Re: What is /are The Logic(s) of Life?... and Adjointness is Fundamental in Categories and Topoi of Biological Systems

[Tim Gwinn <***>]

Hi Ionel,
A couple of comments/questions interposed below.
Regards,
Tim

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Ionel
> Sent: Monday, June 14, 2004 2:04 PM
> To: ***
> Subject: Re: What is /are The Logic(s) of Life?... and Adjointness is
> Fundamental in Categories and Topoi of Biological Systems
>
>
> Hi, Tim:
>
> Please note and consider three very important points that were also
> explained twice before in my postings in this thread on the
> possible Logics
> that we do need to be able to model Life's Complexities:
>
> 1. The original (M,R)-system, as printed in 1958, employed just sets;
>
> 2. Sets- as defined at that time- are subject to the Axiom of Choice (AC,
> cf. also Robert Rosen in  "Essays...", and also widely
> recognized), and the
> Boolean Logic, which is suitable ONLY for automata and machines, i.e.,
> simple systems is at the basis of mathematical set theory;


TG: By this, are you asserting that Rosen's original (M,R)-model, utilizing
the category Ens, is invalid? Or only that Ens (or Set, for that matter) is
inadequate in the role of your RealCAT?


> 3. Robert Rosen explicitely gives up Sets as UNSUITABLE for modeling
> Complex Systems in his "Essays..." book published in 2001, and is in favor
> of 'structured' Categories that aren't Sets.


TG: Can you give me the page reference for that? I can't seem to recall
that.


> Furthermore, "Category Theory
> is intrinsically intuitionistic" says explicitely the latest textbook
> published in 2004 that I referred you to before.
>
> Last-but-not-least, both Lukasiewicz and Intuitionistic Logics are NOT
> 'algorithmic' , or recursive, in general, as you assumed in your posting,
> and Lukn and Intuitionistic (Heyting) Logics ARE NOT SUBJECT to the Axiom
> of Choice; so far these two kinds of Logics are the major break up with 2-
> valued logic (Boolean) which served as the basis for sets. This is the
> major reason for my posting.


TG: I will have to read more, but I think I disagree at least on the
'algorithmic' aspect. From what I read, "intuitionistic" logics are entirely
constructivist in nature: in order for any statement to be true in an
intuitionist logic, a proof - an algorithmic chain of statements - must be
able to be constructed (and similarly, if a statement is to be proven false,
a proof for it must be constructible).



>
> The logic of predicates, or predicative logic, is in essence also Boolean-
> based, and as Rashevsky himself showed in several articles
> published in BMB
> in the 50's, it leads to equivalent results to those that are obtained by
> Sets and Relations for biological and societal organisms. Hilbert's
> predicate theory does not extend to Intuitionistic logic, that you might
> call 'impredicative', as double negation is NOT equivalent to affirmation
> in Heyting Logics (as it is in Boolean, 2-valued Logic).
>
> Regards,
> Ionel
>
>
>
> On Mon, 14 Jun 2004 10:47:24 -0400, Tim Gwinn <***> wrote:
> (shortened message to essentials).
>
> >Hi Ionel,
> >....
> The 'logic' for representing these organizations would be the relational
> models, such as used for the (M,R)-system model.>>
>
> Please note Point#1 above: which (M,R)-system model version are you
> referring to ? The 1958 one in terms of Sets ?, or the 1997/ 2001, and
> 2004  onein terms of Structured Categories ? , because it does make a very
> big difference which one you are referring to.
>
> >>>>>>>
> -----------------------------------------
>
> ..... I am pretty certain hat neither Lukasiewicz nor Heyting logic nor
> some other 'fuzzy' logic will admit such impredicative structures. As best
> I understand them all, they remain entirely algorithmic and predicative.>>
>
> I 'm sorry but this is very easily proven to be incorrect; please see
> points #2 and #3, above. Current Logics cannot be trifled with by what one
> might call 'handwaving' arguments.
>
> ______________________________________
> >Regards,
> >Tim
> >
>
> _________________________