An utter disappointment but not devoid of value. I doubt i'll bother to continue reading, so here are my initial thoughts.
I'm far too dim to understanAn utter disappointment but not devoid of value. I doubt i'll bother to continue reading, so here are my initial thoughts.
I'm far too dim to understand Lakoff + Núñez's ideas. Or maybe they're not saying anything other than people have to use language to express and explain mathematical ideas and language is entirely metaphorical. Or maybe they're saying that mathematics is entirely metaphorical and language is fundamental. There's a philosophical chicken-and-egg problem with this entire book. Or maybe i don't know what i'm talking about. Or maybe i don't know what L+N are talking about. I'm a 25 watt bulb in an array of Klieg lights.
I've always wanted to share my love for this crazy Chick Publication and now might be my best/only chance. While reading L+N's first few "mappings" of a "metaphor" from a "source domain" onto a "target domain," i couldn't stop thinking of the 4th-from-last page of Are Roman Catholics Christians? (note: Chick Pubs are only good if you wanna laugh at a fundamentally disabled mind]
Obviously L+N's book is yet another that i'm unqualified to critique so i searched the interwebs for reviews and found one by a professional mathematician that i wish i'd written.
Assuming you hold no strong prejudices regarding "cognitive science" or "the embodied mind" or "Platonism" or "Aristotelianism," maybe the following quotes from James Madden's article (Notices of the AMS. 2001;48:1182–88) will convince you to be on my side of this futile debate.
Presumably, when an individual is engaged in mathematical work, that person is guided by metaphors that are somehow represented in his or her own brain.... Unfortunately, Lakoff and Núñez do not provide any illustrations of what they suppose goes on in "real time," so this is about as much as I can say.
This brings me to my first main criticism concerning the metaphor hypothesis: What is the quality of the evidence for it?... I would like to have seen direct support for the metaphor hypothesis from the observation of mathematical behaviors. (1184-5)
"After a while, the notion of metaphor seems to become a catchall." (1185) Did Madden grow as tired of the vagueness and ubiquity of the term metaphor as i did?
Madden damns with faint praise and cuts deep into the heart of L+N's premise:
The idea that metaphors play a role in mathematical thinking is quite attractive, but what is needed is a notion specific and precise enough so that people working independently and without consulting one another can discover the same metaphors and agree on the functions they perform. I do not think we have this yet. (1185)
And a summary of sorts:
If I think about the portrayal of mathematics in the book as a whole, I find myself disappointed by the pale picture the authors have drawn. In the book, people formulate ideas and reason mathematically, realize things, extend ideas, infer, understand, symbolize, calculate, and, most frequently of all, conceptualize. These plain vanilla words scarcely exhaust the kinds of things that go on when people do mathematics. (1187)
Madden does give L+N credit for "shar[ing] with us their intuitions about the way the mathematical mind operates," but he's not convinced that anything they said has been scientifically tested even though it's presented to us as if it had been proven....more
I hope that Goodreads is available to you in The Afterlife because i'd like to talk with you about your son Friedrich, the self-proDear Mr. Nietzsche,
I hope that Goodreads is available to you in The Afterlife because i'd like to talk with you about your son Friedrich, the self-proclaimed philosophizer.
I don't know what to do with him. He can't seem to get along with anybody. He undermines everybody else's statements but protects himself from criticism by making no claims of his own (unless "You are wrong!" and "That is stupid!" count?). When we point out the illogic of his strategy, he spews more invective, which is frequently nothing more than name-calling.
There are so many people here who really love your son's work but i find him to be intolerable … and i'm not a Christian! and i'm not one to lightly quit reading a book! and i really wanna read his stuff. He's allegedly crucial to Western philosophy. I'm so mad at him right now that i'm only willing to speculate that the sum total of his contribution is merely the groundwork for the lamest proponents of the lamest forms of post-modernism. Agh! i don't wanna make accusations sans justification. That's hardly useful. So i need to read more but
Enough with the unsubstantiated over-generalizations! Opinions are not truths! Insults are not arguments! Offer something of your own or just shut the fuck up already!
I think Russell equates language with thought. I think the two activities are quite similar but not the same thing. (I wish i could prove either asserI think Russell equates language with thought. I think the two activities are quite similar but not the same thing. (I wish i could prove either assertion.) Nevertheless, i profited from this book and i have quotes to back that up.
