Whereof one cannot speak, thereof one must remain silent.
Why can't we go from conclusions to premises?
Saying that the premises don't follow from the conclusions means that, taking the premises as true, the conclusion is may or may not be true, so it is illogical to draw that conclusion from those premises. Or if you prefer the other way around, if, taking the conclusion as true, the premises could be true or false (or taking the conclusion as false, the premises could still be true or false) then the conclusion does not follow from the premises you found.
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.
> 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).
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.
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"?
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.
Symmetrical (equational) theories contain none.
Information mandates asymmetry.
The erudite/formal lingo aside. Reverse mathematics is a nice metaphor for how justification works in practice.
I also have a soft-spot for Russell and his student Wittgenstein. Tractatus is an incredible, though later redacted, work of pure axiomatic reasoning. While HN focuses mostly on tech, I think that the kind of reasoning found in Analytic philosophers can be a boon to anyone doing anything that requires the sort of logical design found in the technology field.