So Peirce invented both the quincuncial projection and FOL? (02)
Is FOL only useful to people who live in the northern hemisphere too? (03)
No! Please don't justify! I'm sure if the navigator keeps a truer
model of the world in mind, it is possible to make the necessary
Just as when we finally start to look at a more fundamental topology
for meaning it will surely be possible to relate that to one or other
logical simplification at will (05)
If we persist in ignoring the curvature of the Earth in all our
discussions of flat maps, of course, life will appear very puzzling
I don't think there is any danger of logic being "ignored" in this
forum. But I would like to invite those hitherto limited to one or
other logical projection to consider a more fundamental topology for
meaning. Not instead of logic, you understand. Just enough, in the
first instance, to make some of the "intractable" aspects of logic (in
its applications to meaning?) a big more "tractable". (07)
Variations of "many-body theory" (e.g. Vector Symbolic Architectures,
Chris Anderson's "Google") offer an interesting solution. They do
require that we build a definition of "meaning" beneath logic, rather
than trying to graft one on top, but logic itself likely wouldn't
On Sun, Sep 28, 2008 at 11:47 PM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
> This discussion leads to many issues about mappings:
> RF>> The work of Schmidhuber and Hutter avoid these "pitfalls"
> >>> [of logic] by ignoring formal logic and seeking a basis for
> >>> meaning in prediction/probability.
> JFS>> That's like a carpenter who struck his thumb with a hammer and
> >> later avoids the pitfalls of hammers by using nothing but saws.
> RF> I think of it in terms of a different metaphor. I think of it
> > as a cartographer who finds projections to a plane are always
> > distorted, and so decides not to limit herself to flat maps.
> Interesting comparison. It just so happens that C. S. Peirce was
> not only the person who invented the algebraic notation for FOL
> (in 1880-85), he also invented the quincuncial projection of the
> earth to a plane (1879). See the Wikipedia entry:
> Unlike the common Mercator projection, which exaggerates the
> areas of Canada, Alaska, and Greenland, the Q. projection
> preserves relative areas. Although it has some distortions,
> it has the very important property that great circle routes
> (for shipping and airlines) can be drawn with a straight edge
> on that map (to an approximation with negligible error for
> navigational purposes).
> This example shows why a person who rejects flat maps would
> overlook an important application. By that, I do *not* claim
> that people should limit themselves to flat maps, but that
> they should "never say never" to any point of view.
> As for category theory, its basic focus is on maps of all
> possible kinds. There are an infinity of ways of mapping one
> shape to another with many different kinds of distortions,
> some of which highlight different aspects of the things that
> are being mapped.
> Similarly, there are many different ways of mapping language
> to logic or logic to language. The English words 'and', 'or',
> 'not', 'some', and 'every' are landmarks that a mapping might
> preserve, highlight, or distort. But many different ways of
> mapping the content words of language will also preserve,
> highlight, or distort other aspects for various purposes.
> Instead of "ignoring logic", I suggest that people keep in
> mind that it shows up as those ubiquitous landmarks in English
> and other natural languages. Languages wouldn't have those
> words if people didn't find logical aspects important.
> John (010)
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