Scotus also conducted his work in Aristotelian fashion. But his 'Univocity of Being' carried a realism aspect.

Again, Peter Adamson of King's College London does an excellent job explaining this in the video on Duns Scotus that I referenced earlier.

Distinct points/instants are indeed arbitrary and artificial creations of thought, but indefinite infinitesimals/moments are real, with length/duration less than any assignable value and no discernible boundaries. — aletheist

Do you not see the problem here? You yourself said "there is still a role for points--not as the parts of a line, but as the discrete boundaries between its continuous parts". An "infinitesimal" requires such a boundary to exist as an infinitesimal. Do you agree with this, there is no infinitesimal without a boundary to separate it from others? If the boundary is arbitrary, an artificial creation, as you say here, then so is the infinitesimal created by the boundary.

Where do you get the idea that Peirce thought there were infinitesimals which are not created by those arbitrary divisions? As I explained, if the boundaries required for such infinitesimals, actually existed within the medium, then these boundaries would break up the continuity of the medium, such that it would not be continuous.

Do you agree with this, there is no infinitesimal without a boundary to separate it from others? — Metaphysician Undercover

No, I do not agree with this, and neither did Peirce. Infinitesimals/moments are indefinite, not distinct. The principle of excluded middle does not apply to them. Points/instants are arbitrarily inserted as boundaries between continuous segments/lapses of finite length.

Where do you get the idea that Peirce thought there were infinitesimals which are not created by those arbitrary divisions? — Metaphysician Undercover

Again, his view was that infinitesimals/moments are real, while points/instants are artificial creations. I have already provided several quotes from his writings to support this summary. Unless you can produce citations to the contrary, we have nothing more to discuss here.

I totally don't get your position on nominalism.

The word transcendental with regard to Abelard is misleading. That has to do with form. Abelard didn't believe in form. He believed in Cartesian extension. That is what nominalism is. You say Scotus "denies whatever is 'one' is an individual"? One and individual are the same thing! He doesn't deny that tautology. Scotus was not a nominalist so of course he believe in unity that was more than the numerical sum of the parts. Thisness! Yes Scotus also denied Platonic forms. But he did NOT agree with Islamic ideas that we all share a cosmic soul together. And I fail to see where Scotus "disagrees with Aquinas' views on common natures/species".

Scotus did think that prime matter and form could exist somehow separately. Aquinas believed contra that there was only a formal distinction. Nonetheless, I've never seen such splitting hairs as in this thread

Infinitesimals/moments are indefinite, not distinct. — aletheist

I know, I explained this, the boundaries between moments are vague. That's why we can throw the "point" out the window. The "point" does not apply, as special relativity demonstrates. So the point is useless and that's why I said Peirce dismisses it.

The principle of excluded middle does not apply to them. — aletheist

Claiming that the law of excluded middle may be violated does not resolve the problem. It is a matter of contradiction. The existence of infinitesimals in the medium requires that there are natural boundaries.
If there are boundaries within the medium, then the medium is not continuous. Saying that there are boundaries which are "indefinite, not distinct", and concluding therefore that they are not boundaries at all and therefore there is continuity, is simple contradiction.

Peirce is a dialectical materialist, or dialetheist, one who allows for the law of non-contradiction to be violated.

Scotus.....

- Denies whatever is 'one' is an individual. — Mapping the Medium

Can you elaborate on this point? How is there a difference between being "one" and being an "Individual"?

- Accounts for causation in this 'degree of less than numerical'. (Experience and events provide this 'degree' of influential causation. Think about what science is now discovering about epigenetic/environmental/experiential influences.) — Mapping the Medium

And could you expound on this as well? What is this feature of reality which you call "less than numerical", what is this Unity which is less than numerical?

Neo-Platonist principles, which I believe ground Christian metaphysics holds the fundamental unity as the "One". Neo-Platonism is a sort of unified Plato/Aristotle perspective, prior to the more comprehensive unification provided by Aquinas. This prior conditioning of Neo-Platonism (Augustine for example), into Christian metaphysics, is prerequisite for Aquinas' approach towards making Aristotelian principles consistent with Christian principles, thus facilitating this process.

