Lost In Translation (nee Dementia Redux)
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| NB. Reposting this message to the Ontology List
| because it did not make it through to the Archive,
| and was apparently never distributed via Ontology,
| despite what the list server claims to the contrary.
Edward, John, ...
Because this sense of "having heard it before"
arose in the interaction among some discussions
that I've been having in a couple of other places
with some bits of flotsam from my idle surf list,
let me supply some additional context that is
designed to get down to the actual problem.
This is from a discussion entitled "Blocks On The Road of Inquiry" (BOTROI),
which itself refers back to some earlier discussions on the SUO & ONT lists
that had to do with "Hypostatic And Prescisive Abstraction" (HAPA):
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BOTROI. Discussion Note 14
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Re: HAPA 10. http://suo.ieee.org/ontology/msg05121.html
Re: HAPA 11. http://suo.ieee.org/ontology/msg05122.html
In: HAPA. http://suo.ieee.org/ontology/thrd8.html#05089
| Relatives Of Second Intention
|
| The general method of graphical representation of propositions has now
| been given in all its essential elements, except, of course, that we
| have not, as yet, studied any truths concerning special relatives;
| for to do so would seem, at first, to be "extralogical". Logic in
| this stage of its development may be called 'paradisaical logic',
| because it represents the state of Man's cognition before the
| Fall. For although, with this apparatus, it easy to write
| propositions necessarily true, it is absolutely impossible
| to write any which is necessarily false, or, in any way
| which that stage of logic affords, to find out that
| anything is false. The mind has not as yet eaten
| of the fruit of the Tree of Knowledge of Truth
| and Falsity.
|
| Probably it will not be doubted that every child in
| its mental development necessarily passes through
| a stage in which he has some ideas, but yet has
| never recognised that an idea may be erroneous;
| and a stage that every child necessarily passes
| through must have been formerly passed through
| by the race in its adult development. It may
| be doubted whether many of the lower animals
| have any clear and steady conception of
| falsehood; for their instincts work
| so unerringly that there is little
| to force it upon their attention.
| Yet plainly without a knowledge
| of falsehood no development
| of discursive reason can
| take place.
|
| This paradisaical logic appears in the study of non-relative formal logic.
| But 'there' no possible avenue appears by which the knowledge of falsehood
| could be brought into this Garden of Eden except by the arbitrary and
| inexplicable introduction of the Serpent in the guise of a proposition
| necessarily false. The logic of relatives affords such an avenue,
| and 'that', the very avenue by which in actual development,
| this stage of logic supervenes. It is the avenue of
| experience and logical reflexion.
|
| By 'logical' reflexion, I mean the observation of thoughts
| in their expressions. Aquinas remarked that this sort of
| reflexion is requisite to furnish us with those ideas
| which, from lack of contrast, ordinary external
| experience fails to bring into prominence.
| He called such ideas 'second intentions'.
|
| It is by means of 'relatives of second intention'
| that the general method of logical representation
| is to find completion.
|
| C.S. Peirce, 'Collected Papers', CP 3.488-490,
|"The Logic of Relatives", 'The Monist', vol. 7,
| pp. 161-217, 1897.
Another way of stating my concern is to say that something
has evidently been lost in the translation from classical
discussions about higher intentional logic to epi-Fregean
ramblings about the orders of logical formalism. I begin
to suspect that the current fuss about "order" is similar
to those pre-Hausdorff confusions about dimensionality.
Jon Awbrey
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> John,
>
> This is an darn interesting and a very fundamental discussion. Points, as
> you know are not always finite points, but frequently are subsets that map
> into points that belong to certain dimension (in particular a function 'add'
> can be decomposed into how many bits it can add, how many machine cycles
> does it take to execute and so on). Also the mathematics does not provide
> methodology to let you measure the completeness of a set. Perhaps I should,
> but will not bring Gödel in to that.
>
> Claim 1 'claimed by Jon A. and restated by you John S. as "Jon's recent
> example is the theorem that all the points on a two-dimensional surface can
> be put in a one-to-one correlation with the points on a one-dimensional
> line." is general while Claim 3 is particular since you are using not all
> the point but a particular set of points namely functions. How about other
> properties or points such as color of a computer, or in particular its
> speed?
>
> What I'm saying is that we have to careful in defining our 'apples' or they
> may look like 'oranges'. Expanding on your claim that is if we define our
> space in terms of functions only then it is true that our desktop computers
> have not change a bit since its first introduction, but if we include
> attribute such as performance then we have a different 'apple', don't we.
> If I understood Jon correctly he warned about comparing apples and oranges
> since while they do belong to the same category of fruits (and therefore can
> produce a sizable set of 1 to 1 mapping) but as we know apple is an apple
> and an orange is an orange.
>
> Best
>
> Edward
>
> *********1000 0111 -0111***********
> Edward Dawidowicz
> US Army, RDECOM, CERDEC
> Command and Control Directorate (C2D)
> Myer Center
> Fort Monmouth, NJ 07703
> Voice (732) 427-4122
> Fax (732) 427-3440
> edward.dawidowicz@mail1.monmouth.army.mil
> edward.dawidowicz@us.army.mil
>
> -----Original Message-----
> From: John F. Sowa [mailto:sowa@bestweb.net]
> Sent: Monday, April 12, 2004 5:43 PM
> To: Jon Awbrey
> Cc: Dawidowicz, Edward RDECOM CERDEC C2D; SUO
> Subject: Re: Dementia Redux
>
> Jon, Edward, et al.,
>
> There are many useful theorems that are
> worth knowing for two reasons:
>
> 1. They provide useful criteria for dismissing
> many kinds of bogus claims as pure BS.
>
> 2. They are important for self defense, when
> somebody tries to use them to dismiss
> what you're doing.
>
> Jon's recent example is the theorem that all the points
> on a two-dimensional surface can be put in a one-to-one
> correlation with the points on a one-dimensional line.
>
> Claim 2: Two versions of logic are equally expressive
> iff there is a one-to-one correlation of statements
> in one to statements in another.
>
> Claim 3: Two computing systems are equivalent iff there
> is a one-to-one correlation of the computable functions
> in one to the computable functions of the other.
>
> These statements are good to know, but it is also
> important to know all the qualifications that are
> not stated in those claims.
>
> For example, every digital computer that has ever been
> designed so far is equivalent, according to claim 3,
> to a Turing machine. However, everybody who has ever
> replaced a 5-year-old computer by a new one knows very
> well that the new one can finish any computation in a
> tiny fraction of the time taken by the old one.
>
> Similarly, two different langauges that are equivalent
> to first-order logic by claim 2 might be very different
> in their ease of use, readability, etc.
>
> John
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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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