All knowledge, we find, must be built up upon our instinctive beliefs, and if these are rejected, nothing is left. (14-15)
by organising our instinctive beliefs and their consequences, by considering which among them it is most possible, if necessary, to modify or abandon, we can arrive, on the basis of accepting as our sole data what we instinctively believe, at an orderly systematic organisation of our knowledge, in which, though the possibility of error remains, its likelihood is diminished by the interrelation of the parts and by the critical scrutiny which has preceded acquiescence. (15)
The faculty of being acquainted with things other than itself is the main characteristic of a mind. Acquaintance with objects essentially consists in a relation between the mind and something other than the mind; it is this that constitutes the mind's power of knowing things. (27)
what is important is not the fact that we think in accordance with these laws* but the fact that things behave in accordance with them; in other words, the fact that when we think in accordance with them we think truly. (50)
we feel some quality of necessity about the proposition "two and two are four," which is absent from even the best attested empirical generalisations. Such generalisations always remain mere facts: we feel that there might be a world in which they were false, though in the actual world they happen to be true. In any possible world, on the contrary, we feel that two and two would be four: this is not a mere fact, but a necessity to which everything actual and possible must conform. (53)
The fact seems to be that all our a priori knowledge is concerned with entities that do not, properly speaking, exist, either in the mental or in the physical world. These entities are such as can be named by parts of speech which are not substantives [nouns]; they are such entities as qualities and relations. (61)
The world of being [the world of universals] is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence, is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that can do either good or harm, everything that makes any difference to the value of life and the world. According to our temperaments, we shall prefer the contemplation of the one or of the other. The one we do not prefer will probably seem to us a pale shadow of the one we prefer, and hardly worthy to be regarded as in any sense real. But the truth is that both have the same claim on our impartial attention, both are real, and both are important to the metaphysician. (69)
all refutation must begin with some piece of knowledge which the disputants share; from blank doubt, no argument can begin. Hence the criticism of knowledge which philosophy employs must not be of this destructive kind, if any result is to be achieved. Against this absolute scepticism, no logical argument can be advanced. (105)
The criticism [that philosophy aims at] is not that which, without reason, determines to reject, but that which considers each piece of apparent knowledge on its merits, and retains whatever still appears to be knowledge when this consideration is completed. (106)
_______________ *these laws = The (so-called) Laws of Thought = (1) Whatever is, is (aka, Identity); (2) Nothing can both be and not be (aka, Contradiction); (3) Everything must either be or not be (aka, Excluded Middle)....more
One ought to write reviews of books one has read. Ignore that this book will never have more than 11 Goodreads ratings. Thus, a review as such.
One ougOne ought to write reviews of books one has read. Ignore that this book will never have more than 11 Goodreads ratings. Thus, a review as such.
One ought to understand a contemporary's full explanation more readily than the original, 250-year-old text in translation. Oy vey, Kant's reasoning is so hard for me to follow that even Paton's well-written prose frequently befuddles me.
One ought to disregard one's inadequacies when rating a book. Screw that! i'm docking 1 star because a. HJ Paton did not write this book for dilettantes like me and b. my foolhardy overconfidence prevented me from seeing the obviousness of that until i'd repeatedly processed ideas as if they were mere descriptions of Kant's logic only to realize that Paton had actually been pointing out error, contradiction, flaw, inconsistency, muddled terminology, et al.
One ought to read The Five Formulae of Kant's categorical imperative. So even if you read nothing else, go to page 129 and check them out. If you're extra curious, give Groundwork a read, too, and don't forget my recommendation to have this (Paton's) book on hand. I. The Formula of Universal Law Act only on that maxim through which you can at the same time will that it should become a universal law. Ia. The Formula of the Law of Nature Act as if the maxim of your action were to become through your will a universal law of nature. II. The Formula of the End in Itself So act as to use humanity, both in your own person and in the person of every other, always at the same time as an end, never simply as a means. III. The Formula of Autonomy So act that your will can regard itself at the same time as making universal law through its maxim. IIIa. The Formula of the Kingdom of Ends So act as if you were always through your maxims a law-making member in a universal kingdom of ends.