Therefore, I am interested in where this idea of a unity which is somehow not consistent with the arithmetical numerals is derived from. How is there such a thing as a unity which cannot be represented by the numeral "one"? What makes this "unity" different from a normal "unity" which we represent with "one"?

Singular essences are unknowable to us, even though they ARE real. We refer to their reality indirectly by recognizing and differentiating what it is not. Example: Humans develop and recognize 'self' only in relation to that which is 'not' self. — Mapping the Medium

Isn't this fundamental to the nominalist approach? And it is consistent with Aquinas as well. Based in Neo-Platonism, Aquinas emphasizes a distinction between divine Forms with independent existence, and the (abstracted) forms of the human mind, which cannot be independent from matter because they dependent on the human mind which is attached to matter.

It is Aristotle's metaphysics which explains how the Form of the particular, singular, or individual object, must be prior in time to the material existence of that particular, or individual. This necessitates the independent Forms. of the Neo-Platonists. Notice that these Forms are forms of particulars, grounded in the "One", (the Form of the entire unity, the universe). They are not Platonic forms, which are universals which depend on the human mind.

The extreme difficulty is approached in Plato's Timaeus, which is to establish a relationship between the form of the individual, and the form the universal. There are numerous approaches offered, over the centuries, and each gets tangled and lost in numerous twists and turns, and category mistakes. Plato tries to offer the straight and narrow, but puts the universal form as prior, while Aristotle seeing the dead end to this approach turns things around to place the form of the particular as first, and this is represented in Neo-Platonism as the "One".

But again, the nominalists and the realists are still both misguided. So we have all of these 'camps' of thought going round and round on this merry-go-round, and never getting off. — Mapping the Medium

I would not say that either of these camps are "misguided". They each manage to approach first principles, in their own way. To get to this point, of approaching first principles requires serious guidance. However, each has a slightly different approach, and neither manages to get beyond what I called the "extreme difficulty", so both appear to be somewhat misguided. But since the extreme difficulty remains unresolved, we cannot really say that they are misguided because the proper guidance remains unavailable. We'd have to say everyone is misguided, even though they managed to get this far.

The only way to make any difference in what has happened is to try and teach the general public how human beings actually develop and how life interacts with each other. If we only recognize ourselves and our 'medium' by what it is not, then we have to realize that the only way to learn and reach a shared understanding is through dialogue with others who have a different perspective. — Mapping the Medium

This sounds like a Wittgensteinian perspective, which is not really dissimilar to Peirce. The individual's perspective is first, the primary perspective, and we create a shared understanding. The issue is whether we can overcome differences between the individual perspectives, to validate real, true, universals, rather than taking the realist perspective, that the universal is real, prior, and imposes itself on us.

So the point is useless and that's why I said Peirce dismisses it. — Metaphysician Undercover

Citation, please. On the contrary, Peirce does not dismiss points/instants, he clarifies that they are creations of thought rather than real constituents of lines/time.

The existence of infinitesimals in the medium requires that there are natural boundaries. — Metaphysician Undercover

No, the only boundaries within a continuous medium are the artificial ones that we arbitrarily insert at finite intervals for some particular purpose, such as measurement.

Peirce is a dialectical materialist, or dialetheist, one who allows for the law of non-contradiction to be violated. — Metaphysician Undercover

Citation, please. On the contrary, according to his own words Peirce is an objective idealist for whom the principle of non-contradiction does not apply to that which is vague/indefinite and the principle of excluded middle does not apply to that which is general/continuous. In accordance with the latter, he is now recognized as the first person ever to develop truth tables for a rudimentary three-valued logic--true, false, and the limit between truth and falsity.

Metaphysician Undercover and Aletheist...

Thank you. These are exactly the topics I came here to dig deeper into. I appreciate it very much.

I will respond again with my thoughts later during some freer time. I look forward to you both providing some feedback to help me clarify my thinking.

In the meantime....

I'll throw these questions out for contemplation...

1) Do you think that consciousness is 'real'?

2) If so, do you think it can be explained/described numerically?

3) If not, how is consciousness manifested and used if it is not 'real'?

4) Considering the above questions, which came first, consciousness, numbers, or semiotics?

5) How do all of the above questions factor into time, evolution, and ever-changing linguistics?

