopt a similar apophatic method or stance with respect to 'being qua being' or 'the real itself' or 'existence as such' ... actuality;

suppose, instead of speculating on 'What is', we define W by negating every contradictory-undefined predicate ascribed to W, in effect, asserting W by eliminating (epochē) what is necessarily not-W (or necessarily false about W);

and suppose an apophatic study, or contemplation, of 'every a priori impossible way the actual world necessarily could not have been or cannot be described'* - entailing as remainder 'every possible way the actual world could have been or can be described' - that confines speculative inquiry to exploring, or making explicit, impossible worlds/objects/events/agents as eliminable fictions (i.e. inadequate predicates for W):

Can we retain - regain - a speculative absolute by beginning (again) with internal critique via 'negating impossibles'*?

Is 'policing' non-contingent facts (e.g. unconditional events, inconsistent things, incoherent objects, etc) all that's left for rational metaphysics - hygienic, therapeutic, even cathartic - reminders that

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.
- Hamlet (1.5.167-8)

the Ways the World Could Have Been or Can Be Described, explicated and explored, are far far richer and stranger and more dangerous than any & all of our perennial, superstitious, self-serving, wishful woo?

[W]hat we conceive of as 'natural science' comprises what we think we can explain by way of natural principles, metaphysics is concerned in some sense with what explains us, and also what gives rise to those natural principles in the first place. — Wayfarer

Right on. Philosophy does something with us. Or to us. Makes us think. — Mww

What we speculate about and how we go about that, I agree, says everything about us and "... leaves everything" else "as it is." (L.W.) My interest in apophatics is motivated by the prospect of (A) greater self-reflection while 'doing metaphysics' than by the usual kataphatic practices as well as (B) a maximally pluralistic - transfinite / multiversal - phase space-like [sense of] Actuality as such ...  sort of a Spinoza-Nelson Goodman-Quentin Meillassoux chimera, or witches' brew (TBD).

How does one (categorically) predicate that which necessarily precedes, and thereby exceeds, all predicates? — 180 Proof

The original intuition of scholastic metaphysics is that 'intelligible objects' (such as arithmetic proofs and geometric forms) are known in a way that particulars can't be. That is because such logical proofs and so on are seen by 'the eye of reason' so to speak, in a way that sensory vision never provides; knowledge of them is apodictic and immediate, whereas knowledge of particulars is sensible and mediate (i.e. 'mediated' by the senses. This is the basis of 'form-matter' (hylomorphic) dualism. It is very different to Cartesian dualism).

In Christian Platonism, it is axiomatic that what can be intellectually known is nearer to the origin or source of being than anything perceivable by sense, because what is perceivable is 'made' and is therefore mutable and subject to decay (hence, why this is a dualistic philosophy.) Whereas the ideas of things are like archetypes in the intellect. '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.'

Whereas naturalism starts from the assumption that it is 'the particular', i.e. the existing object, that is real, and then tries to work back to its fundamental principles by reducing it to elements and so forth.

I think...

If philosophy is a school, metaphysics is the playground where children do their thing - play, only the toys are ideas. Imagination has a big role.

I think...

I like the idea (Schaffer), that metaphysic is not about what there is (because everything exist), but about what grounds what. For example, theistic debate is not about if god exist, but if human is on ground of god, or god in ground of human.

Personally, I'm comfortable with A. W. Moore's take on it, from his book, The Evolution of Modern Metaphysics: "Metaphysics is the most general attempt to make sense of things." — Jack-N

That's a good way to put it, if a bit vague. It makes sense if you are already familiar with various examples of metaphysics and are trying to generalize from that, but it probably won't be very helpful to someone who really doesn't know what metaphysics is, or has a distorted idea of it, for example, as something to do with the occult.

There is a lot of confusion (one might say 'cross-pollination') between metaphysics as a sub-discipline within philosophy, and metaphysics as a publishing-industry catch-all for squishier occult interests. This is probably due in part to the attempts by people active in the occult to acquire status by association with "philosophy." Which is not unlike many attempts by philosophers to improve their public image through association with "science." I don't know of any easy way through this confusion. But if someone is genuinely interested in gaining a clearer understanding of what metaphysics is, in its more orthodox philosophical sense, then I think Moore's book would be helpful, though admittedly it is not a casual read. If someone "really doesn't know what metaphysics is," then they are in the enviable position of having a chance at being lucky at the outset; of starting somewhere near the center of mainstream philosophy, rather than somewhere out on the dubious fringes.

Energy is defined as the capacity to do work. Energy is not what matter is composed of, it is a property of moving objects. — Metaphysician Undercover

As I said, energy is defined by what it does, not by what it is (essence). Energy is indeed a quality (attribute) of matter, like the redness of an apple, which exists, not in the apple but in the mind of the observer. A Quale is a subjective experience, not an objective thing. So, Energy (potential) is metaphysical, but it can become actual & physical in the sense of E = MC2. Perhaps I should have said that Energy is what Mass is composed of. Mass is also a property of Matter. So again, what substance is Matter or Mass made of?
Qualia https://en.wikipedia.org/wiki/Qualia
Metaphysics "Physics refers to the things we perceive with the eye of the body. Meta-physics refers to the things we conceive with the eye of the mind." http://blog-glossary.enformationism.info/page14.html

Yes, philosophy is relevant, as necessary to avoid misunderstanding, like above. — Metaphysician Undercover

Since quantum physics deals with "things" that are not actual or physical (virtual particles, quantum field), it necessarily involves philosophical metaphysical reasoning about abstractions rather than empirical objects. Quantum theory is paradoxical, and subject to misunderstanding, because it necessarily uses material metaphors to discuss immaterial concepts.
Field a mathematical concept (set) https://en.wikipedia.org/wiki/Field
"Metaphysics is the branch of philosophy that examines the fundamental nature of reality, including the relationship between mind and matter, between substance and attribute, and between potentiality and actuality." https://en.wikipedia.org/wiki/Metaphysics

metaphysics as a publishing-industry catch-all for squishier occult interests. — Jack-N

Yes. Unfortunately, metaphysical Philosophy has been contaminated by association with various mind-over-matter notions (magical thinking) among aficionados of the occult arts. Those "arts" typically use the techniques of stage magic (misdirection, concealment, etc) to simulate psychokinesis or psychic mind-reading. Those mind-games are much more popular than the artless (unfeigned) discipline of philosophical metaphysics.

Perhaps I should have said that Energy is what Mass is composed of. Mass is also a property of Matter. So again, what substance is Matter or Mass made of? — Gnomon

You can't really say 'what substance is', or 'what matter is', because if you could describe it you would be talking about its properties, not substance itself. Substance is what has properties, so you can't really describe it by referring to what properties it has.