One ought to learn, as claimed in the Preface (15), that a. "Kant contrived to say something new about morality." b. "[Groundwork] is an indispensable book for all who profess to think seriously about moral problems." c. "... his actual teaching [as opposed to common misinterpretations of it] … is always reasonable, even if it may not always be correct."
One ought to realize that a. Moral behavior results simply, exclusively from duty (ie, not to get a reward or avoid punishment, though these motives don't necessarily constitute immoral behavior). b. Moral behavior is possible only if rational beings are free. c. Discussions of morality depend upon the stipulation that humans can be rational.
One ought to consider the validity of the following claims. a. "reason is a poor instrument for seeking happiness and that for this purpose it must inevitably fail" (109) b. therefore, "we should [not] abandon reason altogether in favour of instinct" because reason "must serve some higher purpose than the satisfaction of desire" (110; emphasis mine)
One ought to admit one's limitations. Kant said that nobody can prove freedom is inherent to humanity but we must proceed as if we are free (from Ch XXI §2; 217).
One ought to admit that reason is possible and necessary. Or as a much smarter person puts it:
Reason must -- if it is to be reason at all -- regard itself as the author of its own principles independently of external influences. (218)
If reason's conclusions are nothing more than the inevitable effects of causes outside of human reason, then reason itself is the same kind of "force of nature" as the ocean's tides or the progression of the seasons as evidenced by changes in plant life. And humans are nothing more than carbon-based machines capable only of the illusion of self and the illusion of freedom.
One ought to consider the possibility that "The mind affects itself." (235) You might say a. We aren't just bodies and we aren't just minds. b. Mind isn't just a function of the body and the body isn't just an illusion spawned in the mind. There are 2 concurrent, discrete points of view. 1. Obviously we are physical. (Kant's term is "phenomenal.") As such we are subject to the laws of nature; we exist in time; we have irrational desires. 2. There exists an "I" who conceives of the phenomenal self as being self-evident. One might call this the soul or the spiritual self; one might call it the mind. Kant's term is "noumenal."
Paton's historian analogy might help:
If we consider, for example, a historian, it looks -- from one point of view -- as if he stood above the battle as a timeless observer assigning to each historical event its place in a causal series which he understands. Yet when we turn to consider what he has done in composing his history, this too appears as an historical event in the same causal series, and in no way different from any other historical event. But in saying this we seem again to be ourselves above the battle -- only to find on reflection that our judgement is in turn something to be judged as on the same level with its object. Every man is, as it were, the historian of his own life, and it looks as if Kant were right in saying that we must regard ourselves from two different points of view. (235)
One ought to include the quote below. Why? Because i wanted to say stuff about it.
… we suppose that every event is necessary and that we understand its necessity by discovering its cause [the sun must rise + set; why? because the earth rotates]. In this way we explain a conditioned necessity by discovering its condition. But to understand the necessity of the cause, we must discover the cause of the cause [why does the earth rotate? because it was formed by gravity gathering its constituent particles together] and so ad infinitum [why? because mass affects space-time this way]. However far back we go, we never come to anything other than a conditioned necessity, and this is no more satisfying to human reason than the conditioned necessity with which we started [why does mass affect space-time this way? because i'm your mother and i said so!]. Theoretical reason must conceive the totality of causes, which, because it is a totality of causes, cannot itself be caused. It is this Idea [that] gives us the conception, however empty, of an uncaused cause or a free cause. In the same way theoretical reason must conceive the totality of conditions for every conditioned necessity, a totality which must itself be an unconditioned necessity, if there is to be any necessity at all. The conception of the moral law as unconditionally necessary is only a further example of the activity of reason (here of practical reason) in conceiving -- and seeking to realise -- an unconditioned necessity. [bracketed commentary entirely mine; sorry]
We are free. We are rational. We cannot stop ourselves from attempting to resolve the unresolvable. When we make our goal the Resolution of the Unresolvable, we must be satisfied with claims based only on Ideal propositions; empirical evidence is neither possible nor warranted.
One ought to be satisfied with the previous paragraph's assertion. If you can't, then i join Paton + Kant in saying that you are essentially using reason to "prove" that reason is impossible....more