Kit Fine started his course on “Formal Ontology” on Monday afternoon. He said his focus would be on essence: essence as modality, essence as indexed modality and essence as constitutive modality.
Part 1
Kit started with the importance of distinguishing the essential from the accidental properties of things. For instance, Obama is essentially a human being, he’s accidentally the president of the USA. Why differentiate essential and accidental features? Essential characteristics are constraints (e.g., a marriage is between two people) whereas accidental are not.
Many sciences are interested in the nature of things. Metaphysics has a more generic interest instead of a specific one.
Kit then presented a quick introduction to Modal Logic in order to, at the end of this part, present the use of the box operator ☐ with an index, indicating to whom the property is essential. For instance, let S = Socrates, SS = Singleton Socrates, it is essential to SS that S belongs to SS — ☐SS (S ∈ SS) — but the same is not essential to Socrates — ~ ☐S (S ∈ SS) (~ meaning NOT).
Why do this? This places constraints on what they are a constraint of. Another example is marriage: the marriage being of two people is a constraint on the marriage, not on the people. This is the index modality. He didn’t have time to get to the third approach (constitutive modality).
Part 2
Kit started by comparing Modal Logics (ML) which he presented in the first part of the course with Description Logics (DL), which Renata Wassermann talked about just before him. He argued that DL = ML, if you consider that ML’s worlds are DL’s individuals.
He moved on to talk about Mereology (theory of parts). In particular, he mentioned that standard Mereology has done some damage to the field. Most of the times, when there’s a part-whole relation people just think of the whole as a fusion of its parts and that is just not the case.
He took the example of the tower mentioned by Guarino in his talk: a tower with a block B on top of a block A is not the same as the fusion of the parts. There’s also a relation R (A beneath B) which is important for the tower (for instance, B beneath A would be another tower altogether). He proposes the notion of Rigid Embodiments: a1, a2, …, an / R — ax being the proper parts and R being the relation between the parts.
Kit’s course goes very deep in the formalities of logics and metaphysics. Most of it goes beyond my modest knowledge of logics, unfortunately. Please comment if you want to add or correct something.
Part 3
Kit resumed the course with a quick comment on mereological extensionality (ME) and identity criteria (IC). Based on some examples, Kit explained how there are some problems in using ME to provide IC.
He then moved on to a subject in which he has been working for many years: truth-maker semantics (tms — purposefully written in lower-case letters). There are two types of tms: clausal tms, in which truth conditions are given explicitly by a clause; and objectual tms, in which there are things in the world related to the sentence that we are analyzing and that establish if it’s true.
Moreover, objectual tms has different views. In the wordly view, possible worlds are the truth makers. This has been the dominant view for the past 50 years or more and is known as “possible worlds semantics”. In the situational view, aspects or parts of the world (situations, conditions, states) are the truth makers. This is known as “situation semantics”.
By focusing on a part of the world, you ask the question: what exactly in this situation makes it relevant for being a truth maker of something? There are three approaches for this: exact, inexact or loose. According to Kit Fine, then, TMS with capital letters means exact, situational, objectival tms and this is where we want to be.
In TMS, there’s a state space ζ = (S, ⊑), where S is a non-empty set of states and ⊑ is a part-whole relation between states. This can then evolve to a state space model by adding an interpretation function: ζ = (S, ⊑, ||∙||+, ||∙||–) — the + indicates what verifies something, whereas – indicates what falsifies something.
From these, Kit formalized when a state verifies/falsifies something, the negation or something, a conjunction and a disjunction. This, then, is classical state space semantics. A few more detailed (i.e., you-have-to-be-a-logician-to-understand) questions were discussed from this definition. He also mentioned advantages of using this model instead of others, but I wasn’t able to comprehend that. Maybe someone who did can comment on this please? 🙂