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- เผยแพร่เมื่อ 14 มิ.ย. 2024
- A non-technical introduction to platonism in the philosophy of mathematics.
Philosophy of mathematics is important, especially for philosophers interested in metaphysics. Suppose, for instance, you have nominalist tendencies, and you argue against the existence of abstract objects. Well, probably the most important kind of abstract objects are found in mathematics. Any serious nominalist needs to give an account of them.
Yet philosophy of mathematics is also, for obvious reasons, quite technical, and it can be pretty daunting for those who have less mathematical training. Nevertheless, I think the basic arguments can be made accessible to anyone who's interested, and that's what I've tried to do in this video.
For further reading on phil of mathematics, I recommend: "Thinking About Mathematics" by Stewart Shapiro and "Introducing Philosophy of Mathematics" by Michele Friend. These are both fairly orthodox introductions. For an introduction that focuses more on contemporary issues (it has just a few pages devoted to formalism, logicism, and intuitionism, yet a whole chapter on paraconsistent mathematics), I recommend "An Introduction to the Philosophy of Mathematics" by Mark Colyvan.
There is some debate about how exactly to formulate the Quine-Putnam Indispensability Argument. In this video, I've followed Colyvan (see his aforementioned "Introduction").
Re 43:26: I'm not sure why I said that. Obviously, Von Neumann did not hold the absurd belief that every ordinal is the ordinal before it; rather he believed that every ordinal is the set of all ordinals before it.
Re 1:01:18: I should have noted at this point that in her book "Realism in Mathematics", Maddy spends quite a bit of time answering objection (1).
Plenitudinous platonism is also known by the name "full-blooded platonism". Mark Balaguer's exposition of it can be found in "Platonism and Anti-Platonism in Mathematics". This book is also the source of the third objection to Maddy's views, about the difficulties of avoiding the aggregate theory of sets. The objection is explained in somewhat more detail there.
I said that I consider PP the most interesting form of platonism. This is not quite true. In my opinion, PP is not plenitudinous enough. The problem is that it allows only consistent theories. Those of us who are friends of paraconsistency will consider this an unwelcome restriction. Beall presents a more liberal form of PP in this short paper: homepages.uconn.edu/~jcb02005/...
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this is a phenomenal video, im obsessed with anything mathematics and having long videos like this narrated by a calm, professional voice that i can listen to before bed is so nice. you really have a talent for this!
@Kayson Isaiah thanks for the totally irrelevant comments, justice and kayson, aka mr "totally not the same person"
These may be the best philosophy vids on youtube.
Understandable without being simplistic, and well-presented.
You've been doing philosophy videos for 10+ years! What an extremely underrated channel.
Holy cow, this channel is a gold mine!
At 52:56 I am wondering why we're insisting that humans are not abstract or, more precisely, why we're insisting that humans are strictly physical. The whole premise of philosophy is that our minds can grasp spooky things like ideas, concepts, and mind-external relationships so that we may make hay of them - no different than gardeners grasping hoe handles. And if these ideas, concepts, and relationships are maintained within the physical architecture and chemistry of our brains, that would not seem to preclude or disqualify them from fulfilling a further purpose of providing insight into abstracta. Likewise with DNA, guiding the development of certain organisms that experience qualia and the subjective self - aspects that are nowhere to be found within the DNA itself. For me, the essence of quantity is number and the essence of discrete quantities are counting numbers. Those that wish to deny the reality (or existence) of numbers are like people walking in the sunshine, objecting to their own shadows. We can be tidy little monists with respect to a coin (a concrete object, an ontology, a theory of mind, a cosmological origin, etc.) without demanding that the coin be one-sided. I suspect that multiple-aspect properties are a primary reason why we have a reality to argue over in the first place. In mathematical terms, the universe is perhaps only permissible as a zero sum progression. You can't get something from nothing (0 ≠ ε), but both sides of 0 = ε - ε are identically nothing. The offsetting natures of ε and -ε must be born together or not at all. The reality of numbers (as the essence of quantity) and of equations (as the essence of behavior between quantities) explain Eugene Wigner's quandary over the alleged unreasonable effectiveness of mathematics. Within the furniture of the world, one finds mathematics as one among many abstract siblings born in tandem with the concrete. Finally, if abstract objects like numbers still seem to be unlikely citizens within reality, just take a closer look at concrete objects through the lens of particle physics and quantum mechanics!
Nice video! I am a total beginner in abstract math with no knowledge of philosophy, but I was glued to the video from beginning to end.
Great Lecture! this is the first lecture I watch on ur channel , it seems to be great channel ( u discuss Modal logic & Russel theory of description ! ) , so I want to thank you very much . Keep up this Great work!
It seems that the biggest problem with platonism is in determining what claims are made by platonism. It is an ironic reversal of how philosophy ought to be done. Rather than studying reality to discover whether it matches a position, we're forced to study a position to determine its content. So mathematical entities exist, but in what sense do they exist? What kind of existence do they have? There are many subtly different meanings to the word _exist._ Does Sherlock Holmes exist? He exists as a fictional character, but that's a different sort of existence than the existence of a real person.
When we say that a form "literally exists," what sort of existence is meant? It's easy to understand the meaning of saying that Sherlock Holmes literally exists, since that would simply mean that Sherlock Holmes is a real person who was the inspiration for the stories. In that way, the existence of a person is easy to understand, but the existence of a platonic form is very enigmatic. What difference would there be in the world depending on whether platonic forms exist or not? Merely saying that their existence is "literal" does nothing to clarify this concept.
