• Zuhair
    132
    When one for example define a formal theory like ZFC, or even a formal theory of arithmetic, now such theories has infinitely many strings of symbols, that serve as its axioms, theorems etc.. Now proofs can be understood as collections of those strings that are closed under inference rules, and even those rules are also expressed by stings of symbols. Now the whole machinery is assumed to go on infinitely.

    My question is from where we bring the necessary ink to write down all of these symbols?

    If we are defining a formal system then we must be assuming that it can be written in some realm. Otherwise it makes no sense to speak about writing down something that cannot be written.

    I'm of course not speaking about pieces of mathematics that can be written by an actual computer, I'm speaking about theories of theoretic mathematics that has an infinite output. The physical world doesn't have an infinite supply of material. So are we presupposing platonism here? That is, a hypothetical world where all the symbols and sentences of a formal theory or actually of a formal langauge can be written. A world that can provide such unlimited supply of ink?

    If we don't want to make that pre-supposition, then how we can account for speaking about such theories and carrying inferences in them, if there is no world in which their symbols are guaranteed to be written? It appears to me that without that pre-supposition we don't really have a formal theory.

    If that is pre-supposed then a formal theory must start with that hypothetical stipulation of such a world. Like for example in saying:

    IF there exists a world in which we can write down all sentences of the language of arithmetic and any set of those sentences (theories), then in that world we write the following .. and we state our axioms, inference rules, provability criteria, etc...

    This explicit statement would make mathematics clearly based on the Platonism thesis, since without it there is no guarantee for any of its inferences to be carried out.
  • Gregory
    2k
    Platonic forms exist in our minds, not outside
  • Pfhorrest
    3.6k
    Mathematical objects are all hypothetical objects, and the inferences about them are all hypothetical.

    When we lay out some axioms, we're basically saying something like "Suppose there was a thing, let's call it a 'set', and it had these properties and behaved this way." Then we make inferences about what would be true of that hypothetical "set" object if it existed and had those properties / behaved that way. Likewise with "numbers", "triangles", etc: suppose there were these kinds of things and they were like this... what else would have to be true of them?

    It doesn't matter if no such things are actually instantiated in the real world that we observe, since it's all hypothetical to begin with.

    But if you're a certain kind of modal realist, like me, then all these hypotheticals necessarily do exist, in their own possible worlds of sorts, and our concrete world is just the mathematical structure of which we are a part.
  • Asif
    241
    @Gregory If people actually understood that ideas are in our minds then "philosophy" and science might actually progress.
    What mischief Plato and platonism has caused!!!
  • tim wood
    5.6k
    What mischief Plato and platonism has caused!!!Asif
    For clearest thinking, imo it's worth noting that Plato's platonism functioned as the solution to a bunch of problems Plato had, mainly consequent to the Greek view of nature as lacking any precision. The mischief comes later, after, at the hands of people either who did not understand Plato's original project, or had agendas of their own.

    The history of Greek thinking, represented in broadest terms by Pythagoras, Plato, and Aristotle, understood even generally, clarifies and can make sense of a subsequent history of thinking that can otherwise seem in places opaque and unaccountable.
  • Asif
    241
    @tim wood Platos agenda was a totalitarian project and specifically designed for a political elite of "philosopher kings" Aka priests. The mischief was always there and used as a springboard and propaganda for later thinkers and elites to bolster their opium for the masses and justify their methods of oligarchy.
    Which subsequent thinking are you referring to?
  • tim wood
    5.6k
    Platonic forms exist in our minds, not outsideGregory
    But if you're a certain kind of modal realist, like me, then all these hypotheticals necessarily do exist, in their own possible worlds of sorts,Pfhorrest
    And this a species of Realism v. Nominalism. In my view, resolved in the recognition and acknowledgement of collective wisdom, Mind, as both passive and active, as reasoning and passionate, as artist and judge - and so forth. But with the corollary that for there to be Mind, there must be minds. No minds, no Mind.

    One might argue that life is an inevitable consequence of matter, under appropriate conditions, and therefore brains, and eventually minds and Mind.
  • Pfhorrest
    3.6k
    And this a species of Realism v. Nominalism.tim wood

    Just to note, I am definitely not a Realist about abstract objects in the usual sense (a Platonist), and feel much more sympathy for nominalism among the two usual options.

