Assumptive Logic

[Eodnhoj7]

When the evidence for something is sufficiently rigorous then it becomes a fact and from that point on stops being an assumption
Assumptions with regard to axioms are rather different because they use logic rather than evidence but the principle is the same

This is because mathematics is a sub set of logic and so therefore needs logic in order to justify all of its axioms
Also because mathematics is primarily a deductive discipline that deals with definitive truth not probable truth

And yet some axioms within mathematics are very arbitrary indeed

For example the axiom that states a circle has to have 360 degrees when could actually have as few or as many degrees as possible
The only absolute rules would be that each degree would have to equidistant from each other and there would have to be universal
consensus on this especially where there were real world consequences if such consensus was absent such as navigation for example

So if the universal consensus was that there were 60 or 720 or 8000 or 90000 degrees instead it would make precisely zero difference

And 360 is very useful because it has so many divisors [ I 2 3 4 5 6 9 I0 I2 I5 I8 20 24 36 72 90 I20 I80 360 ]
Other numbers have as many and even more but only one was required so that was the one decided upon

You are assuming a definition of "rigor".

[Eodnhoj7]

It is certainly NOT that to me. But, if that is what you assume and BELIEVE it is, then that is exactly what "it is", to you obviously.

It is not that way from the angle of awareness in which you assume reality.

You can word any thing in any way you like, so that things align with your already held assumptions and beliefs, but that is all you are doing here.

You can not equally successfully propose that you KNOW the truth of things but also be saying at the same that you really do NOT know the truth of things because really you are only just assuming it.

Sipping coffee...I assume "void"....

[Eodnhoj7]

This is because mathematics is a sub set of logic and so therefore needs logic in order to justify all of its axioms

I haven't followed this thread but this sentence caught my eye. Didn't Gödel definitively prove that math isn't a subset of logic? Math transcends logic. Gödel's work destroyed the hopes of the logicists, who did believe math could be derived from logic.

Also it is not the case that logic is required to justify the axioms. Math depends on SOME logic, but it could be classical first order predicate logic (the usual default) or it could be intuitionistic logic or some other form of logic. When you say logic you have to say which logic you mean.

Finally the axioms are never justified by logic. Why certain axioms are chosen is a long story, but it boils down to usefulness, having a richer rather than a more restrictive mathematical universe, and various historical trends. But I can't think of any axiom (of set theory, say) that's there for some reason purely pertaining to logic.

The example of the circle being 360 degrees is not a great example IMO. It's just a convention. We could have said 100 degrees or 439 degrees. 360 was chosen by the Babylonians because it's easy to work with, it has a lot of divisors. And it's close to the number of days in the year. But it's not an axiom, just a convention.

An axiom is more like something like the axiom of infinity, which says there's an infinite set. There's no reason to think it's true about the world. And there's no logical reason it should be true or false. It's assumed in modern math simply because it provides a richer mathematical universe.

Usefulness is also an assumption.

[Skepdick]

Usefulness is also an assumption.

So you are only assuming that your ipad is useful, even though you are actually using it?

[Eodnhoj7]

But it does not falsify the notion that mathematics is a sub set of logic which is a statement of fact not a matter of opinion

It's kinda difficult to test/answer this question unless you have some clear conception of what logic is.

If your conception/definition of logic is anything like a formal system, then it's yet another axiomatic system - it's the same as Mathematics, and your ability to quantitatively decide the "equivalence" of any two axiomatic/formal systems stops at Turing completeness.

You cannot create logic without an assumption thus the foundations of logic/math/language is assumption with the assumption of assumption existing as the context which provides coherency and this itself is infinite as no context is a context in itself.

But this is a context, therefore all contexts are void and assumption "is" void (this will sound circular but it isn't necessarily).

Assumption is formless much like context itself is formless, thus assumption is an act of inversion or "isomorphism". It is the curvature of the glass, or the line which separates the air and the water in the glass where seperation is the inversion of one axiom (water in this case) to another (air).

[Eodnhoj7]

Usefulness is also an assumption.

So you are only assuming that your ipad is useful, even though you are actually using it?

Usefulness as assumed is contextual, thus assumption of use is the creation of context.

