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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2014

    added a paragraph about passing from first-order logic to modal type theory to the entry on analytic philosophy.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 27th 2014

    Gave a little more idea of the ’analysis’ in analytic philosophy.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 27th 2014

    Thanks! Do we agree on my “Remark”, then, or would you rather see it qualified further?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 27th 2014

    Well it’s not saying anything much about analytic philosophy, except perhaps that it wrote off Hegel too soon. To tie the parts of the page together, it would be good to find Russell saying something unkind about Hegel, especially that he got in a muddle about language. I’ll have a look.

    By the way, there’s quite a rrevival of Hegel going on. I wish I could find out more about this conference – Hegel, Analytic Philosophy, Formal Logic. Don’t suppose there’s much modal type theory going on.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 27th 2014

    How about this one from Our Knowledge of the External World suggesting that Hegel gets drawn to what is known as the theory of internal relations by use of an old-fashioned logic

    Mr Bradley has worked out a theory according to which, in all judgment, we are ascribing a predicate to Reality as a whole; and this theory is derived from Hegel. Now the traditional logic holds that every proposition ascribes a predicate to a subject, the Absolute, for if there were two, the proposition that there were two would not ascribe a predicate to either. Thus Hegel’s doctrine, that philosophical propositions must be of the form, “the Absolute is such and such”, depends upon the traditional belief in the universality of the subject-predicate form. This belief, being traditional, scarcely self-conscious, and not supposed to be important, operates underground, and is assumed in arguments which, like the refutations of relations, appear at first such as to establish its truth. This is the most important respect in which Hegel uncritically assumes the traditional logic.

    So Russell certainly doesn’t think Hegel had forged a new logic, rather he hadn’t been liberated from the old one:

    The old logic put thought in fetters, while the new logic gives it wings. It has, in my opinion, introduced the same kind of advance into philosophy as Galileo introduced into physics, making it possible at last to see what kinds of problems may be capable of solution, and what kinds are beyond human powers. And where a solution appears possible, the new logic provides a method which enables us to obtain results that do not merely embody personal idiosyncrasies, but must command the assent of all who are competent to form an opinion. (Bertrand Russell, ’Logic As The Essence Of Philosophy’)

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 30th 2014

    I have been reading a bit more in the Vorrede of Phänomenologie des Geistes. That makes it quite clear that he of course knows about ordinary logic and ordinary Räsonnieren, but that he finds this fall short of adressing something deeper that he is after.

    formales Denken, dass in unwirklichen Gedanken hin und her räsonniert […]

    Das Räsonnieren ist die Freiheit von dem Inhalt, und die Eitelkeit über ihn […]

    das begreifende Denken ihm entgegengesetzt

    (formal thinking going back and forth between unreal thoughts … reasoning free of content… opposed to this the “grasping thinking”)

    In the paragraphs leading up to §63 §64 (as counted here) he says explicitly that a genuine philosophical sentence is destroyed when it is read using ordinary logic, and that instead one needs to read it as a kind of Zen koan that tries to say something else than it seems to say. He says that this is the whole point that people miss who complain about philosopical writing (his writing, presumeably, notably included) being hard to understand and requiring re-reading. He says that’s the whole point, that one reads it once, realizes that it means something different than what it would ordinarily seem, and then reads it again to find a deeper meaning. It’s an explicitly gnostic attitude.

    His paragraph about mathematical proof makes clear that when he says “philosophical sentence” here he means something that goes beyond the kind of facts that are considered in (his contemporary) mathematics. He appreciates those, and the logic used to obtain them, but finds that philosophical reasoning is to go to something deeper where this logic is not of help anymore.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 30th 2014

    That seems to mark a distinction between recent analytic and ’continental’ philosophy, how they’ve taken Hegel to heart. I was going to find you a quote from Alain Badiou to illustrate. I found these, which include

    This is also what I would like to call the writing of the generic: to present in art the passage from the misfortune of life and of the visible to the happiness of a truthful arousal of the void. This requires the immeasurable power of the encounter, the wager of inventing a name, as well as the combination of wandering and fixity, of imperative and story.

    Now I see there’s one for us to formalise with our new take on modal logic:

    An event is the creation of a new possibility. An event changes not only the real, but also the possible. An event is at the level not of simple possibility, but at the level of possibility of possibility.