The allegory of the cave does nothing to clarify the puzzle. The things that cast shadows in the cave obviously have the perfectly ordinary existence of ordinary objects, but that tells us nothing about the nature of the existence of platonic forms, since they surely cannot exist in the same way as material objects. What would it mean for us to be in a cave watching the shadows of numbers and colors on the wall? Platonism surely has something in mind for the source of those shadows, but words seem to fail to express the idea.
Platonism is more mysterious than the numbers it tries to explain. We all have a pretty good understanding of numbers, but understanding platonism is a far greater challenge. The question of whether platonism is true depends on whether platonism accurately describes the nature of numbers, and so first we must somehow discover what platonism is actually trying to claim about numbers.
Dear Kane B =)
Thank you for taking the time and effort to both upload and share this video with the youtube family =)
I hope you have a lovely day, Kane B! =)
Kind Regards
Raymond Lai
Many thanks for this quite useful introduction: two thoughts came to mind, especially in its discussion of Maddy's earlier (though ultimately, by her, repudiated) position. The one of these was the impression that the construal of mathematical entities as objects with which we can interact after a fashion with which those of conventional empricist bent can concilate themselves, that such a construal was perhaps advanced by Gottlieb Frege and Kurt Godel. This of course demands a revision to our understanding of perception, and here in a more radical way than perhaps Maddy herself suggested. Here it is interesting to note that in classical Indian philosophy the mind is classed as addtional Sense faculty along with sight, hearing, taste, smell and touch. The second thought which occurred was the possible avail of phenomenology to approach or address these questions. Here a revisting of Husserl might prove suggestive. Merleau-Ponty also might be helpful. I wonder what your thoughts are here?
Excellent contribution.
very useful and important ; thank you very much
this was really helpful, thank you!
This is immensely helpful
Very good video. I'm not sure that pleanitudness platonism solves the epistemological problem. Even if all possible mathematical objects exist, they still wouldn't interact with us, so we still wouldn't have any way of knowing THAT they exist in the first place.
THANK YOU FOR THE WONDERFUL INTRO! the link in the discription cannot open, could you tell me the title of the paper?
I may be misunderstanding here but it seems to have been implied that, for a plenitudinous platonist, truths are relative to their respective parts of the mathematical realm. Truths would have to be stated like so: "in the ZFC part, all vector spaces have a basis" or "in the ZF~C part, not all vector spaces have a basis" (without the "in"s, the statements would be contradictory). However, this makes PP seem not much different from deductivism other than having ontological commitments.
Thank you Sir.
Kane B Do a video on the philosophy of time please! Thanks
great lesson
Hi Kane, what do you think about the video made by Anticitizenx on this topic?
Thanks for the brief on Platonism. The Big Question remains, however : Is the Big Question outside of "our human minds" or not? At what point does subject interface with object on an atomic or even quantum theoretical basis? What are we, in totality? Thou art that? Or, what? Are there unknowns? How do we know, that? Let's get more info. before we speak with authority.
thanks for sharing Kane B
Regarding the Maddy justification or defense beginning about 54:00, it seems to be based on a poor analogy. If a perceive a group of objects, in what way am I perceiving the "set-ness" of the group? And if I look at a group of 12 stones laid out, how does the "12-ness" of them come to my perception? Psychology has suggested I can immediately grasp that 3 stones are a triplet but that I cannot immediately grasp or see the "12-ness" of 12 stones - I have to count them. And so how do I get the numbers so I can begin counting the 12?
Hi. I enjoyed this video. Do you have a video explaining structuralism?
1:11:53 "A standard platonist holds that ZFC and ZF~C cannot both be correct." Must a platonist choose between Euclidean and non-Euclidean geometry? Given Gödel's incompleteness theorem, doesn't geometry build up an infinity of incompatible sets of postulates corresponding to the infinity of undecidable propositions?
I am a mathematical platonist. I see the identification problem as an argument for using category theory instead of set theory as the foundation of mathematics. Yes, I'm a structuralist.
Being a Platonist in mathematics isn't what you think it means. It means accepting definite properties for uncountable sets of size continuum, which is incompatible with the concept of objective mathematical truth.
The link you provide to the short paper by Beall seems to be broken now
Excellent lecture. Tegmaark's argument for the ontilogical status of mathematics is quite strong.
Still struggling to see how confirmation holism entails that we should add numbers and so on to our ontology
Of course, all of you whom responded, as well as the poster (IM) understood what was actually meant by the term “entity”. Yes, no? Interesting to see how one modality of thought invisibly passes by as though all know exactly what was ... said.
It is unclear how a number, 20 for example is reducible to "The set whose member is the set whose member is the set whose member is the set..." Similarly for "20 is reducible to the set whose members are this set and this set and this set, etc." The formula that says the number 20 consists merely of the set of all sets with cardinality 20 makes some sense, although I don't see how the sets can be said to actually have cardinality 20 if the number 20 has not yet been "generated", as it were. This may be an epistemological problem, but there is a question of innateness of number ideas.
Kane, what is your personal opinión, are you a platonist?
Hey Kane,
I'm currently studying a course called advanced logic, but it's rather dry and abstract. It just seems like we are applying a bunch of rules for different logical systems, without thinking too much.
I have had a fascination with mathematical logic and I want to study Gödel's incompleteness theorems. What prerequisites do you think are required to understand what he postulated?
To understand Godel's incompleteness theorem all you need is to learn to program a computer. The proof of Godel's theorem is then transparent. This video is not good, it is all nonsense.
