( Gavin
Ritz 2011.02.11.10.24NZT)
Hi there Chad
Whoever wrote the Wiki on
logic is trying to confuse the whole world about logic. I like things simple so
I can understand it.
Any language is only made
of three types of logical statements and nothing else.
·
Declarative (a statement, e.g. the girl’s
hair is black), it’s either true or false- this really makes up most of
scientific proofs. Basis of mathematics. Set Theory. Proven to be a problem by Gödel.
Often called propositional logic
·
Imperative (a command, e.g. Fix this tap)
it’s either structure or process; there is no accepted calculus for this.
But this logic connects all of living organism. A mate of mine has developed a calculus
which you have. This cannot be true or false.
·
Interrogative (a question, Is this a gun?)
it’s either yes or no and plus statement responses. (basis of black hole
entropy)
Each of these types of
logic is connected by logical connectives and there are only 4 of them. They are
like musical notes they repeat on many levels of abstraction. From concrete
objects to categories of categories of categories.
·
Or-or
·
And-and
·
If-then
·
If-and-only-if.
For example in PCT the reference
signal is like a command, so it’s an imperative logical operator. It sort
of commands the “controlled variable”.
That’s why I have
said there is mathematics to prove PCT both holistically (using mathematical category
theory and Topoi logic for the HPCT) and Fractal mathematics, and internally by
imperative logical calculus developed by a colleague of mine.
Logic is the foundations
of science, maths, and all communication, it’s content free and has a
form (fabric) which I mention above.
Once one becomes aware of
it in a general discourse one is able to discern what types of arguments people
are putting up.
It’s the basis of Elliot Jaques measuring
instrument in Human capability and in some ways it forms the basis of HPCT. (Mentioned
in another thread).
A linear logical
statement would be connected by or-or and by and-and connective and a non linear
one by “if-then” and “if-and-only-if”.
Hope this helps.
Interesting article
below. Hard going.
Regards
Gavin
Gavin, please continue to contribute your insights to
this discussion list. I am determined to catch up with you in spite of the
different language that we both use for the same ideas.
For example, you define logic in terms of the
imperative, declarative and interrogative. I define it in terms of the
classical, intuitionistic, and linear (i.e.,
Linear logic - Wikipedia).
In any event, for those on this list who share an
interest in the connections between computation, logic, topology, and physics,
I encourage you to check out this publication:
Physics, Topology, Logic and Computation: A Rosetta
Stone (Baez and Stay,
2008)
Cheers,
Chad
Chad Green, PMP
Program Analyst
Loudoun County Public Schools
21000 Education Court
Ashburn, VA 20148
Voice: 571-252-1486
Fax: 571-252-1633
Gavin Ritz garritz@XTRA.CO.NZ
2/8/2011 5:35 PM
(Gavin Ritz 2011.02.09.11.22NZT)
[From Rick Marken
(2011.02.08.0930)]
Gavin Ritz (2011.02.08.15.28) re Rick Marken (2011.02.07.1820)
Your comments are correct, as I said there’s no
theory behind his comments
and it also has no controlled variable.
I think there is a theory behind his comments:
open-loop causal
theory. That’s why there is no controlled variable.
The “feedback” in
his diagram would be the controlled variable (some
function of the
feedback, anyway) but Pierce can’t see that because he is seeing
things from an open-loop causal point of view, which
sees input
(feedback) as a cause rather than a controlled result
of action.
But I have not seen any other diagrammatic
representation with a reference
signal and comparator in the brain.
I agree. That aspect of the diagram is really good. He
was sooo close.
Speech is the controlled variable.
Well, that’s a little vague.
That’s why I say it’s all nested. There are levels of
abstraction.
I think speech involves the control of
many perceptual variables simultaneously.
There is no doubt about that
Understanding speech (from
a PCT perspective) is a matter of figuring out what
variables are
controlled, and how they are controlled.
Touche
Certainly, various functions
of the auditory signal are controlled. But the fact
that we can speak
when we can’t hear what we are saying (as in “The
King’s Speech”;
great movie) suggests that there are other perceptions
that are
controlled when we speak, such as the perception of
the position and
change of position of our various articulators
(tongue, palates, lips,
etc).
All of this and more, sight is also a controlled
variable too, in fact
language is a mix of all the energies (sight,
{photons}, sound {phonons},
chemical {taste} etc.
Not to mention the very fabric of all, logic
(imperative, declarative and
interrogative). Which was probably here even before
the Big Bang, how is PCT
going to incorporate this is another issue altogether.
In an older thread I put together the very basics of
how HPCT should look,
from Mathematical Category Theory and Topoi logic.
Determining the variables that are being controlled in
behaviors we see as “speech”, “catching
fly balls” (see Marken, R. S.
(2001) Controlled Variables: Psychology as the Center
Fielder Views
It, American Journal of Psychology, 114, 259-281 to
see the possible
controlled variables involved in catching fly balls
and ways to
determine which are actually controlled), etc. is what
PCT is all
about. Determining what variables are being controlled
and how they
are being controlled when organisms behave is, I
think, the main goal
of understanding behavior from a PCT perspective
I couldn’t have said it better myself.
There’s a lot of work to be done.
Regards
Gavin
Best
Rick
···
–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com