Gnomon
read these two paragraphs. Substitute 'to exist' for 'to be'. — Wayfarer

"God as creator is then a kind of transcendent non-being above the being of creation.

He says "God is" (exists in some sense), but is also "non-being". That's why I use the neologism of BEING to refer to that which exists in a transcendent sense as the potential for creation of something from nothing, real from ideal.

No. The ancients meant something different to what we mean by 'cause' - they meant in a broader 'the reason why things exist'. — Wayfarer

Yes, Laymen and philosophers mean something different by "cause". Most people think in terms of proximate causes (energy), while others look for ultimate causes (EnFormAction).

How can you say that a potential can cause something if you uphold the distinction between potential and actual and see that an act is required as a cause? — Metaphysician Undercover

It's a fine philosophical distinction. Of course, in the real world Potential & Actual occur in pairs : Voltage & Amperage. But, the voltage in a battery can exist unrealized for years, until a circuit is completed by the user (plug it into a device and close the on-off switch). So, in Eternity & Infinity, transcendent Potential could theoretically exist independently, until triggered by a choice, an intention, which completes a circuit from Ideal to Real and back to Ideal again. In this analogy, G*D is both battery and user, both potential and actualizer. The device is our universe.

Sure, but do you see that possessing the power to cause a world to exist is different from actually causing the world to exist? — Metaphysician Undercover

Yes. See the reply above. If G*D is only potential, nothing would ever happen. That's why I assume that G*D must also have Intention, Will, Telos. Of course I don't know how these things would work outside of space-time-matter-energy. It's a mystery. :smile:

No, voltage is a description, not a prediction. According to Wikipedia it is the difference in electric potential between two points. — Metaphysician Undercover

Voltage is a description of what will happen in the future when a path between those two points is completed. Voltage is also Information in the sense of a "difference that makes a difference" : it causes change.

One of the coolest answers is Heidegger's: look around you now and in your mind, place a backdrop of nothingness behind it all. — frank

"A German friend of Heidegger told me that one day when he visited Heidegger he found him reading one of D.T. Suzuki’s books; ‘If I understand this man correctly,’ Heidegger remarked, ‘this is what I have been trying to say in all my writings’”. The truth of this story is unverifiable and irrelevant, but Barrett considers its moral undeniable.

I refer to that, because your statement is very much an expression of what Buddhism calls 'sunyata'. Heidegger's convergences with Buddhism are the subject some literature, although he himself hardly commented on it.

There are two meanings for the word "structure". For most folks it's the physical posts & beams that a building is made of. But, for an engineer, the structure is a diagram of forces and reactions (vectors). Information is both concrete structure (things) and abstract structure (relationships between things). — Gnomon

Well, yes, but I think the platonist view of 'form' is a little more elaborate. The form of something is the idea - not simply 'my idea' or some vague image in the individual mind, but the real meaning towards which any particular strives. The best example is number and numerically-expressed laws. A formula, like Newton's laws of motion, describe the motion of every particular (within a certain range i.e. not at relativistic velocities). So, it is in a sense the 'relations between things' but I feel as though you're not really cutting through to the profound sense in which such relations and laws represent an underlying logos which guides and directs all things: not as a 'god' through acts of will but because they constitute the 'fabric of the cosmos.

The only end of science, as such, is to learn the lesson that the universe has to teach it. In Induction it simply surrenders itself to the force of facts. But it finds . . . that this is not enough. It is driven in desperation to call upon its inward sympathy with nature, its instinct for aid, just as we find Galileo at the dawn of modern science making his appeal to il lume naturale. . . . The value of Facts to it, lies only in this, that they belong to Nature; and nature is something great, and beautiful, and sacred, and eternal, and real, —the object of its worship and its aspiration. The soul's deeper parts can only be reached through its surface. In this way the eternal forms, that mathematics and philosophy and the other sciences make us acquainted with will by slow percolation gradually reach the very core of one's being, and will come to influence our lives; and this they will do, not because they involve truths of merely vital importance, but because they [are] ideal and eternal verities. — C. S. Peirce

Reasoning and the Logic of Things, edited by Kenneth Laine Ketner, with introduction and commentary by Ketner and Hilary Putnam (Harvard University Press, 1992), p. 112 (quoted in Thomas Nagel, Evolutionary Naturalism and the Fear of Religion, from The Last Word.)