I'd recommend youtube channel Carneades.org and his 100 days of logic series. It's a brutal Cliff notes rendition of logic, but with a heavily philosophical perspective. If you take careful notes and stop (frequent pause buttons) to actively think about what is said in the videos (IE study), it is quite profound and in depth.
If you don't like Plato, try Plotinus and preferably Kant. Kant's a priori contains the numbers.
I decided I don't like Plato, but love silly putty.
@@QMPhilosophe similar?
The three levels of reality in Platonic Physics
Roger B Clough, National Institute of Standards and Technology (Retired)
(11-28-2014)
Abstract
Here we combine the top-down metaphysics of Plato and Leibniz with the inside-out categories of C S Peirce to enable us to view the world in a new, more useful light, simultaneously from two perspectives, and in more detail than Leibniz's pre-established harmony. The top down structuring from Plato and Leibniz allows us to view the world as it is: governed cybernetically by thought from the top singularity (the One, comparable to a computer processing unit), rather than from the ungoverned perspective of current science. This allows us not only to understand the world properly, but to structure the world cybernetically. with all creation, perception and control coming in the form of thought from the top down, but inside out using C S Peirce's three categories.
1. Introduction. While C S Peirce is well known to the philosophy of science, the worlds of Plato and his follower Leibniz have been less explored for such purposes. Plato was an Idealisti and Arthur Eddington spent much of his life adapting Plato to science, but his use of Mind in a world thoroughly established in materialism ihas largely blocked exploration of the use of Mind cybernetically, as a singular, mental control point, so that the current world of science is only governed, if at all, in fiefdoms. But more significantly, materialism and a lack of a single cybernetic control from top down has hindered the develepment of an understanding to consciousness, thought and the role and nature of the self. For example, Dennett in his explanation of consciences does not have a perceiver (or at best a fancifal and abstract invention of one). Moreover the perceiver, to obviate the homunculus with homunculus problem, must be on a higher ontological level, and which has to be a living singular entity, not an abstract reference. By application of Leibniz and Plato and common sense as well,, we see that the perceiver must be singular-- the One, the cybernetic Perceiver and control point, the central processing unit, to use a computer analogy.
The learning curve on Plato-Leibniz is a bit steep at first, foreign to most physical scientists because of their unfamiliar top down control, which is also done indirectly by thought rather than directly by physical interaction, but also because of Leibniz's unfamiliar spreadsheet style ontology, using not atoms but complete concepts called monads, which can be nested like sets. That would seem to render Leibniz more understandable to mathematicians and computer science, but his thinking in terms of substances and monads can be off-putting. Once these are understood (through his Monadology [ ]) and if one sticks to the elementary particles scale (the particles are both substance and monads) one can proceed fairly smoothly.
2. The three levels
Firstness -Mind- The One, the Monarch- this is the realm of Plato's Mind. It is life itself, pure nonphysical intelligence. Purely subjective, timeless and spaceless - with innate knowledge and a priori memory, containing the pre-established harmony, necessary logic, numbers - the womb of the WHAT. Mind creates all, perceives all, controls all. Thus the individual mind controls the brain, not the reverse. Mind plays the brain like a violin.
Secondness -- Mental objects so both subjective +objective- The Many. In this, the WHAT separates from Mind and becomes a HERE. Accordingly. Heidegger referred to existence as "dasein". "Being here."
According to Leibniz, all monads are alive to various degrees. There are of three gradations of life in these, according to Leibniz:
a) Bare, naked monads, which we can think of as purely physical ( Eg, a fundamental particle).
b) Animal and vegetative monads, which Leibniz calls souls, which can have feelings, but little intellect.
c) Spirits (corresponding to humans), which have, in addition, intellectual capacities. Mind transforms physical signals in nerves and neurons into experiences. If Mind then reperceives or reflects on these experiences, they are said to be thoughgt or apperceived. To be apperceived is to be made conscious. Thus consciousness is the product of thought. Intentions are also made in the same way, so that we caqn say that thoughts are intentions by Mind.
The human brain is a monad which contains as subsets, mental capacities. Neuroscience tells us that there is binding between monads for parts and functions of the brain, but since monads cannot act directly on each other, this binding must be indirect, through the sequential updates of the perceptions and appetites of the subfunction monads. These must be made by Mind, either directly or through the preestablished harmony PEH). Unfortunately the Stanford Leibniz site on Leibniz makes no mention of the action of Mind on the individual mind, IMHO a gross shortcoming.
Sensory signals and signals for feelings must also go through such a binding process. In a sense, the binding process plays the role of a self, but in conventional neuroscience self is a function of the brain, rather than the other way round, as common sense suggests and the intentionality of self or mind proves, along with the need for a PEH.
This shortcoming in conventional understanding of the brain becomes all the more nagging if we consider thinking, which is closely related to apperception, because it must be conscious.Thinking, we submit, consists of consciously manipulating and comparing such apperceptions.
Through Mind, with its potentially infinite wisdom and intelligence, intuitions and thoughts can arise spontaneously in the individual mind. If these are to be immediate and/or original, it is reasonable to believe that they originate in Mind, rather than indirectly through separate although bound parts of the brain. Anyone who has experienced a vocal duet in which the vibratos are in phase should become convinced of this.
Mind is the monarch of the intelligent mind, which controls the brain. Mind plays the brain like a violin. Mind is also is able to focus on a thought for a brief period, within the context of one's memory and universal memory, for purposes of thinking an comparison, making the biological brain and its complex bindings seem hopelessly indirect and subject to confusion.
