• Negative numbers are more elusive than we think
    It appears that our number system is as of yet still incomplete!Agent Smith

    https://en.wikipedia.org/wiki/Octonion
  • Negative numbers are more elusive than we think
    So -4 = i×i×4i×i×4. A u-turn of whatever +4 is;Agent Smith

    :up:

    Note that you can also go the other direction too using .
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)

    I think we are stuck on this particular issue for now, but I have enjoyed the battle so far, and I hope to break a lance on some other issue at some point.
  • Is the mind divisible?
    converse with other embodied minds and interact with animal embodied minds.unenlightened

    :up:
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    This notion of yours that concepts depend on there being multiple thinking things or mind-independent objects is very wrong.Michael

    Wrong in terms of what ? Your own opinion ? Or something that exceeds and compels us both ? If the latter, you support my point that philosophers as such embrace an externality.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    No need. I just presented an opportunity for you to ask yourself a question. Shouldn’t be any more difficult, or use any other faculties, than asking yourself what would be nice to have for dinner.Mww

    Are you really asking me how I'd apply a concept ? And that's supposed to prove some kind of Platonism ? No one is denying the existence or the application of concepts. The issue is how best to think of them. Functional equivalence classes in an inferential context is one approach. For instance, the words 'and' and 'und' are used pretty much the same way in English and German. Let me be clear that I'm not denying the existence in some sense of abstractions. But I don't commit myself to platonism because I have concepts like 'function' and 'equivalence class.' As I mentioned earlier, these concepts can be understood to be co-performed (in the inferences we allow, etc.)
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    expression which requires only a singular subjectivity, or communication, which requires a plurality of subjectivities, are only possible through a medium that is not subjective.Mww

    That non-subjective is the language we are sharing right now. Even our secret monologues occur in a public language.

    Yeah, well....in Kant, autonomy does not relate to universality, but causality, so whoever said Kant said, or meant, that, has merely suited himself to his own ends. And as you say, we are entitled to interpret, but we do not have license from that entitlement, to subvert.Mww

    I'll grant the possibility that you are right about Kant, but your mere assertion is worth no more than mine or Brandom's. The key point for me is not the force of Kant's reputation but the force of reason itself, which lends Kant whatever value or authority he himself has as a philosopher.

    That said, I will defend the association of Kant with autonomy and not mere causality.


    Enlightenment is the human being’s emergence from his self-incurred immaturity. Immaturity is the inability to use one’s own understanding [= reason] without the guidance of another. This immaturity is self-incurred if its cause is not lack of understanding, but lack of resolution and courage to use it without the guidance of another. Sapere aude! [Dare to be wise!] Have courage to make use of your own understanding [= reason]! is thus the motto of enlightenment.

    It is requisite to reason’s lawgiving that it should need to presuppose only itself, because a rule is objectively and universally valid only when it holds without the contingent, subjective conditions that distinguish one rational being from another.
    ...
    Reason must subject itself to critique in all its undertakings, and cannot restrict the freedom of critique through any prohibition without damaging itself and drawing upon itself a disadvantageous suspicion. For there is nothing so important because of its utility, nothing so holy, that it may be exempted from this searching review and inspection, which knows no respect for persons [i.e. does not recognize any person as bearing more authority than any other—GW]. On this freedom rests the very existence of reason, which has no dictatorial authority, but whose claim is never anything more than the agreement of free citizens, each of whom must be able to express his reservations, indeed even his veto, without holding back. (A738f/B766f, translation slightly modified)
    ...
    To make use of one’s own reason means no more than to ask oneself, whenever one is supposed to assume something, whether one could find it feasible to make the ground or the rule on which one assumes it into a universal principle for the use of reason.

    [N]ot even the slightest degree of wisdom can be poured into a man by others; rather he must bring it forth from himself. The precept for reaching it contains three leading maxims: (1) Think for oneself, (2) Think into the place of the other [person] (in communication with human beings), (3) Always think consistently with oneself.
    — Kant

    Notice that the coherence norm is foregrounded in that last quote.