Assumption is context creation with usefulness being a context necessitating other contexts such as desire for x, etc.

Usefulness is never really defined on it's own terms and under certain contexts it effectively means "desire" or "want" but not "need" and vice versa.

[surreptitious57]

Assumption may be the basis not only of all logic but of all knowledge as well
But when it is confirmed or denied then it ceases to be assumption any more

You start from and ignorance then make an assumption based on reason and then formulate a hypothesis to test that assumption
If the hypothesis has been falsified then it becomes fact because falsification is essentially absolute knowledge by another name
If the hypothesis has been confirmed then it provisionally becomes fact because confirmation is not as reliable as falsification is

Unless you are omniscient or are not curious enough to make assumptions in the first place [ neither of which apply to human beings ]
then they are an inevitable part of acquiring knowledge - there is simply no way round this - so I do not really see what the problem is

It would only be a problem if assumptions could never be confirmed or denied because then knowledge could not be acquired
But hypotheses can be tested empirically and proofs can be demonstrated logically and so knowledge can actually be acquired

[Eodnhoj7]

Assumption may be the basis not only of all logic but of all knowledge as well
But when it is confirmed or denied then it ceases to be assumption any more

Still an assumption, where what we assume is a form. Thus form and assumption are inseperable

You start from and ignorance then make an assumption based on reason and then formulate a hypothesis to test that assumption

Reason is assumed.


If the hypothesis has been falsified then it becomes fact because falsification is essentially absolute knowledge by another name
If the hypothesis has been confirmed then it provisionally becomes fact because confirmation is not as reliable as falsification is

Unless you are omniscient or are not curious enough to make assumptions in the first place [ neither of which apply to human beings ]
then they are an inevitable part of acquiring knowledge - there is simply no way round this - so I do not really see what the problem is

It would only be a problem if assumptions could never be confirmed or denied because then knowledge could not be acquired
But hypotheses can be tested empirically and proofs can be demonstrated logically and so knowledge can actually be acquired

I am bored...

[surreptitious57]

Now is that an assumption or have you just run out of coffee [ maybe you could sip more slowly from now on ]

[Eodnhoj7]

Now is that an assumption or have you just run out of coffee [ maybe you could sip more slowly from now on ]

I think the "Assumption of Inherent Void" thread will give context to the assumptive logic thread as well as identity principles thread.

[Skepdick]

Usefulness is also an assumption.

So you are only assuming that your ipad is useful, even though you are actually using it?

Usefulness as assumed is contextual, thus assumption of use is the creation of context.

Assumption is context creation with usefulness being a context necessitating other contexts such as desire for x, etc.

Usefulness is never really defined on it's own terms and under certain contexts it effectively means "desire" or "want" but not "need" and vice versa.

Usefulness is desire, want, need and more.

Why are you using your ipad? What need drives it?

[Eodnhoj7]

So you are only assuming that your ipad is useful, even though you are actually using it?

Usefulness as assumed is contextual, thus assumption of use is the creation of context.

Assumption is context creation with usefulness being a context necessitating other contexts such as desire for x, etc.

Usefulness is never really defined on it's own terms and under certain contexts it effectively means "desire" or "want" but not "need" and vice versa.

Usefulness is desire, want, need and more.

Why are you using your ipad? What need drives it?

Thus philosophy can be assumed as useful as well as assuming phenomenon.

[Skepdick]

Thus philosophy can be assumed as useful.

If you make such an axiomatic assumption, surely you must have asked and answered the question "What is Philosophy useful for?"

[Eodnhoj7]

Thus philosophy can be assumed as useful.

If you make such an axiomatic assumption, surely you must have asked and answered the question "What is Philosophy useful for?"

In assuming what is useful as well as the nature of use...duh. Isnt that what logic does...give definition of use as a use unto itself?

[Skepdick]

Thus philosophy can be assumed as useful.

If you make such an axiomatic assumption, surely you must have asked and answered the question "What is Philosophy useful for?"

In assuming what is useful as well as the nature of use...duh. Isnt that what logic does...give definition of use as a use unto itself?

Well, you know what they say - assumption is the mother of all fuckups.