Thirdness - Corresponding physical objects as is appropriate- -here the object is born or emittted from the monad--and emerges into spacetime as a particle, becoming completely objective, a WHAT+ HERE +WHEN., In addition the Thirdness of a private thought or experience is its public expression in some appropriate form.
3. Conclusions
This format allows us to examine quantum phenomena from inside out and perception, thinking and consciousness ontologically- from physical nerve signals to mental experiences such as thought, consciousness, and cognition. It also avoids problem encountered in “bottom-up” science, such as complexity and emergence, if for no other reason than there is no apparent way of conceiving of a singular control point at the bottom.
--
Dr. Roger B Clough NIST (retired, 2000).
See my Leibniz site: rclough@verizon.academia.edu/RogerClough
For personal messages use rclough@verizon.net
Bizarre.
I think Penelope Maddy's "seeing vs. perceiving" theory might actually be more accurate and more immune to the criticisms brought up by this video than at first glance. The objections that perception of the physical world would only give a stunted version of set theory are true to an extent, but this criticism fails when we consider how people actually learn mathematics. How DO people learn mathematics? They acquire the reasoning through a combination of the genetic composition of their brain and by their physical environment. As in, books with ink symbols in them, chalkboard drawings and symbols, audio explanations, et cetera. The physical actions of books and other mathematics teachers imbue perception of the mathematical concept. They are transmitted as patterns in the neurons of one set of humans (those who already know the mathematics) into physical objects (a chalkboard, book, lecture video, verbal explanation, et cetera) to affect a perception change in the person learning.
The "set of six things" is present in a half-dozen package of eggs. So where is the "natural numbers" if we can never see an analogous collection of a countably infinite sequence of things? The answer is that the concept is physically manifested as a patterning in the neurons of humans, who can then relay the pattern into the neurons of another brain by using physical objects (the ink in a textbook, the pixels on a screen in a math website or video, the chalk on a chalkboard, the audio of a lecture) that use patterned symbols, initially by analogy to how finite sets behave directly, that leads to increasing refinement of the perception (very rough in toddlers learning to count, extremely advanced for somebody like JP Serre).
A symbol or set of symbols drawn on a chalkboard is literally a physical thing, and can be seen as an advanced technology that is able to inculcate perception with extreme efficiency. Just because they don't "directly" represent the idea (such as the natural numbers being an infinite number of eggs or something) does not necessarily mean that the form isn't being manifest. Many empirical tools are extremely indirect, based off circuit amplifications of minute patterns that are then interpreted as certain physical phenomena. For example, reading a chemical spectrum is arguably very abstract, but still contains the form of at least some property of a concrete physical phenomenon.
Platonism with that idea of the "realm of forms" reminds me a lot of string theory.
What is the foundation of "platonism " since it is not "Platonism " ?
You mean what metaphilosophy is it grounded in? Most commonly it is embedded in naturalism (rejection of first philosophy, defer to science for what commitments, projects, or programs we should persue)
exactly i create the entities with the math just by dreaming it up and then i find it real in the numbers it amazing I have done it many times and i have the proof ready for anyone to see in seconds but no one will ask very strange.
Mark Moody go ahead, reveal your proof of... whatever the fuck you just claimed.
Nice video :)
45:52 Actually for both Von Neumann and Zermelo ordinals it is true that ' 2 ∈ 3 ' , so that is a bad example to make Paul Benacerraf's point.
A better example is to inquire about 1∈ 3. Let us review the ordinal definition schemes.
Von Neumann ordinal definition:
0 = Ø , 1 = { 0 } , 2 = { 0, 1 } , 3 = { 0, 1 , 2 } , or in general n = { 0,1, 2 ... n-1} .
Zermelo ordinal definition:
0 = Ø , 1 = { 0 } , 2 = { 1 }, 3 = { 2 } , or in general n = { n - 1 } .
Clearly 2 ∈ 3 is true in both VN and Zerm ordinals, but what about 1 ∈ 3?
It is true in VN ordinals, but false in Zerm ordinals. So paul's point does stick, sort of.
Is this a contradiction? No, we just have two different but consistent ways to define numbers, VN numbers and Zerm numbers.
But if you are asking about the ontological status of numbers, and if we reduce numbers fundamentally to sets, then yes something is wrong here.
I believe that Russel does show in Principia to show that 1 + 1 = 2, so may
Question:
Lets assume numbers are ontologically real. If numbers are abstract, necessarily true dependent of our minds, and are immaterial then doesnt there need to be an immaterial/necessary intellect to abstract these numbers? Our minds are not necessary, and therefore numbers do not depend on them. But all abstractions are dependent on a mind. Therefore if numbers are necessarily true, then there must be a necessary intellect abstracting them.
Does that follow?
If the numbers are necessarily true, it follows that statements about numbers are objectively true. This is because necessity implies independency. Otherwise we could only talk about possible existence. Now suppose that there must be a necessary intellect abstracting them. But then arithmetic would become dependent on the mind. A contradiction. Hence, if the numbers are necessarily true, existence of an abstracting mind is not necessary.
If numbers are true and objectively real, how do they subsist? Are they just sort of "out there" as platonic entities in your opinion?
Yes, so if numbers are objectively real, it must be that they independently exist in an eternal platonic universe. That is to say that they don't need another entity for their existence. Now mind is just a sufficient tool to discover them but not necessary, it seems to me.
I agree with palindrome06's argument about numbers being true independent of ourselves, but I don't necessarily agree that numbers are objectively real. I highly recommend you refer to Karl Popper's paper: "Epistemology Without a Knowing Subject." Math is a conceptual tool just as language is. It's not exactly right to say numbers are objectively real, but rather that they are abstractions of things that are objectively real. Math is an extremely useful way for us to understand the way the world works, just as language is a useful way for us to discuss theories and ideas, but it is nonetheless a conceptual tool.
