It is embarrassingly conceited even to link my fumbling with contradictions in basic concepts of moral thinking with the brilliant investigations of the contradictions in basic concepts of mathematical thinking by Bertrand Russell *et al* in the late nineteenth and early twentieth centuries. Nonetheless, there are some parallels which help clarify what I am trying to accomplish.

I only outline the main steps in finding the inconsistency in mathematical thinking. Mathematical logicians had shown that all mathematical thinking could be represented as thinking about natural numbers. G. Frege showed that all thinking about natural numbers could be represented as thinking about classes. A basic principle for thinking about classes was that there is a class consisting of the extension of any property. Russell considered the property “the class of all classes which do not belong to itself.” A law of excluded middle of the form: for any classes x and y, x belongs to y or x does not belong to y, was accepted as fundamental in mathematical thinking. An explicit contradiction is reached when both x and y are taken as the classes of all classes which do not belong to themselves.

Of course, the set theory contradiction did not hinder mathematical development in any way. For one, mathematical thinking does not depend upon going back to some foundational ideas such as set theory. Secondly, and relevant to my project, is that the contradictions can be resolved by altering the conceptual scheme for thinking about classes. For example, some set theorists restricted the kinds of properties whose extensions were classes.

**It is the altering of the conceptual scheme which links my reflections on moral thinking with the foundational work in mathematics. **Altering the conceptual scheme leads to a type of skepticism. First, it suggests that our ways of thinking are human inventions for thinking about the way things are. Insofar as they are our inventions the ways of thinking might contain components peculiar to humans and thus not accurately tell us now things really are apart from our thinking. If there were only one way of removing the contradiction, we might have some basis for thinking that we now had the right way of thinking about the topic. Unfortunately, as will be shown in subsequent posts, there are several ways of resolving the contradiction. As a result, one has to take a stance that one specific way of thinking about morality is the correct way.

Of course, conceding that there is no right way to resolve the fundamental contradiction in moral thinking is not conceding that there is no right way to think morally. Indeed a possible stance, which I take, is that after qualifications in the notion of an authoritarian morality to allow acceptance of “Some harm ought to be” we have attained the correct way of moral thinking. I have to concede, though, that I might have taken the wrong stance.

Let me put it as follows. I take the stance “There are absolute moral principles which correctly express the normativity in reality.” I concede that I might be mistaken about reality by taking such a stance. Moral skepticism is not moral relativism. **There is only one correct way of thinking about morality. Unfortunately, I am not absolutely certain that I have the correct way.**

This means that moral arguments have two phases: First, persuade someone to take your stance. Second, convince the other of the correctness of your reasoning within the stance. Also the need to take a stance implies that there may be irresolvable moral disputes.

A significant difference between the mathematical and moral resolution of a basic contradiction is that in the mathematical case a person can enjoy working with the different set theories. In the moral case, only a cynic, switches from one stance to the other. It is morally significant to take a stance and stay with it.

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## Inconsistency of Moral Thinking Resolved by Moral Skepticism

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