A group of undergraduate students at Fort Hays State University recently discovered two new types of categorical claims. It has long been believed that there are four standard forms of categorical claims, but the recent discovery changes everything.
Standard forms of categorical claims are patterns that all previously known categorical claims follow—until now. The traditionally accepted standard form claims are known as A-, E-, I-, and O-claims. During a recent discussion in Dr. Clark's Critical Thinking for Scientists class, students discovered two new forms, U- and Y-claims.
When asked how the discovery was made and why it has taken so long, Dr. Clark said, "I don't know, it's kind of crazy. We were looking at the claims on the board and noticed that they were all named after vowels: A, E, I, and O. I guess no one has noticed it before. One student asked, 'Where is U?' Another student remarked, 'Yeah?' And another said, 'Y is sometimes a vowel too, what about Y?'"
Dr. Clark continued, "In science, and physics in particular, we are often looking for patterns and missing pieces. I thought, these kids are on to something; there must be two missing claim types. After some discussion, we found them. The key was Y, Y is sometimes a vowel, and sometimes it isn't. The traditional standard forms are either affirmative or negative, but not both. So we thought maybe the new claims are both affirmative and negative, a superposition of yes and no, if you will. And sure enough, there they were: the universal-maybe and particular-maybe."
The two new forms discovered by these students, written in layman's terms, are:
- All S are sometimes P.
- Some S are sometimes P.
In more technical terms, they can be written:
- All S are in a superposition of P and ~P.
- Some S are in a superposition of P and ~P.
Dr. Clark commented that he was "really proud of these kids for thinking outside the box. We would have never made this discovery by sticking to the textbook."
When asked about what's next, Dr. Clark said, "Well, I'm not sure we're done here. The landscape of categorical logic could be getting ready to change dramatically. If you look at the square of opposition, with these two new forms we have a chair of opposition. If there were two more forms, we could build a cube of opposition. That would be something special, but it's just the tip of the iceberg, because (as far as we know), there are only six different vowels. Perhaps there are two vowels that we have not discovered yet. It's exciting to think about. A lot of logic still needs to be done, and that's what we are planning to do."