Pointer, please.

neophight

As a neophyte, please excuse....

I have a not-exactly chicken-egg type question (see below). I would like to read/understand any formalized material about how similar problems are characterized, structured, and any generally accepted rules/formulations for dealing with analysis (correctness, completeness, assumptions, methods, etc.). This is kinda-like Logic 101, but not really.

I've read through the forum and have seen a variety of posts related to causality, time, evolution, etc. But haven't seen referenced a generally accepted, structured approach to the problem.

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Presume these two statements are true (not my real problem, but a good substitute):
- Because there is a chicken, there was an egg.
- Because there is an (chicken) egg, there was a chicken.

These statements to not seem to classify as a material biconditional, as the chicken and egg share no kind of equivalence. Similarly, this does not seem to fit into the counterfactual bucket.

Causality is more than implied. It is presumed that the chicken in the first conditional differs from the chicken in the second, or the egg in the first differs from the egg in the second, or both. Said differently, while the statement is correct, the instantiation of the variables (chicken, egg) ensure there is no biconditional.

In my actual problem the chicken in the two conditionals is the same, but exists in a different state, and therefore is in a very practical way a different instantiation of the same chicken (an instantiation of an instantiation, yeah, right). I do not think that twist on the problem relates to the fundamental question, but include it here in case that it might.

I am not interested the implication of "which came first" in the conditional pair, though clearly, the "which came first" question derives directly from this question in the first instance (or did the "which came first" question derive from a query about the origin of the universe :-) ). I am simply attempting to construct an argument along traditional logical (mathematical?) mechanics and ensure I introduce no logical errors or inconsistencies. For example, the rules of contrapositive, inverse and converse seem to continue to apply when state is introduced, but only if there is no instantiation substitution. The same is true for De Morgan's laws, etc.

Frank Apisa

Very complicated word salad here...and I honestly cannot fathom what you are asking or where you are going with it.

But the answer to "Which came first, the chicken or the egg?" is fairly easy to answer.

At some point, a live bird delivered an egg...rather than another living bird. It apparently was an evolutionary development made necessary by the bird's need to fly...which required less weight than would be obtained by gestation 'til complete.

neophight

↪Frank Apisa

Thanks.

Not so interested in the "which came first" question. It simply isn't an important question in this context.

Let me try a different path that might make the "word salad" less obscure.

In computer science we have the important concept of increment: X = X + 1
From a traditional logic perspective, this is absurd. It only makes sense in the context of allowing state, or allowing the variable (register) X to change values (instantiation) over time. Ignoring the original seed, the current instantiation of X is dependent on the prior instantiation of X. There is causality. So, if X has a value x, then there was an X with the value x - 1. Yes, ultimately, this iterates all the way back to the seed (note: ignoring overflow if you know what that means in this context).

Would you state this as X -> X - 1 ? (or X <- X + 1? or, X < X + 1? or ≡? or ⊃? or ⇒ or ⇔... ). If this conditional is true, isn't the contrapositive ¬ (X - 1) -> ¬ X also true?

When we allow general logical variables to change state, and we create situations where the state change is causal (can't think of a case where this couldn't be true), we have a situation where the normal logic rules seem to apply, but not really. Without going into details of "where I'm going" with this (which is far more complex), I am trying to figure out if there is a body of knowledge/rules/techniques for dealing such situations. I'm guessing that there must be, because almost all life is based upon non-static agents. I can't find it. I hope that I'm simply looking in the wrong places and asking the wrong people.

unenlightened

It apparently was an evolutionary development made necessary by the bird's need to fly...which required less weight than would be obtained by gestation 'til complete. — Frank Apisa

Which came first, the crocodile or the egg?

I hope that I'm simply looking in the wrong places and asking the wrong people. — neophight

If I'm understanding you, You are looking for a connection between logic, which in most variants is timeless and static with the dynamics of programming language. As a statement, X = X + 1 is a blatant contradiction, but as a command, it is perfectly understandable.

Generally I think they are simply treated as separate domains, however G.Spencer-Brown manages to derive both time and memory from a very primitive pre-boolean logic. It's actually a bit above my pay grade, and you need to watch out for the psychonauts who are inclined to make a religion of it. But it might be just what you need.

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neophight

↪unenlightened

Thank you. It might take me a little while to get through my new homework. :- ) I'll report back.

BTW, while these domains do seem to be separate, it seems that life's most interesting problems/issues/relationships are dynamic.

knowledge = f(learning) + ...
learning = f(knowledge) + ...

The more I learn, the less I know. What does that say about logic if it can't deal with these things? :wink:

unenlightened

some book indeed! — tim wood

Yeah, its definitely interesting and apparently he used this stuff to design some switching circuits for railway signals that actually work and use the 'virtual' states that he talks about later, which is about where I lose the plot.

Anyway I love the start: "Make a distinction. Call it the first distinction." This is the command mode of mathematics. 'Let x be a number...' It's the God mode - let there be light! Just do it, and see what logic tells you happens.

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Nagase

↪neophight

Some of these ideas are captured by modal logic, especially counterfactual logics (cf. Lewis's theory of causation, for instance). But I'm not sure why logic should study the nature of causation, which seems to me much more amenable to a physical treatment (perhaps along the lines of Bayesian theory).

Pointer, please.

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