It's a fine philosophical distinction. Of course, in the real world Potential & Actual occur in pairs : Voltage & Amperage. But, the voltage in a battery can exist unrealized for years, until a circuit is completed by the user (plug it into a device and close the on-off switch). So, in Eternity & Infinity, transcendent Potential could theoretically exist independently, until triggered by a choice, an intention, which completes a circuit from Ideal to Real and back to Ideal again. In this analogy, G*D is both battery and user, both potential and actualizer. The device is our universe. — Gnomon

Do you see the "choice", as an actuality which is distinct from both the voltage and amperage? If the voltage is potential, it could sit there forever without an actuality (choice in this case) to actualize it. This is the problem with infinite potential. If the potential is infinite, it cannot be limited by any actuality, and this includes the actuality of the being who would make the choice, or any other actuality which might actualize the potential. So if there ever was infinite potential, there would always be infinite potential, which is not what we observe.

My understanding may be erroneous or naturalists (e.g. scientists) may misunderstand what they doing. — 180 Proof

Why do you class scientists as naturalists? Scientists might seek to understand the aspects of the natural world which are proper to their field of study, without reference to metaphysics, but they do not, in general, seek to understand the entirety of the natural wold. So they do not attempt, through their various fields of study, to explain the natural world, only to explain specific aspects of it. Many aspects of the natural world might be understood without employing metaphysics, but understanding an aspect of the natural world does not render the natural world as explainable. And this is where metaphysics is called for.

Do you consider, for instance, that merely assuming 'the natural world is explainable' is a "recourse to metaphysics"? — 180 Proof

Yes I do, because the statement of "the natural world" implies that the entirety of nature is one entity, a unity, and this is a metaphysical assumption. Furthermore, I think that to assume that something which has not yet been explained, is explainable, is a metaphysical assumption.

How can you not know what metaphysics is? You've been interested in philosophy long enough. Learning the branches is one of the most basic, early stage things you do. Check out the "Categories" menu if need be.

You might find Ervin Lazlo's idea interesting. https://en.wikipedia.org/wiki/Ervin_L%C3%A1szl%C3%B3

That is why I reject the practice of metaphysics. — alcontali

You mentioned Popper. He considered metaphysics to be important, but just not a science. He considered it be, although not itself a science, indispensable to science. This is because creative imaginative thought is indispensable to science just as much as it is to the arts.

You mentioned Popper. He considered metaphysics to be important, but just not a science. He considered it be, although not itself a science, indispensable to science. This is because creative imaginative thought is indispensable to science just as much as it is to the arts. — Janus

I am certainly a fan of Popper's epistemic result, and I have completely adopted his seminal publication, "Science as falsification". That does not mean, however, that I would adopt everything that he has ever written.

The same holds true for Socrates, Plato, Aristotle, and Kant. Not everything that they have proposed, has turned out to be equally successful.

I consider the core axis of knowledge to be mathematics, science, and history. However, the reason for this, is neither mathematical, nor scientific, nor historical.

Mathematics deals with patterns that arise in carefully and explicitly constructed abstract, Platonic worlds. Science deals with patterns that arise in the real, physical world. History corroborates witness depositions.

Epistemology is meta-knowledge. It deals with patterns that arise in the abstract world of knowledge as this world of knowledge gradually arises and emerges, while focusing on its essential characteristics, which is, how the knowledge is justified.

Metaphysics, however, has nothing to do with figuring out knowledge justification. It does not revolve around justified (true) beliefs (JtB). It rather tries to rationally question the starting points of knowledge.

I consider that to be nonsensical in, for example, mathematics, because the starting points in mathematics are not the job of anybody else than mathematicians. Seriously, if you have no clue as to what the effect of changes in the starting points will be on the body of theorems that rest on it, then you are clearly doing it wrong.

The problem is clearly of a very similar nature in science and history.

Furthermore, if these starting points had a rational justification, then they would not be starting points. Therefore, the questioning of starting points is mostly in vain, even by people who are aware of the consequences of modifying the starting points. Therefore, I also consider metaphysics to be a futile and often ignorant exercise in infinite regress.

A good example of how all of that goes wrong is Collingwood's "An essay on metaphysics".

