You have already pointed to many exceptions, which in logic and math are unnacceptable. In addition, your basic assumption that we "must" operate under the assumption that our logical system is sound is false. We 'must' not do any such thing, we may, however, choose to do so and as such accept the possibility of error in any subsequent calculation/reasoned response.
Who do you want to win the war?
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You have already pointed to many exceptions, which in logic and math are unnacceptable. In addition, your basic assumption that we "must" operate under the assumption that our logical system is sound is false. We 'must' not do any such thing, we may, however, choose to do so and as such accept the possibility of error in any subsequent calculation/reasoned response.
Summed up, its the Golden Rule. While this is not perfect (even this is relative), it is a good beginning, especially because the good majority of us share many values and expectations for how we want to be treated. Of course, a more complicated version is that of the Categorical Imperative, but I hope this conversation doesn't abstract this far into ethics (with Kant, Mills and co.)
I disagree. We can't have a society without shares understandings and some set of values. And what are you trying to say in your 1st statement above? Are you referring to the Russel's Paradox or Geodell's Theorem, or what?
It is impossible to go to advance math until someone has the basic understanding of the most simple of concepts.
2+2=4.
Try using your fingers and toes to start.
We can discuss gray shades of morality after you grasp the easy stuff.
We cannot have society without agreements, true. My statement was that society (or the participation therein) is a choice that does not necessarily have to be made. Society had not been mentioned previously, but so long as it has now been mentioned. To what degree must understanding be shared for society to be (a) considered society, (b) "just" or "right", (c) fair?
To reiterate, what is a society but the grouping of humans under a certain set of rules (aka agreements)? Does an individual belong if he/she does not agree? Is it "right" to force someone who does not wish to abide by these rules? If these individuals are not a part of the decision-making process are they not free from the oppression of those who do make the rules?
Sorry, you may have missed my comments. They are contained within your quote at the end of each line, except for the <> part which contains an asterisk. In this case, your examples were in principle all the same so I responded to them in concert.
P.S. Your example of 2+2=4 (Mathematics) is a man-created system which does not necessarily reflect reality. Rather, it is a system designed apart from reality (outside the human mind) which has proven useful in the manipulation of our experienced world.
First of all, to some extent all people make-up a global society (especially since throughout time, cultures in all locations (regardless of how ever much isolated) have shared some values. And over time, relations between these smaller societies and cultures and created a broader society of shared values and rules. Moreover, while the Taliban and N. Korea never agreed to the Geneva Convention, I believe Iraq has (although I would have to double check). Either way, the world is pretty small, and I would actually assert that every society and culture agree on some level that soldiers hiding behind women and children and killing fleeing refugees is cowardly and unjust (even if some individuals do not feel this way, and even if some major armies in ancient times did not hesitate to massacre everyone in a conquered area-although they were usually viewed as unjust and barbaric by the rest of the world). Anyhow, we will continue this tomorrow. Night night!
Unless you are arguing that we are capable of knowing nothing but our own existence (in which case our posts and arguments are a waste of time), math is anything but man made! Man has simply come up with symbols to reflect the most objective truth we can know! True, at some level our math is very limited. We can wonder if there are other universes with different mathematics, we can note our finite abilities to comprehend and thus the limits of our ability to understand the objective universe and mathematics, and finally we can point out that our mathematical system is based partly on contradictory definitions. Nonetheless, math as we know it is the most objective tool for understanding the universe and what exists that we have.