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11977213 No.11977213 [Reply] [Original]

Logic requires certain assumptions in order to function.

In the absence of logic, how are these axioms selected?

>> No.11977222

It's a malformed question. Logic is self-supporting. It is built out of the axioms it asserts. You can't have logic without the axioms and you can't have the axioms without logic. The principle of noncontradiction applies to itself as much as it does any normal proposition. The same is true of mathematics. This is why Godel's theorems were so upsetting for many in the mathematician and logician communities.

>> No.11977231

>>11977222
>You can't have logic without the axioms and you can't have the axioms without logic

I understand this -- but we must have some starting set of axioms, right? We have to pick some set of axioms with which to construct the system

How is this set selected? Intuition? Perceived correlation to experience phenomena?

>> No.11977238

>>11977231
>How is this set selected?

This sounds like it's outside of the scope of logic's ability to comment on it -- it's external to the system of logic.

>> No.11977239

From the man himself:
>142. It is not single axioms that strike me as obvious, it is a system in which consequences and premises give one another mutual support.

>> No.11977269

This guy is one of the only analytics I can get into. I'm not sure why though. TLP was super helpful in getting me to think about language and cognition in general.

>> No.11977271

>>11977239
Indeed, logical systems are elaborate tautologies.

>> No.11977279

>>11977222
>Logic is self-supporting. It is built out of the axioms it asserts
Sounds like circular reasoning

>> No.11977281

>>11977231
>but we must have some starting set of axioms, right? We have to pick some set of axioms with which to construct the system
Necessity creates nothing. Just because you need a set of axioms doesn't mean there are valid axioms.
>How is this set selected?
Faith

>> No.11977285
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11977285

What's going on in this thread chaps?

>> No.11977310

>>11977231
It depends what you want to do with your system. Mathematical axiomatic systems are chosen such that the derived mathematics provides the most use, usually.
Finitists would dispute the acceptance of the axiom of infinity in the ZFC axioms, as no observations of physical infinities can even be made, but most people don't care because finitist mathematical systems are much more complicated and impractical.
In that sense they're always arbitrary, and mostly utilitarian.
If you're talking about something more related to 'reality' or what we can say for sure (unshakable truths a la Descartes'), etc. take a look at On Certainty, where >>11977271 is from, it's not the sort of thing you can put into a word or sentence.

>> No.11977318

>>11977310
I meant to say:
>where >>11977239 is from

>> No.11977324

Why don't you ask Euclid he invented the whole thing. His idea was to being with five assumptions about geometry, which seemed undeniable based on direct experience. For example, one of the assumptions was "There is a straight line segment between every pair of points." Propositions like these are simply accepted as true.

Starting from those axioms he established the truth for many additional propositions by using logical deductions from the axioms and previously-proved statements.