1) Do you think that consciousness is 'real'? — Mapping the Medium

Yes, although before going any farther we need to establish what we mean in this context by "consciousness" and "real."

2) If so, do you think it can be explained/described numerically? — Mapping the Medium

I am not sure what that would even mean, but like anything else, I think that it can be explained/described mathematically--i.e., with a retroductive hypothesis that we can then deductively explicate and inductively evaluate. The subject matter of mathematics is much broader than just numbers.

4) Considering the above questions, which came first, consciousness, numbers, or semiotics? — Mapping the Medium

Again, we need to define "consciousness," and numbers are strictly hypothetical. Semiotics is a relatively recent science, so it clearly came last; but if you meant to say semeiosis, the real process that semiotics studies, then I am inclined to believe that it came first.

5) How do all of the above questions factor into time, evolution, and ever-changing linguistics? — Mapping the Medium

My current working hypothesis is that time is a manifestation of semeiosis, the ongoing evolution of the universe as dynamical objects determine sign tokens to determine dynamical interpretants. Linguistics is a special science that studies actual languages, while semiotics is a normative science that studies the nature of signs in general (speculative grammar), good vs. bad reasoning (logical critic), and methods for obtaining true beliefs (speculative rhetoric).

Again, hair-slitting. You either believe that Platonic Forms are real entities separate from God or not. Aristotle, Augustine, and Aquinas all thought not. Neo-Platonic Christianity and Christian Aristotelianism are not different. They just have a little different emphasis

Are bananas upside down when tomorrow is yesterday?

Anyone can throw out questions, but that doesn’t mean they are reasonable questions. You’ll hav to dig MUCH deeper to frame what it is you mean before anyone can decide whether or not they can answer what you have in mind. If those questions are your best attempts then they’re simply not good enough.

1) Given that ‘real’ means ‘real’ - in the sense that ‘numbers are real’ - it is a pretty pointless question. I am conscious. What is ‘existent’ is ‘existent’ due to my conscious state. Once I am no longer ‘conscious’ (including sleep in this case) nothing ‘exists’ for me subjectively (not even the ‘me’).

I won’t go any further here or bother with the rest. I don’t see anything reasonable in your approach and I don’t find these ‘questions’ to be of any use other than to express confusion, become more confused, and to lead down several pointless branches of even more pointless questions.

You appear to be getting messier and messier. Take a step back and explain the obvious before missing several steps and ending up asking questions that only ‘appear’ to mean something - either you’re failing to express your questions fully or you’re thinking is too flimsy to see the gaping chasm you’ve ignored.

Chill, my dear. :wink:

There really is a reason to my rhyme. Time is a juggling act for me, hence my putting some questions out for 'contemplation', not necessarily expecting answers. Putting together thought puzzles is what I do in my writing. I'm really not trying to be difficult. Perhaps this will help....

A very genuine quest....

I need (want) to explain the differences between what mathematician Eric Temple Bell meant when he stated "the map is not the thing mapped", and when Alfred Korzybski (mis)-used Bell's epigram in his own book 'Science and Sanity' when he said "the map is not the territory". Eric Temple Bell's worldview was more realist, and Alfred Korzybski's worldview was more nominalist. Some people here would say that I am splitting hairs, but I seek clues to Scotus' and Peirce's thought dilemmas. The way that the questions above are interpreted might shine some light on some of the differences I am seeking. We DO find answers in differences. I have no doubt of that.

Once I can process understanding this, I can then re-word it in a way that the average person can understand.

I'm going to do some digging into these pages of Eric Temple Bell's book 'Nemurology'. I won't be back here for a while, but feel free to look through them too.

https://babel.hathitrust.org/cgi/pt/search?q1=map;id=uc1.b3527577;view=1up;seq=13;start=1;sz=10;page=search;orient=0

No, the only boundaries within a continuous medium are the artificial ones that we arbitrarily insert at finite intervals for some particular purpose, such as measurement. — aletheist

Infinitesimals are within a continuous medium, and they also require boundaries. Therefore they are artificial, according to what you say here.

