Monthly Archives: April 2025

Logical vs. historical order

The logical order of primacy in an argument isn’t necessarily the same as the historical order of primacy. For example, Morris Cohen argued in An Introduction to Logic and Scientific Method (1934) that the axioms of a system are often discovered after the theorems. According to Cohen, many of Euclid’s theorems were already known to the Ancient Greeks for hundreds of years before Euclid did his groundbreaking work. Euclid’s contribution wasn’t as much to discover the theorems as to discover the axioms for theorems already known. His contribution was largely to systematize already-existing knowledge.

In other words: What was in the history of ideas come up with and made known before and after doesn’t necessarily match up with what’s logically precedent and antecedent.

The phenomenalism of evolution

In Christian cosmogony, it was God who (1) made something out of nothing and then (2) gave that something the order that it has. In Dialogues Concerning Natural Religion (1779), David Hume argued for “a new hypothesis of cosmogony,” which was a challenge to the latter doctrine: that without God, the order in the world of matter has no good explanation. In essence, he argued that the order in the world of matter can be accounted for without hypothesizing supernatural intervention, for that order is the natural result of something that everybody knows: that some configurations of matter are more stable than others. If some matter in an unstable form by chance falls into another unstable form, then by definition (i.e., by definition of the term “unstable”) it’s unlikely for the matter to stay in that form for a long time. It’s when matter instead by chance falls into a stable form that it’s likely to stay like that. Chaos falls into chaos until it settles into order.

Interestingly: In The Selfish Gene (1976), Richard Dawkins used that Humean argument in order to contextualize biological evolution. Hume explained how chaos naturally settles into order (which is an explanation of any kind of evolution, whether biological or not), and to that explanation Dawkins added the idea of a replicator (which is how biological evolution works in that context).

Why are there so many rocks? Because rocks are especially stable. If some matter by chance falls into the form of a rock, then it’s likely to stay like that. And why are there so many birds? Not because birds are especially stable on the level of the individual, like rocks, but because birds are especially stable on the level of the group. They’re especially good at replicating themselves, and thus keeping the group in existence, before themselves falling out of existence.

That Humean argument, however, falls to thoroughgoing subjectivism. The difference between chaos and order isn’t inherent to the world of matter. The difference instead comes out of something subjective: categorization.

Rocks are stable because rocks are rocks whether they’re big or small, rough or smooth, etc. But why categorize like that? A big “rock” can fall and break into small “rocks,” and a rough “rock” can be made into a smooth “rock” after enough time in a river. Our categorization scheme is such that through those transformations they’re all still “rocks.” How stable! Theoretically speaking, though, it’s possible to use any categorization scheme that you want. Anything can be thought of as staying the same through any transformation, and anything can be thought of as not staying the same through any transformation. It’s possible to imagine a categorization scheme that puts even rocks into chaotic flux.

Deixis

When two people are talking to each other, each utterance is such that there’s a speaker and a listener. Furthermore, there’s everybody who’s neither the speaker nor the listener.

When a first-person pronoun is used (e.g., “I,” “me”), the speaker is referring to themselves. But it’s also possible for the speaker to refer to something close to themselves (e.g., “this,” “these”) or somewhere close to themselves (e.g., “here”).

In deixis, there’s:

  1. The speaker
  2. The listener
  3. Neither the speaker nor the listener
  4. The location in space of the speaker, the listener, or neither the speaker nor the listener
  5. The location in time of the utterance

Thus, it’s possible to refer to:

  1. The speaker of the utterance
  2. The listener
  3. Neither the speaker nor the listener
  4. Something near the speaker of the utterance
  5. Something near the listener
  6. Something near neither the speaker nor the listener
  7. Somewhere near the speaker of the utterance
  8. Somewhere near the listener
  9. Somewhere near neither the speaker nor the listener
  10. The past with respect to the utterance
  11. The present with respect to the utterance
  12. The future with respect to the utterance

There’s also:

  1. Male vs. female
  2. Singular vs. plural

Notation in logic

My interest in using notation in logic (e.g., ~ for “not,” strictly defined) is in part a result of often finding it useful to keep track of how I would notate the logical skeleton of what’s fleshed out as natural prose. For example, in natural prose the word “not” doesn’t always mean ~. In natural prose, there’s no 1-to-1 correspondence between the linguistic form and the logical substance. With the symbol ~ strictly defined, you can, whenever doing so would be useful, ask yourself: “Is the present usage of the word ‘not’ equivalent to ~?”

When I’m reading or writing, my internal experience is often such that I visualize ~ and other symbols as furigana. That is, I often ask myself whether I could justifiably put a certain logical symbol above a given word or phrase.

When writing, that technique helps you get the best of both worlds of the artificial and the natural: the artificiality of scientific writing and the naturalness of artistic writing. It helps you keep track of the logic without there being any need for you to artificially limit or regiment how you use natural language.