Heh the morning routine has worked so far, but this morning I think I have an idea about E4, but GSB really is drawing on his extensive knowledge of electronics. I find myself going back to ↪wonderer1 's explanation of one-bit adders, and looking over electronics websites, but instead of bits E4 is changing the wave-form as it is "processed" through E4. — Moliere
Suppose we now arrange for all the relevant properties of the point p in Figure 1to appear in two successive spaces of expres- sion, thus.
P'p
We could do this by arranging similarly undermined distinctions
in each space, supposing the speed of transmission to be
constant throughout. In this case the superimposition of the
•two square waves in the outer space, one of them inverted by
the cross, would add up to a continuous representation of the marked state there. — P.61
Somehow the two waves get "smoothed out", — Moliere
That could very well be what's going on, actually. I said "smoothed out" because the example wave being fed into E4 is a series of marked-unmarked-marked-unmarked equally spaced out (where both the marked and unmarked square waves are equal in length), — Moliere
perhaps the answer to understanding chapter 11.. — wonderer1
What status, then, does logic bear in relation with mathematics? We may anticipate, for a moment, Appendix 2, from which we see that the arguments we used to justify the calculating forms (e.g. in the proofs of theorems) can themselves be justified by putting them in the form of the calculus. The process of justification can be thus seen to feed upon itself, an d this may comprise the strongest reason against believing that the codification of a proof procedure lends evidential support to the proofs in it. All it does is provide them with coherence. A theorem is no more proved by logic and computation than a sonnet is written by grammar and rhetoric, or than a sonata is composed by harmony and counterpoint, or a picture painted by balance and perspective. Logic and computation, grammar and rhetoric, harmony and counterpoint, balance and perspective, can be seen in the work after it is created, but these forms are, in the final analysis, parasitic on, they have no existence apart from, the creativity of the work itself. Thus the relation of logic to mathematics is seen to be that of an applied science to its pure ground, and all applied science is seen as drawing sustenance from a process of creation with which it can combine to give structure, but which it cannot appropriate
. Logic and computation, grammar and rhetoric, harmony and counterpoint, balance and perspective, can be seen in the work after it is created, but these forms are, in the final analysis, parasitic on, they have no existence apart from, the creativity of the work itself. Thus the relation of logic to mathematics is seen to be that of an applied science to its pure ground, and all applied science is seen as drawing sustenance from a process of creation with which it can combine to give structure, but which it cannot appropriate
When the sequences of cause and effect become circular (or more complex than circular), then the description or mapping of those sequences onto timeless logic becomes self-contradictory. Paradoxes are generated that pure logic cannot tolerate. An ordinary buzzer circuit will serve as an example, a single instance of the apparent paradoxes generated in a million cases of homeostasis throughout biology. The buzzer circuit (see Figure 3) is so rigged that current will pass around the circuit when the armature makes contact with the electrode at A . But the passage of current activates the electromagnet that will draw the armature away , breaking the contact at A . The current will then cease to pass around the circuit, the electromagnet will become inactive, and the
armature will return ro make contact at A and
If we spell out this cycle onto a causal sequence, we get the following:
If contact is made at A, then the magnet is activated.
If the magnet is activated, then contact at A is broken.
If contact at A is broken, then the magnet is inactivated.
If magnet is inactivated, than contact is made.
This sequence is perfectly satisfactory provided it is clearly understood that the if . . . then junctures are causal. But the bad pun that would move the ifs and thens over into the world of logic will create havoc:
If the contact is made, then the contact is broken. If P, then not P.
The if . . . then of causality contains time, but the if . . . then of logic is timeless. It follows that logic is an incomplete model of causality . — Mind and Nature
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.