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) from to 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
cc: FB | Differential Logic • Laws of Form