On the contrary, according to his own words Peirce is an objective idealist for whom the principle of non-contradiction does not apply to that which is vague/indefinite and the principle of excluded middle does not apply to that which is general/continuous. In accordance with the latter, he is now recognized as the first person ever to develop truth tables for a rudimentary three-valued logic--true, false, and the limit between truth and falsity. — aletheist

Exactly as I said, Peirce allows for violation of the law of non-contradiction. Therefore he is dialetheist, and in my judgement, dialectical materialist. It is difficult to hold a "process" type metaphysics as Peirce does, without turning either to God or dialectical materialism for foundational support. Since Peirce allows for violation of non-contradiction his appeals to God are vacuous.

Again, hair-slitting. You either believe that Platonic Forms are real entities separate from God or not. Aristotle, Augustine, and Aquinas all thought not. Neo-Platonic Christianity and Christian Aristotelianism are not different. They just have a little different emphasis — Gregory

Are you sure about this? I wouldn't agree to that. Do you recognize that Aristotle identified two types of substance, primary and secondary? Substance has real existence, and also must have form. Yet there are two distinct types of substance, this is fundamental to dualism. If no forms are separate from God, then why are there two distinct types of substance? What creates that division?

God creates the division. Augustine and Aquinas explicitly say the forms are in God. The doctrine of Plato that the forms are separate from God are held by few Christians.

Augustine supported the forcing of the Donatists into the Catholic Church. Aquinas supported the Inquisition. Both very creepy people

On this page of Eric Temple Bell's book, he explains that a map (he's referring to mathematics here) is isomorphic, and not the real thing, as are the geometric relations of connections and betweeness.

https://babel.hathitrust.org/cgi/pt?id=uc1.b3527577

He goes on in the pages that follow about the cosmos, unified theory, Pythagoras, abstracting, idealizing reality, etc., and even discusses doubt and belief. Peircean?

What he then goes on to say about the second law of thermodynamics brings me back to the 'From Being to Becoming' of another of my favorite thinkers, Ilya Prigogine.

He also mentions Augustine.

Lots of help to be found for me here,
.. I think?

God creates the division. Augustine and Aquinas explicitly say the forms are in God. The doctrine of Plato that the forms are separate from God are held by few Christians. — Gregory

Aquinas clearly distinguishes independent Forms ( God's intellect, and angels) from those forms dependent on the human mind (abstractions).

Aquinas supported the Inquisition. — Gregory

I think you have your information mixed up. Aquinas was prior to the Inquisition.

Speaking of mathematicians/physicists named Bell, I recognize another oddity in the way that John Stewart Bell's (Bell's Theorem) is interpreted by nominalists.

"Some regard him as having demonstrated the failure of local realism (local hidden variables). Bell's own interpretation is that locality itself met its demise."
https://en.wikipedia.org/wiki/John_Stewart_Bell

Just another example of the merry-go-round going round and round between realists and nominalists, when they are both misguided. They will always glean what they can to fit into their perspective. There is no end in sight. Clearly, it is related to perspective (observer effect?, if you want to call it that), and how in reality we only recognize anything in relation to what it is not. When we look directly at it without the 'medium' of influences in order to differentiate it, it collapses. There is truly continuity in all things (synechism). Such is the insufficient nature of individual material or cognitive mapping of any sort. It is severely limited representation without the full spectrum of perspective. Gregory Bateson was known for his insistence that we should never go down any path of a singular line of thinking. Charles Peirce understood the importance of a 'community of inquirers'. What we have so prevalent in our world today due to those medieval misguided turns, is the slicing and dicing (nominalism) and the missing of a hugely important component (Cartesian dualism= diadic, versus what should be triadic), ultimately encouraging the idolization of the 'individual'. What will the future of humankind be if we do not recognize and teach the importance of dialoguing with different perspectives and the adhesion of community? <--- Rhetorical question.

Many people decipher Charles Peirce's agapasm to be an evangelical, religious, or devoutly spiritual perspective. They automatically associate it with the Christian concept of 'Agape' (originally Greek), sometimes implying that Peirce started with that concept, trying to 'fit' his logic, philosophy, and science into that box.

I understand it to be a purely logical conclusion, when factoring in semiosis, how biology strives 'toward', and recognizing that there is continuity in all things. The purest forms of creative love are revealed in the Unity of Opposites (Heraclitus). Think of the union of a man and a woman, resolutions of conflict, etc.. These things exist for a reason, and are a glimpse for us of the grand story.