So for you (and Popper) numbers are not necessary for any possible universe but merely are something unique to mankind?
So "anything goes"? This makes mathematics a technical approach. Freedom, but loss of "remembrance of the soal". This development seems a bureaucratic turn. Or is - the other way round - the remembrance of the soal equally valid as a technical approach, if we claim technique is godgiven?
Difference between {{∅}} and ||∅|| is obvious; {{∅}} is Darth Vader, ||∅|| is an NPC Imperial Pilot, in their respective TIE fighter.
penelope is correct i have to the connection and i can and o communicate with the entries via the numbers i finally know what the hell is going on.
I have your set theory already made it explains the entire universe every galaxy and the multiverse. I had no idea what a set theory was when i made it now I see its set. your so convinced (even though you have no rationtional reason the think this), that i'm insane and will refuse to look at a number.Just look and in seconds you would see what it was. But You wont do that. Don't you think that is strange?
I'm sorry, but Bernaceraf's Epistemological Problem is a shockingly bad argument. That humans are _wholly_ not abstract is not at all obvious to me (nor is the opposite obvious to me); that "non-abstract" objects cannot interact with "abstract" objects isn't obvious to me; that the relevant connection we have to objects of knowledge must be some kind of mechanistic connection or isn't obvious to me. It seems to be based on a lot of assumptions which we're expected to accept because they're kind of intuitive or something.
The argument against set theoretic Platonism (for sets larger than the continuum) is Cohen forcing. This argument is airtight, rigorous, and conclusive.
What is Justice?
If none have never seen Justice, only the approximation of Justice through amendable positive laws, why do we think Justice is real?
Why do we fight for Justice?
Plato is trying to tell you that:
Seeing (empirical function) is to believing, as the intellect is to understanding (rational function).
That means we cannot understand understanding which is the intellect itself.
The intellect, is called consciousness, logos, soul, mind, rational and other words that mean consciousness itself.
Justice and consciousness come from the same place, that is, where the Forms are.
How do we know? Well, im conscious. Also, I have never seen true complete Justice, no one has the true, perfect, absolute form of Justice.
We only can dialogue about the spirit of the law that will bring us Justice on earth.
The three cybernetic levels of reality in platonic physics
Firstness- Mind- The One, the Monarch- this is the realm of Plato's Mind. Purely subjective, timeless and spaceless -
with innate knowledge and a priori memory, containing the pre-established harmony, necessary logic, numbers -
the womb of the WHAT. Mind creates all, perceives all, controls all. Thus the individual mind controls the brain,
not the reverse. Mind plays the brain like a violin.
Secondness -- Mental objects so both subjective +objective- The Many. In this, the WHAT separates from
Mind and becomes a HERE. Accordingly. Heidegger referred to existence as "dasein". "Being here."
According to Leibniz, all monads are alive to various degrees. There are of three gradations of life in these,
according to Leibniz:
a) Bare, naked monads, which we can think of as purely physical ( Eg, a fundamental particle).
b) Animal and vegetative monads, which Leibniz calls souls, which can have feelings, but little intellect.
c) Spirits (corresponding to humans), which have, in addition, intellectual capacities. The human brain
is a monad which contains as subsets, mental capacities. Neuroscience tells us that there is binding between
monads for parts and functions of the brain, but since monads cannot act directly on each other,
this binding must be indirect, through the sequential updates of the perceptions and appetites of
the subfunction monads. These must be made by Mind, either directly or through the preestablished
harmony PEH). Unfortunately the Stanford Leibniz site on Leibniz makes no mention of the action of
Mind on the individual mind, IMHO a gross shortcoming.
Sensory signals and signals for feelings must also go through such a binding process. In a sense, the
binding process plays the role of a self, but in conventional neuroscience self is a function of
the brain, rather than the other way round, as common sense suggests and the intentionality of
self or mind proves, along with the need for a PEH.
This shortcoming in conventional understanding of the brain becomes all the more nagging if we
consider thinking, which is closely related to apperception, because it must be conscious.
Thinking, we submit, consists of consciously manipulating and comparing such apperceptions.
Through Mind, with its potentially infinite wisdom and intelligence, intuitions and thoughts can arise
spontaneously in the individual mind. If these are to be immediate and/or original, it is reasonable
to believe that they originate in Mind, rather than indirectly through separate although bound parts
of the brain. Anyone who has experienced a vocal duet in which the vibratos are in phase should become
convinced of this.
Mind is the monarch of the intelligent mind, which controls the brain. Mind plays the brain like a violin.
Mind is also is able to focus on a thought for a brief period, within the context of one's memory and universal memory,
for purposes of thinking an comparison, making the biological brain and its complex bindings seem hopelessly
indirect and subject to confusion.
Thirdness - Corresponding physical objects as is appropriate- -here the object is born or emittted
from the monad--and emerges into spacetime as a particle, becoming completely objective,
a WHAT+ HERE +WHEN., In addition the Thirdness of a private thought or experience is its
public expression in some appropriate form.
--
Dr. Roger B Clough NIST (retired, 2000).
See my Leibniz site: rclough@verizon.academia.edu/RogerClough
For personal messages use rclough@verizon.net
Thank you for that work out. What Here When: ain't it da troot? Actually Samuel Beckett has a famous theatre piece performed by one woman, whose lips moving though the words to the audience is the only physical object the audience is the only entity that can be discerned. It's called "Rockabye," and its effect is uncanny. The woman repeats the refrain in a building shout: what... Here...NOW!!! Classic Beckett. Classic Leibniz? Go figure.
