Dear Franklin, Cathy, Lists -
A small clarification: Peirce's *BxD=A* idea, I think, should not be
taken a device for the arithmetic calculation of exact information size -
it is rather the proposal of a general law relating Breadth and Depth. His
idea comes from the simple idea that when intension is zero, there is no
information, while when extension is zero, there is also no information -
and that is the relation of the two factors in a product. (It is a bit
like his first Boole-inspired definition of universal quantification as a
product - he defines truth as 1, falsity as 0, then, in order to be true,
each single case of a universal proposition should be true - if any single
one of them is false, the total product of them all will be zero.)
The BXD=A idea allows him to investigate what happens if intension or
extension are in- or decreased, etc. - even if not being able to express
that in precise numbers.
Best
F
Den 20/04/2015 kl. 01.14 skrev Franklin Ransom <
[email protected]>:
Cathy, lists,
Well, look at this way: It is possible for there to be objects in the
senses which are yet not perceived, because we do not yet have any idea of
what it is to which we are looking. It takes a hypothesis to introduce a
new idea to us to explain what it is, which hypothesis we can then put to
the test. In order to do so, we must determine what kinds of characters to
look for (deduction helps here) and then look for existent objects
(induction) to learn whether the purported relations between characters
obtain in fact, and in this way we come to understand the thing which we
are experiencing. It is of course induction which gives us more
information; abduction simply gives us the idea which needs to become
informed, and deduction is merely explicative, based on relating the idea
to other ideas and previously gathered information regarding those ideas.
Obviously, we cannot conduct induction without end, because that is a
practical impossibility. Our 'sum', as you put it, far from being always an
infinity, will very likely never be an infinity in practice, in whatever
sense you mean to understand the application of infinity to a 'sum' of
information. Of course, as an ideal, where science, the community of
inquiry as such, continues to investigate, it is possible for the
information of an idea to reach a much greater 'sum' than would otherwise
be possible for individuals such as you or me. But it is a commonplace of
science that ideas that work and continue to work are understood more
thoroughly in their relations to other ideas over the course on inquiry.
This means of course that not only the breadth, but also the depth of the
idea continues to grow. As a result, typically, rather than tending to make
comparisons moot, we start to see a hierarchy of ideas and related sciences
appear.
Consider this passage: "The former [Cows] is a natural class, the
latter [Red Cows] is not. Now one predicate more may be attached to Red
Cows than to Cows; hence Mr. Mill's attempts to analyze the difference
between natural and artificial classes is seen to be a failure. For,
according to him, the difference is that a real kind is distinguished by
unknown multitudes of properties while an artificial class has only a few
determinate ones. Again there is an unusual degree of accordance among
naturalists in making Vertebrates a natural class. Yet the number of
predicates proper to it is comparatively small" (NP, p.238, quoting
Peirce). We can see here that further simplifications are introduced, so
taking what is learned about various vertebrates, a new idea, that of
vertebrates, appears which simplifies the characters involved. Conversely,
species under vertebrates will become much more determinate in terms of
their characters, but be simplified with respect to their extension.
You said above: "Under synechism every real object has an infinite
number of attributes, and every meaningful predicate or general term
effectively has an infinite number of aspects, so a simple multiplication
of B x D is pointless." And yet natural kinds appear, in which certain
attributes, predicates, or aspects appear significant, and others do not.
It is precisely the work of abduction to simplify what is observed so that
what is essential is grasped, and not simply a never-ending multitude of
characters. Such simplification is always with respect to a purpose. With
respect to natural kinds, such purpose, or telos, is objective, and we see
nature all around us selecting certain characters over others as more
significant. If this were not true, natural science would be impossible. As
to real objects, yes they have an infinite number, but not all of them are
relevant to the purpose of interaction with the real object. Certain
meaningful attributes are selected for in attention in order to aid conduct
with respect to some purpose at hand. Information relevant to that purpose
is what is sought for.
I do have a couple of questions for you:
For one, would you explain the idea that propositions can't be counted?
I would suppose that when conducting an experiment, the number of times a
fact is determined relates to developing a frequency ratio, which means
that propositions can be counted in this case, when they are instances of
the same kind or type, or close enough. But if we are talking about
propositions which are all different from each other, than I can see the
point, because that is like trying to count qualities, which isn't very
helpful for comparison. But of course, that's not the same thing as having
so many propositions that they go to infinity and thus can't be counted for
that reason. Is this what is meant, that there are supposed to be so many
propositions that they go to infinity? Perhaps it would be helpful if you
referenced the text where Peirce mentions this.
For two, you said "Even an artifically generated term such as 'red' and
'cow' will still partake of the surprisingness of 'cow' and 'red' taken on
their own." What does surprisingness have to do with what we're discussing?
-- Franklin
On Sun, Apr 19, 2015 at 4:42 PM, Catherine Legg <[email protected]>
wrote:
Hi Franklin,
Sorry for taking so long to reply. Thanks for setting me straight on
Peirce still using the idea of breadth x depth later on in his career. I
have to say though that I don't understand how such a metric might work in
the later semiotic, just because it seems to me that the result of such a
'sum' will *always* be an infinity of an extremely high order, so any
comparisons seem moot. As Peirce notes, propositions can't be counted. Even
an artifically generated term such as 'red' and 'cow' will still partake of
the surprisingness of 'cow' and 'red' taken on their own.
Best regards,
Cathy
