My English is really terrible, I hope, Your German ist good enough to
read Kant, because with Kant in English I can see only logical
problems. no transcendentalphilosophic problems. This is a problem, at
first for the english readers, they only understood the half (Like my
English says only the half, if i speak or write).
But our question ist not a transcendental problem. I wrote in my first
lesson (I am the teacher in this school!): "there is a difference
between putting two numbers together (this give us two elements) or to
add the number 5 and the number 7: the second operation give us 12
elements."
This means, that Bolzano dont think at first on the natural series of
numbers (1, 2, 3, ... n), he think on a series of Elements, of which
we can say, it is the first element, the second, and so on, but its
count every Element only as "one". We can also count the series of
natural numbers: "1" ist the first number, "2" is the second number,
and so on, but every Element of this series is a number, which count
not the same; "1" count one , "2" count two, and so on.
Addition is not counting numbers. If I count the numbers 1, 2, 3, I
get three, like if I count three elements with the value 1 or a other
value. If I add the numbers 1, 2, 3, than I get 6. How Russell tells
us also, means "1" one element, "2" two elements, "3" three elements,
and so on. Addition means, that we have to count the Elements, which
given by the numbers. 1 + 2 + 3 as numbers give one and two and three
elements, counting this elements give us six elements, which means
everything, numbers, triangels, sunsystems. Counting three numbers,
give as three elements, which means three numbers. -- You see the
difference!
Kant start to think about this as a problem of grammar in simple S - P-
sentences (Subjekt und Pr=E4dikat eines einfachen Satzes, z. B.: VxFx).
To give a predicat (not a statement!) to the subjekt is in one point
similar to counting: it says nothing about, how we can construct the
subjekt to get the quality of the predicat. In former centuries, we
have called this problem the ontological problem of "Inh=E4renz" or
"inesse". So is the next step, to think about numbers as proposition,
and addittion should be a defined relation between sentences
(propositions). A number is now a propostion, which say something like
"This element ist the first, second, third, ... and so on" or "This
number have one, two, three ... and so on elements". For example: If I
say: "There is a cow and a horse", than I can count one cow and one
horse, but two animals, or at least two "things". It is the same
structur of the judgment (means logical proposition). -- Bolzano called
the first kind of sentences "unvollst=E4ndige Summendefinition", the
second kind of sentences "vollst=E4ndige Summendefinition". The first
kind of sentences defined the place in a series of undefined elements,
and the relation between such sentences are not formal definable,
because, for example, we dont know, from which side we have start to
count (its remembering me a little on my discovery of the Argument of
Inkongruenz few years befor Buroker).
Only the second kind of sentences allowed to define a complete
relation between the propositions, we called "numbers", and the
relation is defined with a grammar operation, we called in arithmetics
"addition": counting the "elements" of all given numbers (this are the
predicats of the elements as subjekt of the propositions), not
counting numbers (propositions). There is no platonic idea "behind" a
number in the formal solution, about Kant start to think, and which
Bolzano have worked out. "Every concept must be defined by a schema of
constructing"!
Now Your homework: Write me, what You think about Burokers Argument
of Inkongruence in constructs of pure imagination!
Regards
Wolfgang Cernoch
------------------------------
On 11 Apr., 16:26, Malrassic Park <malen...@[EMAIL PROTECTED]
> wrote:
> On Fri, 11 Apr 2008 03:16:58 -0700 (PDT), Wolfgang Cernoch
>
>
>
> <wolfgangcern...@[EMAIL PROTECTED]
> wrote:
> >On Mar 23, 5:30 pm, Malrassic Park <malen...@[EMAIL PROTECTED]
> wrote:
> >> On Sun, 23 Mar 2008 00:07:12 -0700 (PDT), Wolfgang
>
> >> <wolfgangcern...@[EMAIL PROTECTED]
> wrote:
> >> >On 18 Feb., 10:19, "Phil Roberts, Jr." <phil...@[EMAIL PROTECTED]
>
wrote:
> >> >> It has been many years since I've read the Critique of Pure
> >> >> Reason, and perhaps I am misrembering, but I was always
> >> >> perplexed by Kant's insistence that 1 + 1 =3D 2 is a
> >> >> synthetic proposition. If an analytic proposition is
> >> >> simply one that is true by denfintion, e.g.,
> >> >> all unmarried men are bachelors, wouldn't 1 plus 1
> >> >> equals 2 be in this category as well?
>
> >> >> --
>
> >> >> Phil Roberts, Jr.http://www.rationology.net
>
> >> >> .
>
> >> >Kant don't say, that 1+1=3D2 is in any case (perspective of
> >> >construction) a synthetic judgment. But he say this for 5+7=3D12
(Axio=
me
> >> >der Anschauung), and this is in any perspective of construction a
> >> >synthtecic judgment, because there is a difference between putting
> >> >two numbers together (this give us two elements)
>
> >> Or one element, the number 57.
>
> >> >or to add the number
> >> >5 and the number 7: the second operation give us 12 elements. I
think,=
> >> >it means, that in arithmetic is not possible to think about the
number=
> >> >7 as an pr=E4dicat
>
> >> That's 'a predicate' in English.
>
> >> >of a subject, called number 5, its have to be a
> >> >conclusio. But its possible to think about 5+7 as two sentences, and
> >> >the relation between is not >>true<< or >>false<< like in logic, but
t=
he
> >> >constructed number 12. After this it is possible to do this
> >> >>>analytic<<, because we need the rule, not the cause of the rule.
>
> >> That was obscure. But let's just say that constructing the answer to
> >> the problem 5+7 is by synthesis, while 'tearing down' the answer 12
in
> >> to its elements is done by analysis.
>
> >> So to say that 5+7=3D12 is an analytical proposition would be begging
> >> the question, which in this case involves assuming the answer 12 (as
> >> "obviously true") before proving it. This is why Kant stated that
> >> using a much larger arithmetic problem takes away the obviousness of
> >> the solution along with its apparent analyticity.
>
> >> --
> >> How was chirch this morning? - Michael Gordge
>
> >Sorry, my motherlanguage is german, and I have to say, I read Kant in
> >original.
>
> Terrible. English is the best.
>
> >Its the historical argument from Bernard Bolzano (19. century) and
> >from Albert Grote (20. century).
> >With the described operation You never becomes 57. Read exactly!
>
> I did "read exactly." You said that putting two numbers together to
> give one number is different from getting two numbers. Then I replied
> that there is also a difference between the 12 and the number 57. You
> can't seem to explain why adding 5 to 7 doesn't give one number, 57.
>
> > And
> >what i have said to analytic and synthetic judgements is the same as
> >Willard Quine do. Its a diffrence between "Ordinal"-number and
> >"Cardninal"-number! At first we count with ordinal-numbers like every
> >natural arithmetic before the greeks.Than we constructed "numbers"
> >with set-theory like Russell (extensional logik) or like Bolzano
> >(before he used the peano-definition as a short and useful form) and
> >Kant (after he deals with empirical roots) with grammar (intemnsional
> >logic).
>
> We don't need Peano to add numbers, we just add 5 to 7. But why can't
> it give 57 instead of 12?
>
> >Philosophy is a school not a chirch! Good morning! Wolfgang Cernoch
>
> Then how was school this morning? Did you do your homework?
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