Basically I've always wondered this: how does formal logic deal with individuation? I would appreciate being stopped and corrected at any point here given my relative ignorance, but to the degree that logic deals with already-individualized terms and the relations between them — StreetlightX
What do you mean by a term? I ask because the word has a technical meaning in logic, a well-formed string with a denotation (usually of an individual, but it could also be of something else, like a property). If this is what you mean, then terms in logic don't have to be already individuated: they can be compositionally built up from parts, and certainly can come to be organically from how the language's syntax is structured.
So for example if you have a language with a iota operator, this is going to result in an individual when combined with an open formula, to pick out the individual that satisfies that formula. This can have lots of complicated interactions with your logic: you pick out an individual, and not a priori, but rather based on a property it has, and this property might additionally then be sensitive to all sorts of things, like the world parameter in modal logic, which would result in the individual changing depending on the modal context in which it occurs. So there is a lot of room for play in how individuals get picked out of a domain.
Or, if you mean not the terms themselves but the individuals they denote, there's all sorts of apparatuses that do interesting things with individuals rather than just taking them for granted. For example, you have traditional modal logic which separates the domain from possible worlds, capturing the notion that individuals persist across possibilities and that we can talk about the 'same' thing in different situations: but Lewisian counterpart theory will instead say that individuals don't persist in this way, but are rather tied to some single logical possibility or world, and that modal claims about individuals hold in virtue of one possible individual relating to another via a counterpart relation. And more generally the notion of variable domains plays with the idea that what a thing is depends on which possibility is manifested, with individuals being tied more tightly to possible worlds.
There's also apparatuses for trying to capture the way in which the actually existent and the non-existent differ by separating differing levels of the domain, as in free logic, and creating different rules of inference for how individuals behave in the truth conditions of formulas based on which domain they belong to.
There's also tools for dealing with mereology and subpart relations, and for dealing with the complexity of individuals combined from atomic parts (like 'Mary and John'), collective individuals like teams, the way properties either distribute over them atomically, or can apply collectively (as in, 'the crowd split', twhich doesn't mean each individual in the crowd split). There is logic for temporal stages of single individuals and how they persist over time, to model different ways of viewing ordinary individuals, as four-dimensional time worms, or single time-slices, or themselves stages of larger individuals, etc.
But the fundamental problem I think is that you are treating logic as if it were metaphysics. Whether or not logic is metaphysically insightful, and I think it almost always is, it is first and foremost a formal system that combines a syntax with an interpretation procedure. Logics in of themselves are just mathematical objects of a certain sort -- it's a separate question whether they apply to certain metaphysical issues or not. Analytic philosophers I think build logics as the result of certain expressive needs, and these logics can in turn tell us a lot about metaphysical intuitions, including ones about individuation, by formally representing certain relations about statements involving individuals in their truth conditions. This can be very valuable, as philosophizing in the absence of formality gives discussion on complex matters a fuzzy sort of air that becomes difficult to resolve or sometimes even think about in any interesting way.
Also at the back of my mind here is Bergson's critique of the modality of 'the possible' as anything more than a 'back-formation', as it were, where 'the possible' is simply thought of as the double of the actual that simply 'lacks reality' somehow - again the implicit critique is that thinking in terms of 'the possible' is to forego thinking in terms of individuation. — StreetlightX
Modal logic arose out of a desire to capture entailment relations to claims about possibility and necessity, such as the old medieval dictum that must implies can, the Kantian dictum that ought implies can, and so on. In that respect it's remarkably revealing, and different modal systems can be constructed to talk about different sorts of modality. The tack seems to be to develop actual tools for talking in modal terms, rather than to abstractly speculate on notions of the possible, and this is very fruitful. Many discussions about modality are confused because they don't differentiate between modal systems, don't understand the difference between epistemic and deontic modality, and so on. Modal logic itself cannot tell us about the nature of possibility, but again, a logic is a mathematical object, not a metaphysical thesis.
As a further aside, my hunch is that 'continental philosophy' has long been averse to formal logic precisely because kinds of concerns above, but I don't want to dwell on that. — StreetlightX
I think historically speaking this has certainly been a reason given by continental philosophers themselves. But I think a lot of the aversion comes from a more mundane source, which is that continental philosophers just don't get taught it. That is a situation that I think at least Husserl would not be happy about.