[ukj]

You aren't hearing me.

The difference is the order/sequence in which the events take place.

Regular maths starts with premises then looks for conclusions.

Reverse maths starts with conclusions then looks for premises.

So in reverse maths the premises follow from the conclusions - quite literally.

[OJFord]

In writing:

> Even if you go in reverse, finding premises for your conclusions, your conclusion must still follow from the premises you found.

GP means 'follow' in the sense of logical deduction, not follow in time.

Having found the premise (after the conclusion), the conclusion (we started with) must then logically follow from the premises (we later found).

[ukj]

Well, obviously! That's by design.

[tsimionescu]

I am, really, and the idea of reverse maths/logic seems very interesting.

I was just pointing out that the GP's use of the word 'follow' was not about the temporal order of how discoveries are made, but to the logical concept of implication.

That is to say, the GP wasn't complaining that the Tractatus is doing reverse mathematics. They were complaining that the Tractatus is presenting illogical arguments, that it is taking logically unrelated statements and presenting them as conclusions and premises.

[ukj]

I am not sure how to even respond to this coherently... alas - I try.

Do you think "logical implication" (whatever that is) is not bound by temporal order?

That simply tells me that whatever you think "logic" is - it doesn't concern itself with time or downward causation. e.g your idea of "logic" is not Linear/Temporal logic.

So it can't be the logic of this universe then? Perhaps you've heard the saying "One man's modus ponens is another man's modus tollens"?

[tsimionescu]

Yes, a is implied by b is equivalent to me to b implies a, and it is an atemporal relationship. This is how a lot of logic is taught and practiced, whether in mathematics, physics, engineering or programming. I am a programmer by trade, and even in programming most uses of logic have no concept of time.

When I say x + 1 = 7, therefore x = 6, I see the two statements as being true simultaneously, and simultaneously with the implication.

I am sure there exist logics where time is a necessary component of reasoning, and I am not downplaying their importance. But there also exist logics where time plays no part, and they are not more or less true.

[ukj]

The crux of the matter is information.

Symmetrical (equational) theories contain none.

Information mandates asymmetry.

[Koshkin]

Problem is, unlike conclusions, premises are usually sufficient but not necessary.

[ukj]

I'd say ,given the nature and flow of reverse mathematics, conclusions are necessary but insufficient for premises.

The erudite/formal lingo aside. Reverse mathematics is a nice metaphor for how justification works in practice.