Grice e Richeri

 Richeri's Algebrae philosophicae in usum artis inveniendi (An algebra of philosophy, for use in the art of discovery) appeared in print. As the title suggests, Richeri introduced a set of notations to better express logical ideas.

Figure 3. Richeri's set of symbols for representing logical ideas in the Algebrae philosophicae (1761). Digitized by Archive.org from the copy owned by the Natural History Museum Library, London.

As we can see, two circle arcs are used in varying combination to represent logical ideas. For example, the symbol resembling the Greek letter ω$\omega$ is used for statements that are deemed possible, while an inverted version of this symbol ℧$\mho$ is used for contradictory statements. The text continues with an extensive list of symbol pairs that express contrasting concepts in logic: thing and nothing, positive and negative determinations, determinate and indeterminate, possibility and impossibility, mutable and immutable. Most importantly, Richeri's symbols for thing (aliquid) and nothing (nihil) resemble today's symbols for union (∪$\cup$) and intersection (∩$\cap$), respectively. This climax of this short article is a logic diagram that traces the possible outcomes of any object of critical inquiry.

Figure 4. Richeri's tree of logic symbols from the Algebrae philosophicae (1761). Digitized by Archive.org from the copy owned by the Natural History Museum Library, London.

In purely symbolic form, Richeri has given a sort of binary search for philosophical inquiry—indeed, this is the algebraic philosophy that was promised! In words, the tree begins like this:

• Any statement is either impossible (contradictory, the inverted ω$\omega$ in the corner) or possible (noncontradictory, the ω$\omega$ at the left end of the tree);

• If a statement is possible (ω$\omega$), it is either determinate (proven, the lower branch) or indeterminate (unproven, the upper branch);

Following the tree a bit further, we see that any possible, determinate statement must be either affirmative or negative. It's also interesting that Richeri viewed possible, indeterminate statements as being either determinable (provable) or indeterminable (unprovable). All told, Richeri's Algebrae philosophicae is only 16 pages long, with many of those consisting of symbolic representations for various propositions. If you have detected echoes of Leibniz in this paper, you are correct! This is no accident: Richeri specifically cited the Dissertatio de Arte Combinatoria in his work. Specifically, we can see how the subject-predicate form of a proposition has been carried over into the Algebrae philosophicae.