An example that Collingwood gives of this concerns the frameworks (he calls them “constellations”) provided by the Newtonian, the Kantian and the Einsteinian modes of scientific enquiry. Each of these assumes a peculiar notion of causation, and within any one of them, this notion cannot be questioned. It is not thought of as true; it is simply taken for granted. It is an absolute presupposition."

So first Collingwood writes that there are three kinds of physics, Newtonian, Kantian, and Einsteinian. That is bullshit. Collingwood's metaphysical views on physics are totally ignorant of how physics operates. His views were already considered absurd by the cognoscenti even back in the 1930ies when he wrote them. There is simply no such thing as "Kantian physics".

His already wrong views on physics then automatically degenerate into an exercise in infinite regress:

"any question involving the presupposition that an absolute presupposition is a proposition such as the questions ‘Is it true?’ ‘What evidence is there for it?’ ‘How can it be demonstrated?’ ‘What right have we to presuppose it if it can’t?’

So, that is typically metaphysics: ignorant and degenerative, infinite regress.

Do you know anyone who's actually tried to explain the natural world without recourse to metaphysics? — Metaphysician Undercover

No, there's not way to explain it without implicit or explicit metaphysics? Physicalism? well, it's right there. Natural laws? again right there — Coben

To further compliment this: Truth is an epistemic criterion that is meaningless when devoid of the concept of reality. Reality is studied by ontology. And ontology is a leading branch of metaphysics. Hence, there can be no comprehension of truths in the absence of metaphysics. Reworded, regardless of how naive or formal, else tacit or conscious, one's understanding of the latter is, there must be some understanding of it if one is to have any understanding of truths.

And interestingly, ‘ontology’ is derived from the first person participle of the verb ‘to be’ - which is, of course, ‘I am’. The significance being that it emphasises the first-person nature of the subject which is excluded in modern science.

Collingwood writes that there are three kinds of physics, — alcontali

He doesn’t say that, well at least not in the quote you provided. He said ‘knowledge frameworks’ and I think it’s a perfectly valid point. The Bohr-Einstein debates were basically metaphysical in nature, and Bohr’s ‘Copenhagen interpretation’ is arguably Kantian in many respects.

There is simply no such thing as "Kantian physics". — alcontali

and Bohr’s ‘Copenhagen interpretation’ is arguably Kantian in many respects. — Wayfarer

A little known fact about Kant that I find pertinent:

The nebular hypothesis is the most widely accepted model in the field of cosmogony to explain the formation and evolution of the Solar System (as well as other planetary systems). It suggests that the Solar System is formed from the nebulous material. The theory was developed by Immanuel Kant and published in his Allgemeine Naturgeschichte und Theorie des Himmels ("Universal Natural History and Theory of the Heavens"), published in 1755. Originally applied to the Solar System, the process of planetary system formation is now thought to be at work throughout the universe.[1] — https://en.wikipedia.org/wiki/Nebular_hypothesis

He doesn’t say that, well at least not in the quote you provided. He said ‘knowledge frameworks’ and I think it’s a perfectly valid point. The Bohr-Einstein debates were basically metaphysical in nature, and Bohr’s ‘Copenhagen interpretation’ is arguably Kantian in many respects. — Wayfarer

Kant never tested anything experimentally. Therefore, his views cannot be classified as physics in its modern understanding, which already prevailed in the 1930ies, when Collingwood mentioned the term "Kantian physics".

Concerning the Bohr-Einstein controversy, if you receive a sequence of numbers that look random, even though they may have been generated by a pseudo-random number generator, which uses a seed to construct the sequence, and the knowledge of which would allow you to flawlessly predict the next pseudo-random number, then in absence of knowledge of such seed, I recommend to treat these numbers as random. Therefore, I side with Bohr. Furthermore, I do not consider this question to be metaphysical at all.

Furthermore, I do not consider this question to be metaphysical at all. — alcontali

So you're saying that the issue of reality is not a metaphysical issue? I can point to a plethora of references that say it is. Wikipedia being my staple on grounds that it is peer-reviewed.

On what merits to you deny that the study of reality is a metaphysical issue?

Kant never tested anything experimentally. — alcontali

Kant lectured in a wide range of subjects, and indeed his nebular hypothesis still stands, but is known as a philosopher. And I am of the view that philosophy requires no apparatus. In other words, I don't see how any discoveries in physics can really effect Kant's main theses in CPR, which are after all primarily concerned with the nature of reason, not with the composition of physical objects.