    Contrast with the analytic side here:

    The first thing we need to do is to distinguish between material existence and existence in general. Numbers may be an example of things that exist without having material existence. By existence I mean ‘being something or other’. What is overwhelmingly plausible is that it is contingent what material things there are. There could have been more or fewer material things than there in fact are. That is consistent with BF and CBF, because it is consistent with the idea that if, for example, the table we’re sitting at had not been material it would still have been something. It would just not have been something material. Initially, that sounds like a strange claim, and the immediate question is: well, what would it have been? I’m not talking about the table as being a collection scattered atoms. That is still something material, and even those atoms might never have been. What I’m suggesting is that if there had been no such table and no such atoms, there would still have been a possible table, in other words, something that could have been a table and that could have been a material thing. But in those circumstances, it would not have been material, it would not have been a table, and so it would not have been located in space and time. It would have been a merely possible table, a merely possible material thing. Once we see that that is what BF and CBF is claiming, when they are understood with the quantifiers completely unrestricted and not limited to material things, it is much less obvious that there is any inconsistency between what those formulas are committing us to and what common sense is in any position to assert or have any special authority over. It seems that scientifically informed common sense may have some authority over what materially and contingent things there are, but once the question is what merely possible material things there are, that sort of abstract questions is not to be decided by common sense. That question is to be decided by systematic theory. Of course, it is not at all obvious such theoretical considerations themselves will favour BF and CBF, but what I have tried to argue in a series of works is that in fact they do. When we try to develop a systematic theory of metaphysics of quantified modal logic, we get into a mess unless we accept BF and CBF. So, in the end, we are driven, not by some immediately intuitive consideration, but by considerations of the needs of systematic theory into accepting these formulas.

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeDec 1st 2014
    • (edited Dec 1st 2014)

    Is it likely that Hegel was complementing logic with deeper insights into truth (and paths to find the truth) which philosophers call intuition and which precede adherence to particular logical frameworks ? (Intuition in philosophy is rather different from the usage of the term in sciences) In this sense it is not that newer kinds of logic would fully capture Hegel’s search for things beyond classical logic, one still needs the insights into necessity of some truths which appear before the establishment of logical frameworks. I think it would be a mistake to think that with newer mathematics one fully covers his urge to go beyond only logical insight. There are also isnights on necessity before the logic takes the scene.

    • CommentRowNumber9.
    • CommentAuthortrent
    • CommentTimeDec 2nd 2014

    instead one needs to read it as a kind of Zen koan that tries to say something else than it seems to say. He says that this is the whole point that people miss who complain about philosopical writing (his writing, presumeably, notably included) being hard to understand and requiring re-reading. He says that’s the whole point, that one reads it once, realizes that it means something different than what it would ordinarily seem, and then reads it again to find a deeper meaning. It’s an explicitly gnostic attitude.

    I don’t know exactly what Hegel means, but Schlegel has a similar attitude: “The mind understands something only insofar as it absorbs it like a seed into itself, nurtures it, and lets it grow into blossom and fruit. Therefore scatter holy seed into the soil of the spirit, without any affectation and any added superfluities.”. This is the literary-poetic analogue of Feynman’s “what I cannot create, I do not understand”. Schlegel purposely wrote his philosophical fragments in a stripped down form such that readers can create the rest of a given fragment for themselves, and thereby understand the given fragment. (And that the reader has to finish it does not necessarily mean that there is not a privileged way to finish it).

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2014

    Zoran, re #8,

    that’s true, I agree, it would be voodoo to expect that there is a full formalization of these feelings in some “new mathematics”. But something may still to be found. I am reminded vaguely of Brouwer (a more clear-cut case, hence maybe good for comparison) whose thoughts seemed mystical to contemporaries, and yet when the new mathematics of topos theory appeared it turned out that what he said were theorems (e.g. that every function between the reals is continuous).

    • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeDec 2nd 2014

    You are doing good work. People in philosophy who are science oriented are so much biased toward the analytic school nowdays that I hear so much scorning of anything from “continental” tradition. It is good that you (in tradition of Lawvere and others) are finding sound value in parts of continental tradition…