Infinitesimals are within a continuous medium, and they also require boundaries. — Metaphysician Undercover

Are you just not paying attention? Infinitesimals do not have distinct boundaries, which is why the principle of excluded middle does not apply to them.

Exactly as I said, Peirce allows for violation of the law of non-contradiction. — Metaphysician Undercover

Are you just not paying attention? He held that the principle of contradiction (not the same as LNC) does not apply to that which is vague/indefinite.

Therefore he is dialetheist, and in my judgement, dialectical materialist. — Metaphysician Undercover

Are you just not paying attention? Your judgment is incorrect; Peirce vehemently rejected materialism, explicitly identifying his metaphysics as objective idealism.

Aquinas said heretics should be burned at the stake. He was hard core into torture. My middle name is named after him. I know all about that freak.

As for forms, your comments are all over the place. For Aquinas God has infinite form, angels are form, and humans are form and matter. When a human understands something, it's form enters the intellect. That's it. There is not much else to his philosophy on this. I have no idea where you are going with your posts on here

Yes, although before going any farther we need to establish what we mean in this context by "consciousness" and "real." — aletheist

Agreed.

I am not sure what that would even mean, but like anything else, I think that it can be explained/described mathematically--i.e., with a retroductive hypothesis that we can then deductively explicate and inductively evaluate. The subject matter of mathematics is much broader than just numbers. — aletheist

Agreed.

Again, we need to define "consciousness," and numbers are strictly hypothetical. Semiotics is a relatively recent science, so it clearly came last; but if you meant to say semeiosis, the real process that semiotics studies, then I am inclined to believe that it came first. — aletheist

Agreed.
I deliberately mixed up the terms 'semiotics' and 'semiosis' in order to point to the points you already made. It is a sad shame that 'semeiosis' was recognized centuries ago, but dismissed of its importance in the triad of human understanding until recently.

My current working hypothesis is that time is a manifestation of semeiosis, the ongoing evolution of the universe as dynamical objects determine sign tokens to determine dynamical interpretants. Linguistics is a special science that studies actual languages, while semiotics is a normative science that studies the nature of signs in general (speculative grammar), good vs. bad reasoning (logical critic), and methods for obtaining true beliefs (speculative rhetoric). — aletheist

Agreed.
'Semiotic causality' is receiving a LOT of attention in several fields of study. One of the reasons I am so fond of Mikhail Bakhtin is because he was a semiotician who also worked in linguistic studies. In the field of literary criticism, he always applied 'otherness' to the examination of semiotic causality in written works. I also found GEMS of thought in his 'Toward a Philosophy of the Act'.

To be clear to the readers, subjective idealism says the universe has no reality except in our minds. Objective idealism says we create the world and it's real. George Berkeley believed in the former, while Hegel, Royce, Peirce, and Giovanni Gentilies probably can be said to be objective idealists

Objective idealism says we create the world and it's real. George Berkeley believed in the former, while Hegel, Royce, Peirce, and Giovanni Gentilies probably can be said to be objective idealists — Gregory

That is painting with far too broad a brush. Peirce's objective idealism does not say that we create the world, it describes "the physical law as derived and special, the psychical law as primordial" such that "matter is effete mind, inveterate habits becoming physical laws" (CP 6.24-25; 1891).

Huh? Pierce says the world is mind right there

Peirce

It appears that your concept of mind is too narrow. "The world is mind" does not entail that "we create the world."

Physical laws being derived, habits becoming laws.. It sounds like splitting hairs again aletheist. Are you saying Peirce is a subjective idealism instead of an objective idealist?

I've been reading about Buddhist logic on Wikipedia just now. I guess we can say that the world is either real, not real, in-between, a combination of one of those three, or beyond all these four. Actually it seems to go infinitely in every direction, so it's hard to draw lines within which philosophers can fall. I see that. The same applies to God. There is pantheism, and also panentheism (where the world is inbetween emanation and creation, as with Leibniz's "fulgaration"). There can be a combination of both, there can be neither, or infinite inbetweens. HOWEVER, notwithstanding all that, if we stick to the simple definitions of "subjective idealism" and "objective idealism", maybe the full quotes from Peirce haven't been provided yet on this thread for us to know which side he was on