Concerning the Bohr-Einstein controversy — alcontali

Nothing you have said there corresponds with anything I have read about the nature of the controversy. In a nutshell, Einstein was a scientific realist, who believed that the job of physics was to disclose facts about independently-existing objects. His disagreement was with the notion of 'observer dependence' which physics suggested. He was never reconciled to that.

A current popular 'interpretation' of quantum physics is Everett's, in which worlds multiply indefinitely whenever measurements are made. Apparently there are an infinite number of such worlds, which differ in every possible number of degrees, from zero to infinite, that exist in parallel. That too is a metaphysical theory, however one that is untethered. from anything in classical metaphysics.

On what merits to you deny that the study of reality is a metaphysical issue? — javra

There is no knowledge possible without an epistemic knowledge-justification method; two of which, in the context of the real, physical world, are science and history. So, there we have two epistemically sound knowledge domains.

Epistemology, which does not study the real, physical world, but the abstract, Platonic world of knowledge is also sound, because it faces an already committed world of knowledge as it has emerged already. Hence, the detection of patterns in these existing commitments is not merely spurious.

What principle would force a bit of sanity in metaphysics?

In my opinion, there are no constraining structures that enforce soundness in the activity of merely investigating presuppositions; not even the effect on theorems that already make use of these presuppositions.

It is possible to investigate presuppositions in mathematics, because they are freely chosen or even arbitrary, and they do not claim to be the construction logic of the real, physical world anyway. A good example is the analysis on why the axiom of determinacy is incompatible with the axiom of choice in set theory.

The construction logic of the real, physical world, i.e. the theory of everything (ToE) is unknown. Therefore, a similar exercise is impossible in that context. Still, that is what metaphysics tries to do in vain.

And I am of the view that philosophy requires no apparatus. — Wayfarer

I agree for epistemology, even though it still needs access to the body of existing knowledge in order to detect patterns in it; which Immanuel Kant more than successfully did. Karl Popper also did that magisterially.

Pointing out an existing meta-knowledge pattern in knowledge is important, because it allows the downstream knowledge practitioners to take note of these findings in their quest for the discovery of new knowledge.

That is the difference between epistemology and metaphysics. Unlike epistemology, there are no downstream practitioners who need any output from metaphysics. It just gets ignored, and that has been the case for almost 2500 years now.

There is no knowledge possible without an epistemic knowledge-justification method; two of which, in the context of the real, physical world, are science and history. So, there we have two epistemically sound knowledge domains. — alcontali

but it's not an either or situation. Scientists often work(ed) with a certain epistemic knowledge justification method while at the same time having metaphysical assumptions about the world and reality. These may have biased them at times but also have been fruitful. One does not need to choose between metaphysics and having a rigorous method and no one does. Or, better put, no one with a rigorous method lacks a metaphysics.

Unlike epistemology, there are no downstream practitioners who need any output from metaphysics.

They are not reading journals of metaphysics, but they have trickle down metaphysics.

I'm in agreement with @Wayfarer in that Kant focuses on issues that precede the "epistemic knowledge-justification method" of modern empirical science and of history. Both employ reasoning, and Kant's focus was in significant part on what reasoning is constituted of.

What principle would force a bit of sanity in metaphysics? — alcontali

The same overall principle that forces sanity in mathematics: accord to our experiences of what is. No?

Theoretical (pure?) mathematics can get a little disjointed from reality at times, last I heard. And unlike the sciences of biology, neurology, cognitive sciences, etc., physics is quite heavily reliant upon mathematical ideas - M-theory and Everett's many worlds as just two physicist hypotheses that have no falsification ability to them. Yet are nevertheless widely enough endorsed.

As to metaphysics, as an abstract principle to be ideally pursued, make its affirmations falsifiable via reasoning and/or experience.

The same overall principle that forces sanity in mathematics: accord to our experiences of what is. No? — javra

Mathematics has nothing to do with real-world experience. It is completely divorced from it. It is about consistency in abstract language-only expressions. Seriously, if a claim is about the real, physical world, then it is not mathematics.

