It has never surprised me that Abraham Lincoln was so deeply interested as an adult in Euclidian geometry. Admittedly, few people share that fascination as geometry is viewed frequently as being deadly dull. But there is one essential thing that one learns when one studies geometry with any sort of depth, and that is the importance of assumptions. When I studied geometry at least, the predominant aspect of the study consisted of the reading and practice of proofs. One started with a few assumptions that one used to prove simple things, and then one used those simple proofs that one had come up with to prove more complicated things, and so on and so forth. One’s ability to understand the world and to prove things about it that one could solidly rest on–given various assumptions, obviously–is something that is valuable when one wants to advance far into theoretical mathematics and it is useful in recognizing the basis of logic in our own lives and in our own discussions of others. In looking at the way that people talk with others, it is clear that there are a lot of aspects of logic that people do poorly at, and perhaps the most troublesome aspect is the matter of assumptions.
Most of the time when we discuss something with someone else, especially someone with whom we disagree with, there are a great many assumptions that are not shared in common, and it is those assumptions that cause a lot of the difficulties that exist between people and that lead to people talking past each other and thinking the worst of others. For example, there are people I know who would be horrified at the thought that I have yet to wear a facemask during this particular Coronavirus difficulty, largely because I do my best to keep distant from others (no particular difficulty for one as reclusive as myself) and because I view the risk-reward proposition as being heavily slanted away from the risk of getting or spreading the disease, which has been a non-issue where I live for the most part and more towards the problems of breathing through restricted airspace. And if you live outside of the crowded Bosnywash metropolitan area or Chicago, and if one is not in prison or in an assisted living facility, that is probably the best thing to do at least based on current statistics. And at least from what I read in social media, a great deal of people agree with me and state their case even stronger than I would.
Many people disagree, though, and they disagree because they work from different assumptions that view the disease as a mortal and serious threat and view the lack of wearing a facemask as being an act of great folly and selfishness because even if a facemask does little to help oneself out when it comes to getting rid of the tiny particles that make up such a disease, it can do a great deal more in limiting the spread of particles from someone who was already sick. And if I knew that I had the disease I would wear a facemask not to try to protect myself from the disease but instead to protect others from me. Again, though, we are dealing with different assumptions. While in my mind wearing a facemask is equivalent to being super vigilant about not eating extra donut bites or ordering sweet tea in the knowledge that one may possibly risk some harm to oneself by doing so, but by no means certain or even likely harm assuming one keeps oneself within some boundaries, other people view it far differently. It is assumptions that help lead to differences in people. And there is nothing wrong with having different assumptions. Being aware of one’s assumptions is important, not least so that we can allow those assumptions to be amenable to changed facts. If we think that things are less dangerous than we thought before, to the extent that we are aware that safety was an aspect of our assumptions we can change our behavior to be less worried and concerned as a result. If we find ourselves in a more dangerous situation than we had thought, then we can revise our behavior in light of corrected assumptions. If we are unaware of our assumptions, though, and the assumptions that guide others, then we will have little chance of meeting people where they are and dealing justly with them, because we will judge them by our assumptions while they judge us by theirs, both misjudging quite often and quite seriously.
It is often hard for us to know our assumptions, though, because we simply live them and do not often stop to reflect upon them. When we are forced to prove something in a geometry class, we know what we assume as axiomatic and we know what we have previously proven and what can be used to prove something else. Most of the time in our conversations and debates and arguments, though, we make assumptions that we are not aware of, and are not aware that we are dealing with assumptions that we have not proved but rather taken for granted. And that is dangerous, because other people can make fewer or more or simply different assumptions than we do and come to wildly different conclusions that they justify just as well as we justify our own conclusions. And yet we can be unable to see the justice in their own reasoning even as they are unable to see our own reasoning. The antebellum thinker John C. Calhoun made a long disquisition on American politics based on a set of assumptions that lasted for hundreds of pages, but there were flaws in his premises and so all of his careful reasoning on those assumptions was mistaken and flawed as well. Such a fate can easily happen to all of us in the life we live, and most of us do not take care to know or state our assumptions clearly where they can be examined by others or by ourselves.