--- Andree Ehresmann <Andree.Ehresmann@u-picardie.fr> wrote:

It uses categorical tools, e.g. completion theorems, for explaining the=20 emergence of higher order cognitive processes and the formation of a=20 Semantics (possibly without necessarily language). http://perso.wanadoo.fr/vbm-ehr

STRUCTURES AND THEIR PRESENTATION It appears that Prof. Ehresmann=92s category theoretic work on SEMANTICS WITHOUT LANGUAGE provides the necessary concretisation of the experiences mentioned by Prof. Wells (12/20/01) and Prof. Vickers (12/21/01) regarding concepts & words. Also Prof. Lawvere (12/3/01) has pointed that =91concepts=92 (at least in mathematics) can be construed as categories and that these algebraic structures are distinct from =91their presentations=92 (and yet closely related), which are needed to calculate various features of concepts. More importantly, he states that SKETCHES provide the algebraic framework necessary to mathematically capture the =91presentation of concept.=92 Can we bring this mathematical framework of concepts and their presentations in terms of categories and sketches to bear on what appears to be an analogous problem of concepts and language in cognitive science? Secondly, I was wondering whether the two approaches (Prof. Ehreshman & Prof. Lawvere) to the problem are same or different. It seems to me that the problem they are addressing is same (semantics & language, concepts & presentation). --- Steve Vickers <S.J.Vickers@open.ac.uk> wrote:

replacement of talking by pictorial concepts

Sometimes our thinking is not in terms of words but is in terms of what appear like images (pictures, diagrams=85). According to Fodor, to the extent thinking =91says something=92 (proposition), the images in thinking can=92t be the kind of images we see (face of Mono Lisa). You can replace some words with pictures, but how are you going to make a sentence (that can take truth value; true or false) with pictures?=20 Thinking, based on introspection, has, at times, no words but has word-like-images (those =93images=94 that can be used as building blocks of propositions). Some of the devastating arguments against =91thinking can be imagery=92 (the kind you see on TV) are due to Wittgenstein. =93A picture which corresponds to a man walking up a hill forward corresponds equally, and in the same way, to a man sliding down the hill backward=94 (Fodor 1975, 1998). Pictures, by themselves, don=92t support propositions that take yes-or-no truth-values. A string (a concatenation) of images cannot replace well-formed formulae, assertion. I dare not speculate as to whether non-Boolean truth-value object of topos has any bearing on Wittgenstein=92s =91proof against pictures in thinking.=92=20

diagrammatic metaphors (grab an object, place it somewhere, link it to other objects to handle certain events, etc.) get implemented in rather different ways in different languages.

Given images are transformed into words, can we mathematically capture the process? (cf. Cartesian geometry) I would like to have your comments on the above. I am not sure where I stand in this debate; I don=92t even know =91the difference between the way a picture of a circle (black contour on white background) refers to the concept CIRCLE and the way the equation x^2 + y^2 =3D r^2 refers to the same concept CIRCLE?=92 Thanks so much for your time. Thanking you, Sincerely, Posina venkata rayudu Fodor (1975) The Language of Thought, HUP, Cambridge, pp. 174-195. Fodor (1998) When is a dog a DOG, Nature 396:325-327. You will love Fodor (or you will hate him). =3D=3D=3D=3D=3D Posina Venkata Rayudu C/o: Sri. S. S. Chalam Advocate & Notary Public H.No: 39-4-10, Innespeta Rajahmundry =96 533102 Andhra Pradesh, India Phone: 91 (0883) 444232 __________________________________________________ Do You Yahoo!? Send FREE video emails in Yahoo! Mail! http://promo.yahoo.com/videomail/