I really enjoyed this podcast discussion between Cathy Legg and Matt Teichman. The topic is C.S. Peirce, and particularly his theory of categories, or modes of being. As Legg and Teichman explain, the idea of modes of being fell out of favour in the 20th century, especially due to the influence of Quine, who said there was one mode of being: existence. But here is some motivation for categories, from the show notes:
Yet in the nineteenth century, philosophers considered not only what exists, but how things exist. They considered modes of being. Here’s one basic reason to appreciate their consideration: Reality can entail things that don’t exist (at least in the way you can verify experimentally) but that nonetheless are true. And these truths can be more than analytical, that is, true because we define them to be true; no, we can find these truths in our experience of the world. For instance, as is mentioned in the podcast, host Matt doesn’t have a sister; but if he did, she wouldn’t speak Swahili as a native. That possibility, we can say, is false. This possibility has another mode of being than existence, which we know not through science, but perhaps through philosophy.
Peirce’s categories are called firstness, secondness, and thirdness. Again from the show notes: “These modes of being entail things and properties, but also relationships, thoughts, and language — to say nothing of more cosmic senses of being.”
Firstness is a category of monads: things considered in and of themselves, without relation to anything else. Legg gives the example of properties such as “redness.”
Secondness is a category of dyads: relationships between pairs of things. Legg gives the example of walking into a room and accidentally hitting her leg on a table. There is an action/reaction between the table and her leg.
Thirdness is a category of triads: relationships between groups of three. Legg provides the example of giving a gift: there is a giver, a receiver, and the gift. Representation is triadic.
Teichman asks why there is not fourthness, fifthness, etc. The answer is that Peirce saw you could always reduce fourthness (and “higher” categories) to thirdness. Legg gives an example relating four things: purchasing a house, where there is the buyer, the seller, the real estate agent, and the house. Peirce saw that you could reduce this to triads by talking in terms of an event (e.g. a purchasing event). The event E has a buyer X (a triad), the event E has a seller Y (a triad), the event E has an agent Z (a triad), and the event E has a house H (another triad).
If you have a background in linguistics or natural language processing, this might sound very familiar to you. The reason is that it is essentially a type of semantic representation associated with Donald Davidson, typically called neo-Davidsonian semantics these days. For example, see Chapter 15 of Jurafsky & Martin’s book on speech and language processing. It’s fascinating that Peirce had already developed these ideas so long ago.
Peirce also saw that the thirdness category is necessary and can’t be reduced to secondness. Legg and Teichman don’t go into detail on this, but we can give a simple example. Consider again the gift-giving triad mentioned earlier. Let’s try to reduce it. So we’ll first say we have a gift-giving event E, and E has the giver G. But that’s still a triad — we haven’t reduced anything.
It’s not a long (or difficult) episode, and I highly recommend it if you want to learn some of Peirce’s core ideas.