    My view is a third way, wherein there isn’t some realm of abstract forms wholly separate from the concrete realm, or just the concrete realm with no abstract, but rather everything is fundamentally of the same nature as the abstract, and “concrete” is just indexical: the abstract object we’re a part of. Every other abstract object is also concrete, relative to anything that’s a part of it.
  • tim wood
    5.6k
    I think that if everything looks pink to you, or any other color, you should check your lenses and ambient light sources. Imo yours is a highly colored interpretive view, even Procrustean.

    First step is remembering that you are not, nor I, in oh so many ways, his audience. As a practical matter, then, one approaches Plato while mindful as best one can be of distances and barriers. You get, eventually, more or less, Plato. What you make of it, is what you make of it, but the making makes the made not-Plato.
  • tim wood
    5.6k
    but rather everything is fundamentally of the same nature as the abstract, and “concrete” is just indexing: the abstract object we’re a part of. Every other abstract object is also concrete, relative to anything that’s a part of it.Pfhorrest

    I'm thinking the only place this - I have to think somewhat poetically described - structure/being can be is collective wisdom/MInd, comprised of minds and their activities. Do you buy this or have you another reasonable alternative?

    Mind being the cognitive "plastic-man" that can stretch as needed, accommodate as needed, store as needed.
  • Asif
    241
    @tim wood I know what I have read. I understand platos mindset and what his project was and how its now used.
    Your method of interpretation is yours mine is mine.
    I do find it amusing you defending plato and making assumptions that you understand him and others need your help in doing so.
    I dont need lenses!
  • tim wood
    5.6k
    Your method of interpretation is yours mine is mine.
    I do find it amusing you defending plato and making assumptions that you understand him and others need your help in doing so.
    I dont need lenses!
    Asif

    It would be nice if you put your mind in gear, or checked your direction before setting out. In finding "it" amusing, you're finding amusing something that isn't there except as you have put it there. I am by no means defending, nor does my thinking at all run along the rails you have it on.

    And in saying that your interpretation is your interpretation, "mine is mine," and then claiming you understand him, you make my whole point and make yourself foolish.

    You're in the position of a man who says it means what you say it means, and that's what Plato meant! Only a fool....
  • Asif
    241
    @tim wood Once again your lack of comprehension and straw manning shines through.
    Let's put it this way,you make it out that it's so hard to understand Plato as a whole,his main gist. That's your problem,not mine. The point is,I back my intelligence,I dont require your bogus logic to learn.
    You have no point. Ponder that through your out of focus
    purple eye glass. :cool:
  • tim wood
    5.6k
    If you aspire to be the lead ignorant a**hole of TPF you shall have to get in line. I realize it will be hard for you to grasp, but there are actually posters here with larger credentials than yours, although mainly based in repetition and longevity. To be sure, and to your "credit" though, you're making a good running start.

    On the other hand, if you will check your ego and apparent need to preen at the door and instead think a bit, then you might ascend to a higher level of participation, and not of destructive adolescent narcissism. I leave you with that.
  • Tzeentch
    841
    Platos agenda was a totalitarian project and specifically designed for a political elite of "philosopher kings" Aka priests.Asif

    "He will gladly take part in and enjoy those which he thinks will make him a better man, but in public and private life he will shun those that may overthrow the established habit of his soul.” “Then, if that is his chief concern,” he said, “he will not willingly take part in politics.” “Yes, by the dog,” said I, “in his own city he certainly will, yet perhaps not in the city of his birth, except in some providential conjuncture.” “I understand,” he said; “you mean the city whose establishment we have described, the city whose home is in the ideal; for I think that it can be found nowhere on earth.” “Well,” said I, “perhaps there is a pattern of it laid up in heaven for him who wishes to contemplate it and so beholding to constitute himself its citizen. But it makes no difference whether it exists now or ever will come into being. The politics of this city only will be his and of none other.” “That seems probable,” he said." - Plato, The Republic, Book 9, section 592.

