On Sat, 23 Aug 2008 23:24:03 -0700 (PDT), Immortalist
yahoo.com> wrote:
>On Aug 23, 4:42 pm, John Larkin
>
highNOTlandTHIStechnologyPART.com> wrote:>> On Sat, 23 Aug 2008 16:05:47 -0700 (PDT), Immortalist
>>
>>
>>
>>
yahoo.com> wrote:>>>On Aug 23, 10:06 am, John Larkin
>>>
highNOTlandTHIStechnologyPART.com> wrote:>>>> On Fri, 22 Aug 2008 23:49:12 -0700 (PDT), Immortalist
>>
>>>>>On Aug 21, 11:21 am, nada
gmail.com> wrote:>>>>>> Another idiot who doesn't know what the subject line is supposed to be
>>>>>> used for!
>>
>>>>>The Problem of the Criterion
>>
>>>>>A general argument against the invocation of any standard for
>>>>>knowledge has come to be known as "the problem of the criterion." As
>>>>>we have just seen, there have been disputes about standards of
>>>>>knowledge. Some are about particular kinds of arguments that provide
>>>>>evidence for knowledge claims. As we will see shortly, others are
>>>>>about the degree of evidential support or reliability required for
>>>>>knowledge. The Pyrrhonian skeptics argued that such disputes cannot be
>>>>>settled.
>>
>>>>>If the dispute is to be settled rationally, there must be some means
>>>>>for settling it. It would do no good of each side simply to assert its
>>>>>position without argument. So how would a standard of knowledge (or
>>>>>"criterion of truth," in the language of the Stoics) be defended? It
>>>>>could only be defended by reference to some standard or other. If the
>>>>>standard under dispute is invoked, then the question has been begged.
>>>>>If another standard is appealed to, the question arises again, to be
>>>>>answered either by circular reasoning or by appeal to yet another
>>>>>standard. So either the process of invoking standards does not
>>>>>terminate, or it ends in circular reasoning, and thus the dispute over
>>>>>the standard cannot be settled rationally.
>>
>>>> Mathematicians worked this out long ago. We agree to accept a few
>>>> basic axioms, and prove the rest within that context. The axioms
>>>> include some principles of logic that facilitate the "proof"
>>>> processes.
>>
>>>> Works fine until somebody demonstrates that one of the axioms is
>>>> false, which doesn't happen much nowadays.
>>
>>>> John
>>
>>>I agree, it kind of goes with the stereotype; "assume that A = X" But
>>>I disagree with you idea that the higher level statements are
>>>contradicted by new evidence, it seems that there are small changes
>>>almost daily to sum assumed axioms.
>>
>>>Here Kant tries to show how adding two numbers is really a complex set
>>>of entirely independent arguments.
>>
>>>V. IN ALL THEORETICAL SCIENCES OF REASON SYNTHETIC
>>
>>>A PRIORI JUDGMENTS ARE CONTAINED AS PRINCIPLES
>>
>>>1. All mathematical judgments, without exception, are synthetic. This
>>>fact, though incontestably certain and in its consequences very
>>>important, has hitherto escaped the notice of those who are engaged in
>>>the analysis of human reason, and is, indeed, directly opposed to all
>>>their conjectures. For as it was found that all mathematical
>>>inferences proceed in accordance with the principle of contradiction
>>>(which the nature of all apodeictic certainty requires), it was
>>>supposed that the fundamental propositions of the science can
>>>themselves be known to be true through that principle. This is an
>>>erroneous view. For though a synthetic proposition can indeed be
>>>discerned in accordance with the principle of contradiction, this can
>>>only be if another synthetic proposition is presupposed, and if it can
>>>then be apprehended as following from this other proposition; it can
>>>never be so discerned in and by itself.
>>
>>>First of all, it has to be noted that mathematical propositions,
>>>strictly so called, are always judgments a priori, not empirical;
>>>because they carry with them necessity, which cannot be derived from
>>>experience. If this be demurred to, I am willing to limit my statement
>>>to pure mathematics, the very concept of which implies that it does
>>>not contain empirical, but only pure a priori knowledge.
>>
>>>We might, indeed, at first suppose that the proposition 7 & 5 = 12 is
>>>a merely analytic proposition, and follows by the principle of
>>>contradiction from the concept of a sum of 7 and 5. But if we look
>>>more closely we find that the concept of the sum of 7 and 5 contains
>>>nothing save the union of the two numbers into one, and in this no
>>>thought is being taken as to what that single number may be which
>>>combines both.
