The syllogism is a logical system that was invented by Aristotle which deduces valid inferences from given premises. It is categorical in nature because each of two premises and the conclusion has an internal relationship of belonging or inclusion. Specifically, there is a major premise of a general nature and a minor premise that is usually specific, or of reduced generality. Both are combined deductively to reach or prove the conclusion.
Both premises and the conclusion deal with three categories two at a time, a subject term (S), a middle term (M), and a predicate term (P), joined by one of four binary inclusion relations. The major premise deals with M and P, the minor premise deals with S and M, and the conclusion with S and P. The four types of relations are denoted by the letters A, E, I, O (also a, e, i, o) and are described below. The premises may have M first or second, but the conclusion always has the S first and the P second.
S = Subject
M = Middle
P = Predicate
A = a = XaY = All X are Y
E = e = XeY = All X are not Y
I = i = XiY = Some X are Y
O = o = XoY = Some X are not Y
Major premise: MxP or PxM, x = a, e, i, or o
Minor premise: SxM or MxS
The distinction between the four Figures concerns the placement of the middle term M in each of the premises. In order to highlight this order, I’ve written them with ( and ) on the side of the relation where the M is.
There are only 24 valid inferences out of all possible combinations, six for each of the four Figures (and some of these may be erroneous sometimes due to the existential fallacy). In addition, they were given mnemonic names in the Middle Ages by adding consonants around the vowels of the relations. And so the valid inferences and their names (or something close to it) are as follows (by my notation and in no special order):
Lo! ’t is a gala night Within the lonesome latter years! An angel throng, bewinged, bedight In veils, and drowned in tears, Sit in a theatre, to see A play of hopes and fears, While the orchestra breathes fitfully The music of the spheres.
To understand all (causally) is to forgive all (normatively). To understand all (normatively) is to forgive nothing, for it is to talk about norms, not people; about mathematics, in which there is no error and no responsibility, and not about mathematicians, who do make mistakes.
— Lewis White Beck
Here is a set of distinctions by philosopher Lewis White Beck that may have some relevance to thinking about human determination and action. Beck was most renowned as a scholar of Kant.
Agent: a person X who thinks they are responsible and free in choices and actions (essentially a “free” agent), with motives and reasons
Actor: a person X who thinks they are an agent but is judged by a Spectator Y to not be free and instead determined by external causes
Spectator (diagrammed as Viewer): a person Y who observes any X and explains their actions exclusively by causal terms, and so judges them to be an Actor
Critic: a person Z who is in a position to agree with X that X is indeed an Agent or a Spectator Y that X is instead an Actor
A great deal of language revolves around explaining our behavior and that of others, both for the benefit or detriment to ourselves and others. All of us would usually rather be free and responsible agents than causally determined actors, but certainly we are not entirely free to act no matter how little we are not. Philosophical discussion of human action continues to be commonly cast into terms such as agency, action, intention, and even authenticity.
Beck later returned to these ideas for his Ernst Cassirer lectures, and a book of them was published in 1975. By the title and a short description, it appears that Beck reduced the fourfold to a mere dual, in order to simplify as well as elaborate his ideas (but I cannot say for sure as I have not read it). Still, I like the original fourfold scheme that in my mind bears likenesses to others presented here (for example, Modal Verbs.)