Theoretical (pure?) mathematics can get a little disjointed from reality at times, last I heard. — javra

There is no other mathematics left than pure mathematics. If it is about reality, then it is a downstream discipline, such as physics or another subdivision in science, or engineering, or some other downstream activity.

Mathematics does not compete with physics or with science in general. That is epistemically impossible.

As to metaphysics, as an abstract principle to be ideally pursued, make its affirmations falsifiable via reasoning and/or experience. — javra

In that case, it tries to compete with disciplines that do that already; and it miserably fails.

There is no knowledge possible without an epistemic knowledge-justification method; two of which, in the context of the real, physical world, are science and history. — alcontali

Note the reflexive equivocation of 'real' and 'physical'. You write from a perspective which assumes the reality of the sensory domain - as us denizens of a sensate culture are inclined to do! But what if the source, and the goal, of metaphysics is not within that domain at all?

It's worth recalling that in the Analogy of the Divided Line, which is the central to Platonic metaphysics and epistemology, that whilst knowledge of maths and geometry (dianoia) is higher than mere opinion or belief (pistis or doxa), it's still not quite so high as knowledge of the ideas (noesis). I am inclined to think that what this refers to has actually been altogether forgotten by modern culture - so, to us, it appears a nothing, a non-entity, nonsense. But that's because we're configured to think in certain ways. This is why critical philosophy really is critical - it calls into question most of what sober and sensible people take for granted.

Seriously, if a claim is about the real, physical world, then it is not mathematics. — alcontali

You keep repeating this, as a dogma, and oppose anyone who challenge it as 'constructivist heretics'. But the weakness of this claim is that we're utterly surrounded by devices and technologies which would not exist, were mathematics not applied to the physical world. There's not two domains, an imaginary Platonic realm which exists only in the imagination, and a physical world devoid of mathematical realities. In fact these domains are inextricable, which is a fascinating philosophical issue.

Mathematics has nothing to do with real-world experience. It is completely divorced from it. — alcontali

There is no other mathematics left than pure mathematics. — alcontali

I'd say bring it down to Earth a bit. We learn as toddlers about mathematics how? By noticing quantity in reality and the relations between quantities - and by giving these quantities and relations names such as "one" and "plus". 1 + 1 = 2 is not pure mathematics. It is a fact that is thoroughly entwined with the reality in which we live. (And I'm not denying Platonic-like ideals in saying this - after all, logos is logos.)

Mathematics does not compete with physics or with science in general. That is epistemically impossible. — alcontali

I've a former friend (but sticking to the point ...) who got himself a doctorate in maths. According to his learning, one can easily construct a coherent theoretical mathematics that blatantly contradicts everyday aspects of reality such as that of gravity. Axioms are what you want them to be and you simply construct from them. In examples such as this, mathematics does (or at least can) compete with empirical physics and with empirical science in general.

Note the reflexive equivocation of 'real' and 'physical'. You write from a perspective which assumes the reality of the sensory domain - as us denizens of a sensate culture are inclined to do! But what if the source, and the goal, of metaphysics is not within that domain at all? — Wayfarer

Well, we can discuss Matrix-like philosophies, but they are not knowledge, because they are about the real, physical world but not justified from anything else therein.

I am a fan of the Matrix idea. I like it quite a bit, but I also know the limitations of that kind of thought exercises, and I do not classify them as knowledge or meta-knowledge. These things are hypothetical conjectures. Si non vere, bene trovato.

You keep repeating this, as a dogma, and oppose anyone who challenge it as 'constructivist heretics'. — Wayfarer

Well, in a sense, I am just continuing the Brouwer-Hilbert controversy, but in the end, there is rather a consensus that Hilbert won that debate. So, yes, I believe that Hilbert was right and that Brouwer was satanically wrong.

But the weakness of this claim is that we're utterly surrounded by devices and technologies which would not exist, were mathematics not applied to the physical world. — Wayfarer

Yes, but it always goes through a downstream discipline which makes the necessary perspective shift.

For example, mathematics is distinct from computer science (CS), because CS has to contend with equipment that does not compute instantaneously fast nor has infinite memory. Mathematics does not have to do that. Engineering also has to deal with real-world trade-offs and cost considerations. There you have again other elements that kick in. It is the purity itself of mathematics that creates the need for downstream disciplines that are not completely pure.