>>
>>>The concept of 12 is by no means already thought in merely thinking
>>>this union of 7 and 5; and I may analyse my concept of such a possible
>>>sum as long as I please, still I shall never find the 12 in it. We
>>>have to go outside these concepts, and call in the aid of the
>>>intuition which corresponds to one of them, our five fingers, for
>>>instance, or, as Segner does in his Arithmetic, five points, adding to
>>>the concept of 7, unit by unit, the five given in intuition. For
>>>starting with the number 7, and for the concept of 5 calling in the
>>>aid of the fingers of my hand as intuition, I now add one by one to
>>>the number 7 the units which I previously took together to form the
>>>number, and with the aid of that figure [the hand] see the number 12
>>>come into being. That 5 should be added to 7, I have indeed already
>>>thought in the concept of a sum = 7 & 5, but not that this sum is
>>>equivalent to the number 12. Arithmetical propositions are therefore
>>>always synthetic. This is still more evident if we take larger
>>>numbers. For it is then obvious that, however we might turn and twist
>>>our concepts, we could never, by the mere analysis of them, and
>>>without the aid of intuition, discover what [the number is that] is
>>>the sum.
>>
>>>Just as little is any fundamental proposition of pure geometry
>>>analytic. That the straight line between two points is the shortest,
>>>is a synthetic proposition. For my concept of straight contains
>>>nothing of quantity, but only of quality. The concept of the shortest
>>>is wholly an addition, and cannot be derived, through any process of
>>>analysis, from the concept of the straight line. Intuition, therefore,
>>>must here be called in; only by its aid is the synthesis possible.
>>>What here causes us commonly to believe that the predicate of such
>>>apodeictic judgments is already contained in our concept, and that the
>>>judgment is therefore analytic, is merely the ambiguous character of
>>>the terms used. We are required to join in thought a certain predicate
>>>to a given concept, and this necessity is inherent in the concepts
>>>themselves. But the question is not what we ought to join in thought
>>>to the given concept, but what we actually think in it, even if only
>>>obscurely; and it is then manifest that, while the predicate is indeed
>>>attached necessarily to the concept, it is so in virtue of an
>>>intuition which must be added to the concept, not as thought in the
>>>concept itself.
>>
>>>Some few fundamental propositions, presupposed by the geometrician,
>>>are, indeed, really analytic, and rest on the principle of
>>>contradiction. But, as identical propositions, they serve only as
>>>links in the chain of method and not as principles; for instance, a =
>>>a; the whole is equal to itself; or (a & b) a, that is, the whole is
>>>greater than its part. And even these propositions, though they are
>>>valid according to pure concepts, are only admitted in mathematics
>>>because they can be exhibited in intuition.
>>
>>>2. Natural science (physics) contains a priori synthetic judgments as
>>>principles. I need cite only two such judgments: that in all changes
>>>of the material world the quantity of matter remains unchanged; and
>>>that in all communication of motion, action and reaction must always
>>>be equal. Both propositions, it is evident, are not only necessary,
>>>and therefore in their origin a priori, but also synthetic. For in the
>>>concept of matter I do not think its permanence, but only its presence
>>>in the space which it occupies. I go outside and beyond the concept of
>>>matter, joining to it a priori in thought something which I have not
>>>thought in it. The proposition is not, therefore, analytic, but
>>>synthetic, and yet is thought a priori; and so likewise are the other
>>>propositions of the pure part of natural science.
>>
>>>3. Metaphysics, even if we look upon it as having hitherto failed in
>>>all its endeavours, is yet, owing to the nature of human reason, a
>>>quite indispensable science, and ought to contain a priori synthetic
>>>knowledge. For its business is not merely to analyse concepts which we
>>>make for ourselves a - priori of things, and thereby to clarify them
>>>analytically, but to extend our a priori knowledge. And for this
>>>purpose we must employ principles which add to the given concept
>>>something that was not contained in it, and through a priori synthetic
>>>judgments venture out so far that experience is quite unable to follow
>>>us, as, for instance, in the proposition, that the world must have a
>>>first beginning, and such like. Thus metaphysics consists, at least in
>>>intention, entirely of a priori synthetic propositions.
>>
>>
>>
>> What blather. I bet Kant was bad at math.
>>
>> John
>
>We might, indeed, at first suppose that the proposition 7 & 5 = 12 is
>a merely self-evident proposition, and follows by the principle of
>contradiction from the concept of a sum of 7 and 5. But if we look
>more closely we find that the concept of the sum of 7 and 5 contains
>nothing save the union of the two numbers into one, and in this no
>thought is being taken as to what that single number may be which
>combines both.
>
>The concept of 12 is by no means already thought in merely thinking
>this union of 7 and 5; and I may analyse my concept of such a possible
>sum as long as I please, still I shall never find the 12 in it. We
>have to go outside these concepts, and call in the aid of the
>intuition which corresponds to one of them, our five fingers, for
>instance, or, as Segner does in his Arithmetic, five points, adding to
>the concept of 7, unit by unit, the five given in intuition.
>
>In other words, the summation is a separate group of arguments from
>the adding together arguments, and sometimes it is better to say, "let
>assume not to bugger Kant" that A=x for the sake of consistency, but
>not certainty, no no.
What's your day job?
John