It is highly irritating, presumptive, and totally arrogant to assume that no one accepts Plato's theory of forms. More likely what the lecturer means is that no cloistered group of detached academics who are firmly committed to atheism, materialism and post modernist thought believe in Plato's theory of forms. The problem with being a member of academia is that one has to keep dismissing the truths of the past and developing new hypothesis or theories, or actually fantasies , in order to get "published" and accepted. Just my opinion. I gave the video a like, because I believe this lecturer has a right to his opinion as well, and does express himself in a skilful manner.
Our generation has blurred the fine line between skepticism and ignorance. "Scientists" are ignorant nowadays. If we actually had physicists looking into stuff based on the Bible and Plato; we might have actually discovered a lot more by now.
The problem is that Plato is describing the structural features of consciousness, which is something we inherited as a survival mechanism by way of natural selection. Higher symbolic reasoning is derivative of our perception of space, and so we understanding qualitative differences in terms of spacial metaphor. If that's the case then the relationship of geometry to sociology, ethics, or politics becomes obvious if people can only think in geometric metaphor which they inherit through evolutionary psychology.
Plato is describing what are basically modern ideas but with an ancient Greek vernacular. And so hack academics and poor scholars assume he is talking about something supernatural when he says "the soul," when in reality he is talking about the form of the human psyche which experiences consciousness. It would be no more supernatural than the form of black or the form of a table.
I actually think Plato's theory of the form accurately describes human reality and the relationship between reality and abstraction. It's really true that all of western philosophy consists of foot notes to Plato, as Whitehead said. Plato's ideas are more relevant than ever and I think we're finally getting to a point where we can understand them again. We're still like medieval scholastics misunderstanding the literature of a more sophisticated civilization and philosophical discourse.
"...the form of the human psyche which experiences consciousness." excellent definition of the soul. I guess you and I just disagree on what is meant by "supernatural".
Chuck Sampson You :"voiced"my thoughts entirely. The aether theory and Decartes are what I defend although it is difficult to explain that by changing terms and names they've had to come up with dark matter to replace the original Greek philosophical idea that "something" fills space. Yes, they disproved one aspect of the theory through Einstein and that group of physicists, but that was only a part of the idea. For a long while after they convinced everybody space was a vacuum and now they've got to fill it because they've found more missing matter than they can see. So, as far as I am concerned, that is the aether and Descartes' ideas should be noticed more. But, as you say, they change the names and come up with "black hole" for vortex and "dark matter" for aether. All science is built on previous discoveries and there is nothing wrong in acknowledging their predecessors, or any reason because of that to not earn a Nobel because something was theorized long ago--they are just expanding and proving and adding onto them.
@@chuckjlsthat's called the mind and also their are a multitude of definitions of the soul
Who told You that we are physical objects? Intuition or what?
There are a lot of Platonists and platonists today.
Plotinus.
Math is deductive, yet I do not understand how Math is connected with Logic.
Logic, like mathematics, depends on concepts. Logical phrases can be given in many different languages, and humans can understand those logical phrases. There is a universality of logic similar to the universal nature of mathematics, which goes beyond mere languages such as "English" or "German." There are concepts behind the words, which give meaning to letters. Mathematical concepts are placed onto numbers ( 1 vs the roman numeral "I") and similarly logical concepts are placed onto language but are not the languages themselves. So the symbol "1" is not actually the concept of "One" but it is merely an expression. Logic works the same way, there is a universal way of reasoning expressed through symbols on a computer screen/ paper.
They are both formal systems, also math uses logical deduction, so logic is a subfield of math
@@5hape5hift3r The other way around. Math is a theory inside logic.
@@orlandomoreno6168 math generaly builds uppon logic
so math is a generalization of logic
So logic is a subfield of math
Technically math is a theory and logic is a theory
but one builds uppon the other
mathematical equations are also called arithmetic propositions and can be analyzed similarly to the ways in which a logician analyzes non-arithmetic propositions
Hopefully I can deduce some points about the philosophy of mathematics from the posting below. Mathematicians seem to think that numbers or calculations are causative, That seems to be the belief behind computibilism, if I remember the name properly. Indeed, Stephen Hawkings recently said that there was no need for God, the universe was created by the laws of physics. This is absurd,tantamount to a belief in magical incantations, because laws are simply descriptions of reality, not creators of reality. They have no power or force to do anything even if they had some intelligence.
My own understanding is that numbers almost seem to have magical properties, I am always astounded at the results of number theory.. But numbers are similar to words, except that they do seem to demonstrate such tricks. So they are special
words, which brings me around to Leibniz's search for a language of computing or logic, in which all issues could be simply
simply answered with that logical language. Numbers seem to have such powers, but I am too stupid to go forward with the idea.
God luck on your searches.
Dr. Roger B Clough NIST (retired, 2000).
See my Leibniz site: rclough@verizon.academia.edu/RogerClough
For personal messages use rclough@verizon.net
--
Roger Clough
That is so extremely simplistic it seems doubtful that you have even cursory knowledge of any of the professional literature on the subject.
Even Hawking himself addresses that very objection so it is obvious that you haven't even read his work, so stop trying to sound like you know what you're talking about - you don't.