    And here's a scholar summarizing:

    We saw above (§1.4) that Kant characterizes reason in terms of a self-reflexive procedure. Reason is autonomous and submits to no external authority; it gains authority from submitting itself to critique; and critique involves rejecting any mode of thinking or acting that cannot be adopted by all. In less abstract terms, the self-scrutiny of reason is scrutiny by all those who demand justification for any particular mode of thought or action. Such a view does not assume that we are necessarily bound to our interests and inclinations (as the instrumental account does). It does not ask us to rely on what others do accept (as the communitarian account does). It does not involve the fantasy that we already know or intuit what everyone should accept (as the perfectionist account does). It proposes, instead, a vision of human beings who are able to step back from their particular inclinations, habits and intuitions, and who are willing to use this ability to seek terms that all can accept—to construct an intersubjective order of co-existence, communication and cooperation on terms that all can accept.
    https://plato.stanford.edu/entries/kant-reason/#ReaArbEmpTru
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    You'd have to separate the mind into two halves - that which holds what is the case, and that which holds beliefs about the other half (which can then be wrong).Isaac
    :up:

    This was basically the insight that inspired me to define the world (minimally) as that which a self can be wrong about. The concept of a self is hard to stabilize without such a non-self. A man trapped in a video who doesn't know what's around the next corner is in a world.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    What....you never heard the expression “thinking outside the box”? What is a culture if not a box? Being in a culture and conditioned by it, does not necessitate being restricted to it.Mww

    Of course. Clearly the box is extended by intellectual pioneers...and more literal pioneers who bring back moon rocks or deepsea lifeforms. Clearly concepts are extended, introduced. No one disputes the role of individuals in our 'open source' communal operating system (the language itself and the concepts we've adopted and mastered together.)

    ....but there’s nothing in that that says the philosopher’s minimum commitment has to be language.. I would say a philosopher’s minimum commitment, is understanding.Mww

    Your version of understanding, if we grant a nonlinguistic version of this in the first place, isn't enough. What sense can 'philosophy' have if no conversation is possible ? If no beliefs can be settled publicly and reasonably ? Understanding without language is pointless, unless you really are happy with some kind of paradoxically solipsistic or mute theory of rationality and science. Here we are, sir, trying to settle the way we ought to conceive the minimal epistemic situation, mostly in English, our jointly inherited and even largely-self-constituting software.

    “Something better” and “broken theory” are subjective judgements. Who says it’s better, and, better than what?Mww

    We settle it, the rational community as a whole. We make and defend claims, presenting candidate beliefs for the tribe. Our second-order tradition takes no claim or claimant to be sacred As Kant saw, reason is autonomous, one and universal, and we 'rational ones' (who acknowledge only reason(s) as an authority) hash it out, as you and I are doing here, playing our relatively tiny roles.
    I claim that what Ryle calls the 'official story' is indeed broken, essentially passing on the (old) news that a strong case has been made a certain metaphysical tradition. 1781 was a very good year, but it was not the end of philosophical history.

    And what’s broken about some extant theory?Mww

    I've mentioned quite a few issues already. I understand that folks think Wittgenstein is trying to steal their soul, so I'd recommend Ryle. I recall that you hate linguistic philosophy, but language is what you must make your case in. If you hide from this simple fact...the humans make a case for their beliefs in a shared language...then you seat yourself at the children's table. It's fine to postulate something like Platonic-forms, God-given Concepts, whatever...but a case must be made in the language we share, in the 'koncepts' we share. The rest is escapism, mysticism, diarykeeping....

    So....you know what justice is because you’ve experience things that seem just or unjust to you? How does an experience of an unjust incident inform you of how it could be so, if you didn’t already have an idea what form justice itself must have?Mww

    Are you so sure that AI couldn't be train to predict with high accuracy whether the description of an action as unjust ? Does it have an idea ? Especially as translation software gets better, we should pull back on our theological certainties about our divine source. Or can kangaroos have their own kangaroo Kant, spelling out their eternal structure of kangaroo experience ?

    We could actually talk about semantics if you want. The best story I've heard lately is inferentialism, which I'd call a structuralist approach to meaning. For instance,
    Observational vocabulary is not a vocabulary one could use though one used no other. Non-inferential reports of the results of observation do not form an autonomous stratum of language. In particular, when we look at what one must do to count as making a non-inferential report, we see that that is not a practice one could engage in except in the context of inferential practices of using those observations as premises from which to draw inferential conclusions, as reasons for making judgments and undertaking commitments that are not themselves observations.The contribution to this argument of Sellars’s inferential functionalism about semantics lies in underwriting the claim that for any judgment, claim, or belief to be contentful in the way required for it to be cognitively, conceptually, or epistemically significant, for it to be a potential bit of knowledge or evidence, to be a sapient state or status, it must be able to play a distinctive role in reasoning: it must be able to serve as a reason for further judgments, claims, or beliefs, hence as a premise from which they can be inferred.
    https://sites.pitt.edu/~rbrandom/Texts/Pragmatism_Inferentialism_and_Modality_i.pdf
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    How about “no human can know the future”.Michael

    Is that an empirical claim ? Or a metaphysical claim ? If it's a metaphysical claim, it's a claim about the concepts knowledge and future, it seems to me.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    It’s no different to saying “no human has two heads” which is true if I’m the only human or if I’m one of seven billion.Michael

    I disagree. The form is similar, but I claim that concepts are special. Consider the claim: It’s no different to saying “no human has two heads. It's a claim about norms that bind us both, that either transcends you or has no force.
  • Is the mind divisible?

