Cf: Differential Logic • Discussion 5 http://inquiryintoinquiry.com/2021/06/17/differential-logic-discussion-5/
Re: Laws of Form https://groups.io/g/lawsofform/topic/differential_logic/83557540 ::: Lyle Anderson ( https://groups.io/g/lawsofform/message/330 ) <QUOTE JA:> The differential proposition dA is one we use to describe a change of state (or a state of change) from A to (A) or the reverse. </QUOTE> <QUOTE LA:> Does this mean that if A is the proposition “The sky is blue”, then dA would be the statement “The sky is not blue”? Don't you already have a notation for this in A and (A) ? From where does “state” and “change of state” come in relation to a proposition? </QUOTE> Dear Lyle, The differential variable dA : X → B = {0, 1} is a derivative variable, a qualitative analogue of a velocity vector in the quantitative realm. Let's say x ϵ R is a real value giving the membrane potential in a particular segment of a nerve cell's axon and A : R → B is a categorical variable predicating whether the site is in the activated state, A(x) = 1, or not, A(x) = 0. We observe the site at discrete intervals, a few milliseconds apart, and obtain the following data. • At time t₁ the site is in a resting state, A(x) = 0. • At time t₂ the site is in an active state, A(x) = 1. • At time t₃ the site is in a resting state, A(x) = 0. On current information we have no way of predicting the state at time t₂ from the state at time t₁ but we know action potentials are inherently transient so we can fairly well guess the state of change at time t₂ is dA = 1, in other words, about to be changing from A to (A). The site's qualitative “position” and “velocity” at time t₂ can now be described by means of the compound proposition A dA. Resources ========= Logic Syllabus https://oeis.org/wiki/Logic_Syllabus Logical Graphs https://oeis.org/wiki/Logical_Graphs Minimal Negation Operators https://oeis.org/wiki/Minimal_negation_operator Differential Logic https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3
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