That's a pointless assumption that all actions and movements come from agents. The difference between an agent and a mechanism is only of perspective, it doesn't matter if an object falls by mechanism of the universe or if tiny dwarfs drag it down as long as you can correspond both theories and they describe the same. A circle is the same curve wether we use the parametric equation (sin t, cos t) perspective or the euclidean distance x^2+y^2=r^2 perspective. An animal works the same way wether it's a mechanical brain moving a body or some sort of agent making decisions based on a strategy.
There is no reason to look for the ultimate mentalistic agent behind everything. It wouln't really be inconsistent with a mechanistic materialistic system view of everything.
why you have have half the subscribers you deserve
That embarrassing Platonic strain in western metaphysics
Since materialism, or bottom-up causation, dominates current western science and philosophy,
any mention of Platonism, or top-down causation, in which Mind is the sole active agent creating
and controlling reality, is treated as blasphemy or superstitious anathema. It has been so at least
since the Enlightenment, which quite successfully replaced superstitious religious ideas, such as
mind and spirit, with atheistic reason.
Yet the universe must necessarily be governed, as it appears to be, only by a single governing agent
if universal order, such as is found in thermodynamics (constancy of energy) , is to be maintained. Plato
called this creator and regulator the One, which reaches out cybernetically to control the Many.
Leibniz called this the pre-established order. Kant invoked the idea of the necessary importance of mind,
at least on the human level, in his man-centered metaphysics, for us to make sense of what we observe
by sorting sensory information into his mental Categories. Even Aristotle, no friend of Plato, had to make
the human mind or soul the local regulator of controller, although like Dennett, who seems to be a
follower of Aristotle in this sense, Aristotle's bottom-up philosophy had painted him into a corner,
since mind is necessarily top-down. Thus Aristotle had to claim that mind actually does not sort,
but in some sense, becomes, what it observes. Even Aquinas had trouble with that one.
Similarly In science, the world is controlled bottom-up in Aristotelian fashion, which is a puzzle, since
there is no intelligent bottom. And even Einstein was disturbed to think that there could be "spooky action at
a distance" (which in fact is an inherent property of thermodynamics if constancy of energy is to be maintained)..
More recently Stephen Hawkings, otherwise perhaps the most brilliant scienstist of all time, dismissed
the idea of a Creator God as being uneccessary since the universe was created by its laws. This
makes no more sense than saying that highway speed laws will keep vehicles from speeding.
I could go on, but either you get my point that the universe cannot be one of bottom-up causation,
but must be ruled by universal top-down causation, or not. I hope you can see the light
that only top-don causation (Platonism) is possible.
--
Dr. Roger B Clough NIST (retired, 2000).
See my Leibniz site: rclough@verizon.academia.edu/RogerClough
For personal messages use rclough@verizon.net
A bit late for a response, but thanks for explaining Platonism so well. I've been trying to explain these things for a while, but yours was very clear and well supported
"This makes no more sense than saying that highway speed laws will keep vehicles from speeding." The correct interpretation is actually similar to the vehicles being unable to speed by their very own nature.
- mathematics is what's left after the universe is gone -
If you are a mathematical platonist, mathematics and some logic are the only things that will exist (exist in the ontological sense) after the universe is long gone and no longer exists. If you are a mathematical constructivist there is no maths or logic left after the universe is gone, because mathematics is dependent on human minds.
Under this formulation, if you define _universe_ as 'everything that exists', then, trivially, mathematical realism is false. So 'universe' has to be defined carefully for this disagreement to even make sense.
It seems like the disagreement between mathematical realists and mathematical constructivists would be like the difference between watching a cartoon versus watching the cartoonist draw the animations and asking where the cartoonist got the idea or inspiration for his cartoons. For the observer, no practical difference exists. Even if mathematical realism is false, it is a useful fiction because to think about someone's idea, that idea has to have some kind of ontological existence, even though temporary - it is always callable at a moments notice.
Mathematics as a level of reality (Secondness) in platonic physics
The three levels of reality in platonic physics are given below.
Mathematics, like ideas in general -- that is to say, mental objects-- is a form of Secondness,
which in turn is an object of Mind or Firstness. Mind is the timeless, spaceless central
domain of Plato's metaphysics, containing a priori certainties such as necessary logic,
arithmetic and numbers, as well as Leibniz's pre-established harmony. It does all of the
thinking, controlling and perceiving of the universe. Nothing is done without it
and its control is cybernetic.
Mathematics, as Secondness, is simply a mental object nlike monads are, but
it is not monadic in that it has no correponding physical bodies. Insterad, it is a
special language with a special grammar, in particular arithmetic and logic, but on its
own can do nothing, create nothing, or achieve anything anymore than a human
can using mathematics as a tool of thought. Or Shakespeare could with the english language.
This is in line, if we consider mathematics as a language, with the idea of computationalism
en.wikipedia.org/wiki/Computational_theory_of_mind
" In philosophy, a computational theory of mind names a view that the human mind or the human brain (or both)
is an information processing system and that thinking is a form of computing."
which unfortunately has been construed by some to give anthropomorphic or god-like powers to mathematics.
The universe was not constructed by mathematics alone, as it is mental, not physical.
While this passivity may seem to some to diminish the power of mathematics, it in fact frees it from
the limitations of the outer world, such as the limitations of Leibniz's pre-established harmony,
and limits it only to its inherent logic and arithmetical constraints. This is particularly useful in
abstract mathematics.
In addition, due to what has been referred to as "the unreasonable effectiveness" of mathematics
in the world, it appears that mathematics is predominantly the language of the pre-established harmony
of Leibniz.
