The Wayward Axolotl

The continuum fallacy is to deny the meaningfulness of discrete categories, just because they are a somewhat arbitrary partition of a continuum. More generally, it is to deny the meaningfulness of fuzzy and/or somewhat arbitrary categories, just because they cannot be precisely defined in terms of necessary and sufficient conditions. The spectrum of visible light is a common example. There is a continuum of frequencies. Each frequency of light corresponds to a point on the spectrum. We (somewhat arbitrarily) partition the spectrum into discrete colors: red, yellow, green, blue, violet. This discretization is not random. Each color is an interval of the spectrum. It would be fallacious to claim that colors do not exist, just because they exist on a spectrum and the categories are somewhat arbitrary. The continuum fallacy is a type of representational nihilism. It rejects a representation of reality just because it isn’t exactly the same as reality. Of course, there is room to...

Responding to critics is an important part of rational thought and persuasion. Criticism is a way to test ideas. If an idea passes many tests, we develop confidence in it. Conversely, if an idea is held off-limits to criticism, we suspect it of being wrong. There are two requirements for substantive criticism: The critic must identify a specific claim or assumption in the content that the critic disagrees with. If it is a claim, then the critic should provide the quote where it is asserted. If it is an assumption, the critic should show where the author relies on it. The critic must present a rational argument against the claim or assumption. Disagreement without argument is not substantive criticism. If criticism satisfies those two requirements, it is a test of the content. It could still be wrong, but at least it has the right form. If it doesn’t satisfy those requirements, it is not a test of the content. There can be valid criticism that is not su...

Economists and other social theorists often take the concept of utility for granted. In theory, utility is a measure of value. I will denote the utility of X to Y as U(X, Y) or simply U(X) if Y is clear in the context. For a single individual, we can think of utility as a mathematical function that maps objects or outcomes to points on the continuum. This mapping is called a “utility function”. (In this context, “function” has its mathematical meaning, not its ordinary meaning.) To think about society, we might want to define utility for a group, not just a single individual. Collective utility is typically defined as the sum of individual utility over the collective. This assumes that utility is defined on the same scale for everyone. The concept of utility is used to model individual and social decision-making. It is used in game theory to define benefits and costs. It is often used in moral philosophy to define the “goodness” of actions and outcomes. In a utilitarian m...

In this essay, I will debunk the concept of market capitalization. But first, let’s consider something else: the mass of a pile of bricks. Suppose that I have a pile of identical bricks. I want to know the total mass of the bricks for some reason. So, I measure the mass of one brick on a scale. The mass of one brick is M. I then count the bricks. The number of bricks is N. I then caculate the total mass of the bricks as M × N. M × N is meaningful. There are N units of size M, so N × M represents the total size of the units together.. The meaning of M × N is “the total mass of the bricks”. It is not just “M × N”. Note that I could use another method to get the same quantity. I could put each brick on a scale, measure its mass, and add up all of those numbers. If I had a really big scale, I could put all the bricks on the scale together, and measure the total mass directly. The meaning is not the method. The meaning is what the number represents. Now, let’s consider...

In comments on the essay The Case Against Moral Realism , I challenged someone (Stephen Lindsay) to define good and evil, or in other words, to define moral value. In response, he wrote a defense of belief in objective morality: Three Perspectives on Objective Morality . In the essay, he gives a definition of moral rightness and wrongness: • Right (in the moral sense) - behaviors, ideas, philosophies, etc., that are thought to overall positively impact individuals and society. Wrong is the opposite. There can exist behaviors, ideas, and philosophies that are neither right nor wrong. However, this definition does not actually define moral value. It does not explain what moral goodness and badness (or rightness and wrongness) are. It presupposes moral value. To call something “good” or “bad”, in a moral sense, is not a description. Moral value is normative. To call something “good” (in a moral sense) means that it ought to be, and that we should try to create...