    :roll:
  • Asif
    241
    @tim wood Jealousy will get you nowhere timmy!
    Corona derangement syndrome plus getting schooled by a newbie!
    Number of posts doesnt equal Intellect.
    As I said a few days ago your low level sarcasm and patronising manner are indicative of a lack of philosophical acumen. :cool:
  • Asif
    241
    @Tzeentch You are aware plato also has a dialogue after this called "Laws" and you are also aware that plato puts several ironic and dialectic arguments into the mouth of Socrates.
    The republic and many of platos dialogues lay the foundations and principles for rule by priest and authoritarian means. You want to take an ironic passage and say Plato was just writing an expansive thought experiment. Maybe you havent heard of the holy lie.
  • Tzeentch
    841


    "I think we should employ the method of search that we should use if we, with not very keen vision, were bidden to read small letters from a distance, and then someone had observed that these same letters exist elsewhere larger and on a larger surface. We should have accounted it a godsend, I fancy, to be allowed to read those letters first, and examine the smaller, if they are the same.” “Quite so,” said Adeimantus; “but what analogy to do you detect in the inquiry about justice?” “I will tell you,” I said: “there is a justice of one man, we say, and, I suppose, also of an entire city.” “Assuredly,” said he. “Is not the city larger than the man?” “It is larger,” he said. “Then, perhaps, there would be more justice in the larger object and more easy to apprehend. If it please you, then, let us first look for its quality in states, and then only examine it also in the individual, looking for the likeness of the greater in the form of the less.” “I think that is a good suggestion,” he said. “If, then,” said I, “our argument should observe the origin of a state, we should see also the origin of justice and injustice in it.” “It may be,” said he. “And if this is done, we may expect to find more easily what we are seeking?” “Much more.” “Shall we try it, then, and go through with it? I fancy it is no slight task. Reflect, then.” “We have reflected,” said Adeimantus; “proceed and don't refuse.” - Plato, The Republic, Book 2, section 368d - 369b.

    It's not exactly hidden. :chin:
  • Asif
    241
    @Tzeentch Come on. The republic is a big book and you want to quote a few passages of dialect?
    Let me ask you in your own words. What did Plato write these political tracts for? Entertainment? Thought exercises? What was the holy lie all the death penalties and the elaborate hierarchy and stratification for?
    I suppose Marx and Nietzsche were just interested in the intellectual fantasy of writing as well?
  • A Seagull
    621

    I think one has to realise that the ancient philosophers were grasping at ideas out of virtually nothing, like Thales' 'all is water' and Plato's forms, they are starting points for the development of further ideas. To consider that they are somehow sacrosanct or perfect is ridiculous.
  • Asif
    241
    @A Seagull A lot of the presocratics were naturalistic thinkers yes,and I'm sure they built on the ideas of earlier greeks but added their own as well.
    Plato is overtly and absolutely political as well as positing a demiurge,laws for society and an explanation and supposed origin of the phenomenal world. Platos blueprint has been used down the ages and adjusted for by politicians and thinkers after him till the present day.
    Egypt was the springboard for his ideas.
    I dont see why people dont call him out for the totalitarian that he was.
  • Tzeentch
    841
    The premise of The Republic can best be summarized by the following passage:

    “But to come now to the decision between our two kinds of life, if we separate the most completely just and the most completely unjust man, we shall be able to decide rightly, but if not, not. How, then, is this separation to be made? Thus: we must subtract nothing of his injustice from the unjust man or of his justice from the just, but assume the perfection of each in his own mode of conduct. In the first place, the unjust man must act as clever craftsmen do: a first-rate pilot or physician, for example, feels the difference between impossibilities and possibilities in his art and attempts the one and lets the others go; and then, too, if he does happen to trip, he is equal to correcting his error. Similarly, the unjust man who attempts injustice rightly must be supposed to escape detection if he is to be altogether unjust, and we must regard the man who is caught as a bungler. For the height of injustice is to seem just without being so. To the perfectly unjust man, then, we must assign perfect injustice and withhold nothing of it, but we must allow him, while committing the greatest wrongs, to have secured for himself the greatest reputation for justice; and if he does happen to trip, we must concede to him the power to correct his mistakes by his ability to speak persuasively if any of his misdeeds come to light, and when force is needed, to employ force by reason of his manly spirit and vigor and his provision of friends and money; and when we have set up an unjust man of this character, our theory must set the just man at his side—a simple and noble man, who, in the phrase of Aeschylus, does not wish to seem but be good. Then we must deprive him of the seeming. For if he is going to be thought just he will have honors and gifts because of that esteem. We cannot be sure in that case whether he is just for justice' sake or for the sake of the gifts and the honors. So we must strip him bare of everything but justice and make his state the opposite of his imagined counterpart. Though doing no wrong he must have the repute of the greatest injustice, so that he may be put to the test as regards justice through not softening because of ill repute and the consequences thereof. But let him hold on his course unchangeable even unto death, seeming all his life to be unjust though being just, that so, both men attaining to the limit, the one of injustice, the other of justice, we may pass judgement which of the two is the happier.” - Plato, The Republic, Book 2, 360a - 361a