In addition, all of Plato's philosophy of mathematics should hold.
plato.stanford.edu/entries/platonism-mathematics/
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The three levels of reality in platonic physics
FIRSTNESS -FIRST PERSON (I) -Mind- The One, the Monarch- this is the realm of Plato's Mind. It is life itself, pure nonphysical intelligence. Purely subjective, timeless and spaceless - with innate knowledge and a priori memory, containing the pre-established harmony, necessary logic, numbers - the womb of the WHAT. Mind creates all, perceives all, controls all. Thus the individual mind controls the brain, not the reverse. Mind plays the brain like a violin.
SECONDNESS - SECOND PERSON (YOU RIGHT HERE) ental objects so both subjective +objective- The Many. In this, the WHAT separates from Mind and becomes a HERE. Accordingly. Heidegger referred to existence as "dasein". "Being here." Some of these objects, such as ideas, or mathematics, are not monads, since they have no corresponding physical bodies.
According to Leibniz, all monads are alive to various degrees. There are of three gradations of life in these, according to Leibniz:
a) Bare, naked monads, which we can think of as purely physical ( Eg, a fundamental particle).
b) Animal and vegetative monads, which Leibniz calls souls, which can have feelings, but little intellect.
c) Spirits (corresponding to humans), which have, in addition, intellectual capacities. Mind transforms physical signals in nerves and neurons into experiences. If Mind then reperceives or reflects on these experiences, they are said to be thoughgt or apperceived. To be apperceived is to be made conscious. Thus consciousness is the product of thought. Intentions are also made in the same way, so that we caqn say that thoughts are intentions by Mind.
The human brain is a monad which contains as subsets, mental capacities. Neuroscience tells us that there is binding between monads for parts and functions of the brain, but since monads cannot act directly on each other, this binding must be indirect, through the sequential updates of the perceptions and appetites of the subfunction monads. These must be made by Mind, either directly or through the preestablished harmony PEH). Unfortunately the Stanford Leibniz site on Leibniz makes no mention of the action of Mind on the individual mind, IMHO a gross shortcoming.
Sensory signals and signals for feelings must also go through such a binding process. In a sense, the binding process plays the role of a self, but in conventional neuroscience self is a function of the brain, rather than the other way round, as common sense suggests and the intentionality of self or mind proves, along with the need for a PEH.
This shortcoming in conventional understanding of the brain becomes all the more nagging if we consider thinking, which is closely related to apperception, because it must be conscious.Thinking, we submit, consists of consciously manipulating and comparing such apperceptions.
Through Mind, with its potentially infinite wisdom and intelligence, intuitions and thoughts can arise spontaneously in the individual mind. If these are to be immediate and/or original, it is reasonable to believe that they originate in Mind, rather than indirectly through separate although bound parts of the brain. Anyone who has experienced a vocal duet in which the vibratos are in phase should become convinced of this.
Mind is the monarch of the intelligent mind, which controls the brain. Mind plays the brain like a violin. Mind is also is able to focus on a thought for a brief period, within the context of one's memory and universal memory, for purposes of thinking an comparison, making the biological brain and its complex bindings seem hopelessly indirect and subject to confusion.
THIRDNESS - THIRD PERSON (IT OVER THERE) Corresponding physical objects as is appropriate- -here the object is born or emittted from the monad--and emerges into spacetime as a particle, becoming completely objective, a WHAT+ HERE +WHEN., In addition the Thirdness of a private thought or experience is its public expression in some appropriate form.
3. Conclusions
This format allows us to examine quantum phenomena from inside out and perception, thinking and consciousness ontologically- from physical nerve signals to mental experiences such as thought, consciousness, and cognition. It also avoids problem encountered in “bottom-up” science, such as complexity and emergence, if for no other reason than there is no apparent way of conceiving of a singular control point at the bottom.
--
Dr. Roger B Clough NIST (retired, 2000).
See my Leibniz site: rclough@verizon.academia.edu/RogerClough
For personal messages use rclough@verizon.net
I don't think Benacerraf is correct.
Humans are not abstract.
Mathematical entities are abstract.
Therefore, souls exist :)
PS: I don't personally endorse this line of argument, but I'm not moved by the epistemological argument against platonism either.
Roses are red
Violets are blue
Therefore, pineapple doesn't go on pizza
But I'll eat it anyway
Kane,
The terminological alternative to the pejorative 'Mathematical platonism' is "Mathematical Fictionalism". It is very, very difficult to find mathematicians outside of a few department chairs who do not practice mathematical platonism. Most treat it as fictionalism. And I think even the best authors on the subject cannot reduce (as I do) mathematics to Scientific Realism.
We might be able to reduce all of christianity to the ritualistic indoctrination of the extension of kinship love to non kin. The rest is nonsense. The same with mathematics. One to one correspondence and positional names and all of mathematics (measurement) results from that combination of pairing off (one to one correspondence) and positional naming, and adding and subtracting positions. It's that simple. Math is that simple, and Christianity is that simple. Why do disciplines (Theology and Mathematics) preserve Fictionalisms?
You can't say platonism is not founded in Platonism and then refer to Platonism. The pythagorean anti-metaphysical view is illogical. It is a religion with a bias against explicit metaphysical belief at the root of the West. This therefore irrational philosophically .
It might come historically from it but the views have become very different, the same way math and science come from philosophy but are completely different.
I’m so tired of brute fact claims that all possible *insert noun here* exist.
Intuitionists won't talk about TRANSFINITE NUMBERS? What an incredibly stupid thing to say.
What in side us is out side us.remember all things are numbers .and latter ,and all things are made up of add an even ,it is funny how you speaking in number .black is black ,but there are many shade of black ,but it is still black 🧩
Boring.