I've been thinking through some assumptions which seem to be entailed by classical logic. I'm sure these have been mentioned in a thousand places, in much better ways (I don't actually blog about what I've taken the time to study; I'm blogging to put off that stuff). However, I am interesting in what people have to say about the following.
Problem #1: Both the law of identity (A=A) and the law of non-contradiction (A /= ~A) require that the same token have two instances. This already assumes that something can be repeated as exactly the same thing in multiple instances (maybe it even implicitly brings in Parmenides?). If everything is simply more or less similar to other things, then this is not obviously true.
Problem #2: The law of non-contradiction assumes that we can truly make negative statements. A is not ~A, where both A and ~A refer to A. Therefore, whatever A is, it cannot be ~A. However, if we always have some positive idea in mind when we make an assertion, then we never do actually refer merely to ~A; we refer to some B, which we take to be ~A. But B is not simply ~A, and refers to something other than A. As such, further investigation into B could show that it is really not incompatible with A, and so our actual use of the law of non-contradiction failed.
For something completely different: I'm currently signing up for classes for next semester. I'm presently planning on taking Kant, Early German Idealism (Fichte, Schelling, Jacobi, Hölderlin, etc.), and Neoplatonism (with an emphasis on how the early NP commentators worked with Aristotle). Should be an interesting semester.
2 comments:
Hi Michael. First, two things about (1) and (2):
Concerning your (1), A could be either a token or a type. In fact, given the current conventions of notation, A represents either a proposition or a predicate. As a stand-in for a proposition, A represents something that expresses some a state of affairs. Of course, states of affairs are made up of instances and relations between instances. As a stand-in for predicates, they can represent types or tropes, i.e. a property that is unique to some instance, such as Bill Clinton's charisma. But suppose both As represent some instance. The presumption is that they refer to the same thing, which obviously entails only a single instance. If one A represents one instance and the other represents a different instance, the two instances are As only equivocally.
Concerning your (2), assuming A represents some property, ~A needn't entail B, i.e. something positive. ~A could just be that: a privation.
Now to address your deeper question: yes logic has metaphysical implications. For instance, any adequate logic can't get off the ground without a distinction between variable and predicate. At the least, drawing this distinction implies a distinction between concept/word and object, and, some would argue, property and object.
While I admit that these would be the ways of explaining logic, my thesis is that our means of expression do not allow for this. So, for (1), we might not be able to actually express states of affairs, but we can only expressively intend things that are close enough to pass for the same when not looked at critically (given rise to an illusion that we refer to a single state of affairs and/or proposition with multiple utterances).
For (2), I'm saying that in actual practice, it may be that we don't ever intend simply a privation; if we did, that would make the logic work. We actually intend some B, however; always have and always will, due to how we think.
Maybe on the other hand everything works well and logic has no problems in its use; I'm simply trying to show that this is not as straightforward a proposition as it may seem.
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