Mathematics/science end in contradiction

[Eodnhoj7]

Any axiomatic system cannot be the following 4 things simultaneously:

1. Recursive (e.g algorithmic/computable)
2. Sufficiently powerful to prove anything about the natural numbers.
3. Complete
4. Consistent

You can't have your cake and eat it to so, a choice exists: Which of the above properties are you willing to sacrifice when appealing to logic?

The dilemma presented above effectively means that adhering to the Law of non-contradiction is a subjective choice (sorry, Aristotelians!)

For I can CHOOSE (personal preference is all) to adhere to recursive, powerful and complete logical systems while accepting contradictions as a consequence of my choice.

The above is a general truth about all formal axiomatic systems - colloquially called "logic". Through deduction one can conclude that the same issues which plague logical formalisms also plagu foundationalist approaches to philosophy e.g Kant and most of his followers.

Further reading for the curious minds:
* Godel's completeness and incompleteness theorems.
* Church-Rosser theorems
* Turing's halting problem
* Curry-Howard-Lambek correspondence

You can get rid of the first 3 of your listed 'properties', they are surplus to requirements of an axiomatic and logical system.

How one can determine whether an axiomatic system is consistent or not is a moot point.

Provide a logical answer for why it is a moot point.

[Eodnhoj7]

You can get rid of the first 3 of your listed 'properties', they are surplus to requirements of an axiomatic and logical system.

How one can determine whether an axiomatic system is consistent or not is a moot point.

Observe that while my argument was entirely descriptive (enumerating the various systemic properties of logical systems) you have opted in for a prescriptive argument. In doing so - violating the is-ought gap.

How and why have you CHOSEN consistency and why have you ignored the other three?

You claim that logical systems have "requirements" . Evidence required.

Unfortunately your post makes no sense. It is as though you are stringing words together in a semi-random way, the result is entirely devoid of meaning.

Actually his post makes perfect sense.

[A_Seagull]

Unfortunately your post makes no sense. It is as though you are stringing words together in a semi-random way, the result is entirely devoid of meaning.

I guess I can try again.

First - there is the prescriptivist vs descriptivist distinction ( https://stancarey.wordpress.com/2010/02 ... u-want-it/ ).

A descriptivist is somebody who describes - e.g states how things are.
A prescriptivist is somebody who prescribes - e.g states how things should be.

I am describing how logic is.
You are prescribing how logic should be.

I am describing that logic has (at least) 4 properties: recursiveness, provability, consistency and completeness.
You are prescribing that logic should have only one property: consistency.

Logic is the way it is. You insist that logic ought to be some other way.

In philosophy this is known as the is-ought gap ( https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem ).

You can get rid of the first 3 of your listed 'properties', they are surplus to requirements of an axiomatic and logical system.

Care to convince us why you think logic has "requirements" and where they come from? The very word "requirement" sure sounds very prescriptivist to me..

isought.jpg

Still meaningless.

[Logik]

Unfortunately your post makes no sense. It is as though you are stringing words together in a semi-random way, the result is entirely devoid of meaning.

I guess I can try again.

First - there is the prescriptivist vs descriptivist distinction ( https://stancarey.wordpress.com/2010/02 ... u-want-it/ ).

A descriptivist is somebody who describes - e.g states how things are.
A prescriptivist is somebody who prescribes - e.g states how things should be.

I am describing how logic is.
You are prescribing how logic should be.

I am describing that logic has (at least) 4 properties: recursiveness, provability, consistency and completeness.
You are prescribing that logic should have only one property: consistency.

Logic is the way it is. You insist that logic ought to be some other way.

In philosophy this is known as the is-ought gap ( https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem ).

You can get rid of the first 3 of your listed 'properties', they are surplus to requirements of an axiomatic and logical system.

Care to convince us why you think logic has "requirements" and where they come from? The very word "requirement" sure sounds very prescriptivist to me..

isought.jpg

Still meaningless.

I can only explain it to you. I cannot understand it for you.

The reading material to fill in your knowledge-gaps has been referenced.

Educate yourself. Or don’t.