1 + 1 = 2 is not pure mathematics. It is a fact that is thoroughly entwined with the reality in which we live. — javra

These are empirical patterns in which people detect some form of consistency. Mathematics is only about that consistency, and nothing else. It is not empirical. The language expression "1+1=2" is handled by math, because it is language. What you see in the real, physical world, is not handled by math.

According to his learning, one can easily construct a coherent theoretical mathematics that blatantly contradicts everyday aspects of reality such as that of gravity. Axioms are what you want them to be and you simply construct from them. — javra

Of course. Language can create abstract, Platonic worlds that have nothing to see with the real, physical world. That is not even specific to mathematics. Science fiction movies do that too. The difference is that mathematics has an extremely elaborate notion of consistency. Mathematics will still not allow you to contradict yourself inside that world without gravity. Otherwise, anything flies, because that is the name of the game.

satanically — alcontali

use of that word says something!

These are empirical patterns in which people detect some form of consistency. Mathematics is only about that consistency, and nothing else. It is not empirical. The language expression "1+1=2" is handled by math, because it is language. What you see in the real, physical world, is not handled by math. — alcontali

You might be using language in a very specific sense. In which case, yes, relations between quantities is not a human language used to convey meaning. All the same, in a broader sense of language, how is mathematics - which is codified quantity and relations between quantity (right?) - not an abstracted form of language employed by humans for various purposes? In physics, such as for the purpose of understanding the world and for predictions.

Of course. — alcontali

OK. So I take it that we agree that what you previously stated is "epistemically impossible" is actually possible.

satanically — alcontali


that's says something. — Wayfarer

"Satanists" are the Abrahamic way of describing those whom you dislike.

His disagreement was with the notion of 'observer dependence' which physics suggested. He was never reconciled to that. — Wayfarer

The analogy with random numbers is exactly that: observer dependence. The randomness of numbers depends on the observer. They are not (necessarily) intrinsically random (which is something we do not even know). That is where Kant's epistemic consideration kicks in:

Prolegomena, § 32. 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.

Therefore, if something consistently appears to you in a particular way, then you can proceed with the idea that they are in that particular way. What else are you going to do anyway? So, I side with Bohr.

All the same, in a broader sense of language, how is mathematics - which is codified quantity and relations between quantity (right?) — javra

No, I disagree because most of mathematics is not about codified quantity or relations between quantity. Only number theory to some extent is. Furthermore, the dominant axiomatization is currently set theory, and that has been the case for almost a century.

The ontology of mathematics is not a settled matter. Everybody still disagrees with everybody else. Still, the idea that it would be about quantity is considered very, very restrictive. For example, is a combinator or a function related to quantity? In another example, I don't think that, for example, category theory even ever mentions quantities. It is rather about structures, mappings between these structures, and possible preservation of structure. I don't think you'd ever see a quantity in that context.

not an abstracted form of language employed by humans for various purposes? — javra

It is language and permissible manipulation of the symbols in the language. However, that does not settle the matter of the ontology. Far from.

The ontology of mathematics is an outstanding problem.

Therefore, if something consistently appears to you in a particular way, then you can proceed with the idea that they are in that particular way. — alcontali

There's much more to it than that. We can infer and predict outcomes, based on mathematical analysis of observations - this is near to Kant's synthetic a priori. Whence this predictive relationship between mathematical reasoning and material facts? I find Eugene Wigner's essay on it very interesting.

For example, is a combinator or a function related to quantity? — alcontali

No, I'd say those are complex relations regarding quantity. In other words, they would be pointlessly meaningless - correct me if I'm wrong here - in the complete absence of expressions of quantity such as that of "1".

I don't think that, for example, category theory even ever mentions quantities. It is rather about structures, mappings between these structures, and possible preservation of structure. I don't think you'd ever see a quantity in that context. — alcontali

I'll be explicitly transparent. Yes, I took calculus in high-school, but I'm no mathematician. Not my thing.
Still, I have an exorbitant degree of confidence that none of the above means anything sans representations of unity, aka quantity. A geometric point, for all its marvels of being volumeless, is yet a quantity, for instance.

If the semantics of "quantity" needs better clarification, let me know. Alternatively, if you find I'm mistaken - but understand that "1" represents an idealized perfect integrity, or unity, of existent stuff - please offer some references to maths devoid of notions of quantity (such as the concept of "1", and its derivatives).