    I like yours too.

    FWIW, I'm largely paraphrasing Robert Brandom who finds his own sources in Kant, Frege, Wittgenstein, Sellars, and Hegel. According to Brandom, Hegel's accomplishment was describing how groups could be bound by the norms that they were ( eventually self-consciously ) co-creating in the first place.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    But that “soft” externality is the kind of externality that the solipsist denies can be known. They don’t deny knowledge of the metaphorical externality that you apply to such things as maths. The solipsist accepts that we can get maths wrong.Michael

    To me the tricky part is that the solipsist is making claims about any rational agent, existence or not. Your counter might be that 'If X exists, then X has nature N,' but this is still a claim about what is possible and impossible in the world. It can be framed like this : It is this case that it's impossible that a rational agent both exists and is legitimately certain that ...
  • Is the mind divisible?

    Division by zero isn't allowed because zero has too many divisors.

    https://en.wikipedia.org/wiki/Zero_divisor
  • Is the mind divisible?
    Interesting. My personal view is that the self is a modeling assumption used to delineate non-entropic forces from entropic ones. It locates the boundary between the system which is to be retained and the forces which would reduce its improbable structure to a nice even Gaussian distribution of variables.Isaac

    Different uses for different contexts ! I like your version...reminds me of @apokrisis's. But consider how selves function here on the forum. We track claims, hold one another to coherence norms, and just generally keep score.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)


    But note that I'm accusing the solipsist of conceptual incoherence, which is to say wrong in terms of the universal rational norms that bind the philosopher as such. The very notion of philosophy binds its participants to something self-transcending.

    If I can't be wrong about the concept of knowledge, it's not external to me. If I can be wrong about the concept of knowledge, it is external to me. If I assert, in the name of reason, in its authority, that knowledge of the external is necessarily uncertain, I present knowledge that's intended to transcend me toward the very concepts that secure my role as philosopher. The madman can say it, but the philosopher cannot.

    I can't prevent you from softening the meaning of 'external' to make your case. I just think that you simultaneously diminish the significance of the claim, as if the solipsist is merely denying a particular metaphysics of the external world (such as Epicurean atomism, or the 'reality' of everyday objects) --- as opposed to the external world itself.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    You could explain it without using a spatial metaphor?Michael

    I've suggested that we look to the appearance/reality distinction that probably informs this issue in the first place. Reality plays the role of the 'external.' Appearance (the given, the internal) can deceive me, so I can mistake (have incorrect beliefs about) the external.

    The skeptic seems to need this picture, this distinction, to get off the ground.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    Is the concept of a horse something that I can encounter and pick up?Michael

    Is it something you can be right or wrong about ? Can one be wrong about the square root of 2 ? Or whether a promise was made ? If not, why not ?
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    I have no idea what it means to say that a concept is external. Is the concept of a horse something that I can encounter and pick up?Michael

    Why do you assume that the external is an object? It's just a spatial metaphor.

    I've already suggested a 'safer' more neutral understanding of this metaphor.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)

    FWIW, I don't think there's a perfectly 'right' answer here. We are clarifying concepts as we debate an edge case.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    Any thinking thing, whether there be just one thinking thing or two thinking things or seven billion thinking things.Michael

    Is this just the solipsist's conception of a thinking thing (a 'private concept,' if that makes sense) ? Or do his claims aim at truths about a concept that binds all rational agents ?

    I claim that that concept itself is either external or not worth talking about. His statements about the concept are either truth-apt (and can thus be wrong) or not. If truth-apt, then external.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    skepticism is the position that we could be wrong.Michael
    What is it that we could be wrong about, according to the skeptic (in this case the epistemological solipsist), who makes an assertion about us ?
  • Is the mind divisible?
    why not ditch the idea that minds are private at all, or singular, or anything.Isaac

    I suggest that we understand the self primarily in normative terms, as a locus of responsibility. I ought to keep my story straight (maintain a coherent set of beliefs), report simple facts reliably, keep my promises...
  • Is the mind divisible?
    0 isn't divisble. 0x=0 where x is real.

