On 30 Nov 2012, at 13:33, Roger Clough wrote:

Hi everything-listPerhaps Penrose's emphasis of intution, and the noncomputabilitythereof,is that intuition is is closely related to meaning, to semantics.I think that a necessary feature of any machine to emulate humanthoughtis to be able to understand meaning, the science of which is calledsemantics.My limited understanding of current semantics is that meaning isrepresentedsyntactically (sentence diagramming).

`In computer science, semantics is often represented by infinite sets,`

`which describe in extenso the meaning of some syntactical construct`

`("number").`

`For example the semantics of "x + 1", might be given by the infinite`

`set {(0,1), (1,2), (2, 3), ...}.`

`The semantic of "factorial" can be given by the set {(0,1), (1,1), (2,`

`2), (3,6), (4,24), ...}`

Or the semantics of "number" can be {0, 1, 2, 3, ...}.

`You can see computation as being an association from syntax to`

`semantics.`

Like from "x+1" to "{(0,1), (1,2), (2, 3), ...}".

`You can see learning as being the inverse association, where you give`

`the "reality" (semantics) to a machine, like a sequence of finite`

`portions of "{(0,1), (1,2), (2, 3), ...}", and the learning machine`

`will build a syntactical construct (program) like "x + 1". A "learning`

`machine" is given (portion of a) reality, or meaning, semantics, and`

`the machine proceeds to the synthesis of program (finite syntactical`

`construct) accounting for the data given.`

`Roughly speaking, for those who reminds what the phi_i are:`

`computation, abstractly is in the i -> phi_i, or (i, x) -> phi_i(x)`

`type of arrows. Learning is in the phi_i -> i direction.`

`Likewise the semantics of a theory (syntactical) is given by a`

`mathematical structure (usually infinite), called "model" which`

`satisfies (in some sense) the axioms and theorems of the theory.`

`Usually theories have many models.`

`With this, it should be clear that a semantics is not typically a`

`finite syntactical object, but an infinite structure, plausibly an`

`object "in the mind".`

Bruno

Peirce seems to have abandoned arithmeticreasoning (I may have overstated that) in favor of a new, semioticor graphics-basedreasoning (semiotics), which is as vital to understand as it isdifficult.One can even conceive of an iconic- or graphics-based computer. See below for an alternate discussion of this topic: http://jeannicod.ccsd.cnrs.fr/docs/00/05/33/40/HTML/index.html"The central idea developed in Peirce's account of necessarydeductive reasoning is that it proceeds by constructions ofdiagrams, which are a species of icons. This is as true for logicalreasoning as it is for mathematical reasoning, which is in fact theparadigm of deduction. Such a conception has important bearings notonly for a conception of iconic logic, but for certain peculiaritiesthat are attached to mathematical deduction as well.3.1 The main characters of the iconAn icon is a sign which 'refers to the Object that it denotes merelyby virtue of characters of its own, and which it possesses just thesame, whether any such Object actually exists or not' (2. 247). "<SNIP>"The first things I found out were that all mathematical reasoningis diagrammatic and that all necessary reasoning is mathematicalreasoning, no matter how simple it may be. By diagrammaticreasoning, I mean reasoning which constructs a diagram according toa precept expressed in general terms, performs experiments upon thisdiagram, notes their results, and expresses them in general terms.This was a discovery of no little importance, showing as it does,that all knowledge comes from observation. "[Roger Clough], [rclo...@verizon.net] 11/30/2012 "Forever is a long time, especially near the end." -Woody Allen --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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