Re: Differential Logic • Discussion 4
Re: Laws of Form • Lyle Anderson
- JA:
- The differential proposition
is one we use to describe a change of state
(or a state of change) fromto
or the reverse.
- LA:
- Does this mean that if
is the proposition “The sky is blue”, then
would be the statement “The sky is not blue”? Don’t you already have a notation for this in
and
From where does “state” and “change of state” come in relation to a proposition?
Dear Lyle,
The differential variable is a derivative variable, a qualitative analogue of a velocity vector in the quantitative realm.
Let’s say is a real value giving the membrane potential in a particular segment of a nerve cell’s axon and
is a categorical variable predicating whether the site is in the activated state,
or not,
We observe the site at discrete intervals, a few milliseconds apart, and obtain the following data.
- At time
the site is in a resting state,
- At time
the site is in an active state,
- At time
the site is in a resting state,
On current information we have no way of predicting the state at time from the state at time
but we know action potentials are inherently transient so we can fairly well guess the state of change at time
is
in other words, about to be changing from
to
The site’s qualitative “position” and “velocity” at time
can now be described by means of the compound proposition
Resources
- Logic Syllabus
- Logical Graphs
- Minimal Negation Operators
- Differential Logic • Part 1 • Part 2 • Part 3
cc: Cybernetics • Ontolog • Peirce (1) (2) (3) (4) • Structural Modeling • Systems Science
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