    What follows? Any ideas?
    Agent Smith

    Say what ?

    You must mean isn't defined, (roughly) because of the last part of your statement. In other words, is not one-to-one and hence not invertible.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    In philosophy, to say that a statement is truth-apt is to say that it could be uttered in some context (without its meaning being altered) and would then express a true or false proposition.

    How can I make a statement that's true or false without something I can be right or wrong about ?

  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)

    What can truth-apt mean for a philosophical solipsist ? ( But we can drop if if you want.)
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    Trying to argue against the coherency of solipsism is just wrong.Michael

    Wrong within the dream of the solipsism or wrong for any rational agent ? If the concepts he discusses do not transcend the epistemological solipsist (play the role of something external), then his claims seem to lose their status as genuinely philosophical.

    I do not deny that madmen can fear they are caught in a dream. I dispute that the philosopher as such (willingly subject to the force of the [non-subjectively ] better reason) could coherently impugn the 'externality' of their own concepts, essentially asserting, if an epistemological solipsist, that it's wrong to assume we could be wrong.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    I understand your dukkha - something's wrong, I second that motion.Agent Smith

    Perhaps elaborate ?
  • Shamanism is the root of all spiritual, religious and philosophical systems
    It just struck me that a shaman is/was basically a comms channel between us/people and the great unknown - they (shamans) bridged this terrifying gap as best as they could and brought some semblance of what in psychology is known as closure in our/people's lives.Agent Smith

    :up:
  • Shamanism is the root of all spiritual, religious and philosophical systems
    Shamanism has always been romanticised by hippies! :sweat:javi2541997
    :up:
  • Negative numbers are more elusive than we think
    I still don't see the confusion over negatives and their operations, but then I "do" math every day. Oftentimes familiarity makes it difficult to see how others must view the same.Real Gone Cat

    Consider also the joys of being a crank. If I can make a case that all the geniuses got it wrong, then what's that make me ? "All of math is a contradiction [,and only the great Me can see it]." To be fair (sounds like we've both taught/teach math), students (who want a grade to get a degree to get a job) often actually struggle, thankfully mostly with a humility that makes it possible to correct them.
  • Negative numbers are more elusive than we think
    accommodates increasingly general uses of arithmetic, which in my opinion and following Wittgenstein's general philosophy, is best understood in terms of games of increasing generality .sime

    :up:
  • Negative numbers are more elusive than we think
    The numberline shows us an order, and this order gives zero a place. But zero has no place within an order, because it would mean that there is a position of no order within that order, which is contradictory.Metaphysician Undercover

    :down:

    You are getting lost in metaphors and intuitions, as if a checkmate is illegitimate because involved the bishop was never baptized.
  • Negative numbers are more elusive than we think
    In one sense, geometry's anti-negative numbers and in another sense it is pro-negative numbers!

    What up with that? Anyone have any ideas?
    Agent Smith

    I think it's fair to assume that mathematicians prefer concepts to generalize as smoothly as possible, but it's just not always clear how to make a metaphor work smoothy in every possible context. I think we agree that negative numbers are intuitive for adding and subtracting. The tricky part is multiplication. If one gets to the point of realizing that multiplication by is a rotation by , then one can have a pretty sensible Cartesian plane.

    To fix the conceptual issue with taking square roots, you can just embrace the idea that magnitudes are positive and ignore the negative numbers altogether. When teaching algebra, it's sometimes convenient to ignore the complex numbers and speak of no (real) solutions. Complex solutions may not make sense in the practical context, and it's the same with negatives.

    Consider dual numbers, which are useful to autodifferentiation...but not much else, so far as I'm aware. You can train neural networks more intuitively with these, but they are not as computationally efficient as backprop.
    https://en.wikipedia.org/wiki/Dual_number
  • Is there an external material world ?
    They most certainly did not have any attitude at all towards the proposition "the stopped clock is working" when and while they trusted what a stopped clock said about the time.creativesoul

    :up:
  • Is there an external material world ?
    Which is to prefer doing different things with the very same words/marks. There's nothing - in and of itself - wrong with doing thatcreativesoul

    :up:

    They knew they were fallible. The general aim was to minimize the likelihood of being mistaken(of forming, having, and/or holding false belief) while increasing the likelihood of better understanding the world and/or themselves .creativesoul

    :up:
    Language less creatures do not have language, do not understand words, and thus cannot understand propositions. Propositions are utterly meaningless to language less creatures.creativesoul

    :up:

    The issue seems to be whether beliefs are best understood or not in terms of propositions.