    Plato describes two kinds of men. One completely unjust, but with the appearance of a just man. The other completely just, but with the appearance of an unjust man. He then makes the point that, when given the choice, one should always choose the just man over the unjust man.

    This is the core of what The Republic is about; the role of justice in the soul of man. The city-state is used as part of an analogy to make his point, as has been shown in the passage I quoted previously.

    But I am not here to lecture you on Plato. After all, you profess to have sufficient understanding of his works. I obviously didn't come up with this on my own, and I could help you to some sources, but as they say 'pearls before swine'.
  • Asif
    241
    @Tzeentch I'm interested in original personal understandings not just regurgitating sources. You keep quoting this analogy as if thats the premise of all platos work. Thats just weak. I'm wondering if you've read any other dialogues or in fact the whole republic?
    As for the swines Pearl's,gosh so subtle and original.
    Seems like ad hominem is par for the course with lower level intellects.
  • A Seagull
    621

    I think a lot of philosophers had personal agendas that underpinned the structure of their philosophies. For some it was religious, or as you point out for Plato it was political, others have social agendas (Marx) etc etc. The underlying motive for Kant was to refute Hume.
  • Asif
    241
    @A Seagull I agree. Really the wider point I'm making is that all philosophers have personal agendas and that is obvious. These personal values underpin their ideas and thought. Every human has values and this is reflected in their thought processes and behaviour. I think folks would understand thinkers better if they treated them as expressing their personal values rather than thinking they are some
    Cold abstract truthseekers. Ditto scientists.
  • tim wood
    5.6k
    I dont see why people dont call him out for the totalitarian that he was.Asif

    @Tzeentch, it seems to me, has gone to great trouble to support his own arguments. Which you have not. But here's a claim of yours. Keeping in mind you claim your understanding of Plato is interpretation-free, have at it; make your case. (You might start by researching "totalitarian.")
  • Asif
    241
    @tim wood Great trouble! Your strawmanning and patronising lowbrow wit is indicative of your feeling un comfortable. I'm wise to your "debate" tactics you will always ask for more and more evidence,and then you will say oh,I dont understand. I discuss with folks who want an even handed exchange and can agree to disagree or refine understandings,not pendants who find themself alarmed by new thinking. Tbh,your not worthy of discussion,I've seen you in other threads, rigid pompous and pathetic.
  • tim wood
    5.6k
    For you, asif, silence would be wisdom.

    An online search for "totalitarian" - I don't have an OED - shows the word coined in English c. 1928. Common era, that is, or around 2,275 years after Plato had breathed his last. Calling him a totalitarian, then seems to me grossly interpretive, and probably equal parts just plain wrong. I buy @Tzeentch as right, in at least suggesting that Plato is not captured by such a word, or even, given the word's meaning, touched by it.
  • Asif
    241
    @tim wood As I said previously you are pedantic and low level. Your arguments above highlight this. Trying to use a dictionary to refute and appealing to a guy quoting a few passages of the republic whilst ignoring the import of plato in general. As are many you are mired in appeals to authority, a sign of an unoriginal derivative knowledge.
    :cool: Silence? ! I'm too eloquent and high energy for you.
    Maybe like plato you would like poets to be quiet. And there my point on plato is proved once again. :halo:
  • Asif
    241
    @Tzeentch With respect,you havent really engaged in dialogue but just a few isolated quotes whilst ignoring the import of the republic and Plato in general. This minimalist approach you forward as discussion whilst ignoring numerous questions I have asked.
    And then a smiley!? Come on! If you have a point write your own words.
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