    I am quite curious to see exactly what you're going to do differently than me.creativesoul

    Lately I find Sellar's myth of Jones illuminating. Note that Jones lives in a implicitly behaviorist society. They don't even think of themwselves as such, because it's Jones who first postulates 'internal speech' or 'talking without talking.' In the same way that the atomic theory could prove itself with increased powers of prediction and control, Jones' peers come to embrace thoughts as useful fictions. With practice, they even get good at guessing what they are thinking.

    Now Jones could even extend his theory to creatures who never talk at all, explaining the beaver's movements in terms of its belief that food was waiting on the other side. Note that beliefs are still propsitional here, without us being committed to the animal 'having' them 'directly ' (inside their postulated ghostly consciousness.)
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    There seems to be this sense that because we can imagine a horse, the concept of a horse must be private (I needn't tell anyone what colour it is...shhh!)Isaac

    Precisely. The trivial possibility of keeping a secret (which isn't always so easy, by the way) is radicalized into an quasi-mathematically NSA-proof beetle-box (infinitely encrypted, robust against the high-tech prying of the Neptunian secret police circa 4059.


    What we're imagining is not a horse, it's a hippopotamus. So my imagination cannot be the concept 'horse', otherwise it couldn't be wrong.Isaac

    Exactly. The OP is about our minimal rational epistemic commitment. If words mean whatever we think they mean, we can't even begin to settle beliefs rationally.

    Just as keeping a secret is radicalized into an inaccessible ghost as that alone which is given, so is the fact that mastery of a concept varies radicalized into an absurd essential privacy of concepts.




    .
  • Please help me here....
    it only follows from The Cogito that "doubting exists", not the doubter herself.180 Proof

    :up:
  • What do normative/moral terms mean on a realist construal?
    Yes, I think people are, wary of relativism ("the Nazis were right, from their perspective"), but it's never something I've found in the least worrying. I'm embedded in a culture (and I'm probably wired with several moral-like beliefs from birth, like any other human).Isaac

    It also doesn't bother me. While a philosopher (and his less pleasant cousin, the sociopath) might be able to see around some of the tribal norms more than others, he or she is still mostly reliant upon them. To strive to be reasonable is to be willingly captured by Enlightenment autonomy norms.

    The OP doesn't want to admit it, but it sure looks likes a demand for justification, which implicitly invokes this autonomy norm, for which he can't find a source in his telescope yet, I presume.
  • Our Minimal Epistemic Commitment (Fixing Descartes' Cogito)
    To show that we have a private concept of 'exists' you need to show not only that mental activity is private, but that the grouping of some of that mental activity into a clear concept called 'existence' is also private.Isaac

    Typically, some metaphysical version of 'private' is intended in these cases. I take it to be grammatical, in that it's, by definition, not empirically decidable. The arbitrarily convincing P-Zombie is ( by definition ) all science can ever touch with its scalpels and scanners. What we end up with is a mystified X, with no content save the thereness of the there itself. We are back to building shrines for tautologies.



    From Ryle's SEP entry:
    Ryle’s criticism of the Official Doctrine begins by pointing out an absurdity in its semantic consequences. If mental conduct verbs pick out “occult” causes then we would not be able to apply those verbs as we do; so something must be wrong with a theory of mental phenomena that renders so inadequate our everyday use of these verbs. For, according to the Official Doctrine

    when someone is described as knowing, believing or guessing something, as hoping, dreading, intending or shirking something, as designing this or being amused at that, these verbs are supposed to denote the occurrence of specific modifications in his (to us) occult stream of consciousness. (1945, 17)

    Ryle’s criticism of the view is that if it were correct, only privileged access to this stream of consciousness could provide authentic testimony that these mental-conduct verbs were correctly or incorrectly applied. “The onlooker, be he teacher, critic, biographer or friend, can never assure himself that his comments have any vestige of truth.” And yet,

    it was just because we do in fact all know how to make such comments, make them with general correctness and correct them when they turn out to be confused or mistaken, that philosophers found it necessary to construct their theories of the nature and place of minds. Finding mental-conduct concepts being regularly and effectively used, they properly sought to fix their logical geography. But the account officially recommended would entail that there could be no regular or effective use of these mental-conduct concepts in our descriptions of, and prescriptions for, other people’s minds. (1949a, 17)