Intro and types
I’ve been paying very close attention as of late to a special type of discourse: Namely, about what is possible and what is impossible. This study has led me to be very careful about my language use when speaking of such things because there are multiple types of possibilities: Logical, epistemic, physical, metaphysical, practical, technological etc. I have even created a modified version of modal logic that can handle multiple types of possibilities.i Logical possibility we ought to call L-possible, epistemic possibility we ought to call E-possible etc.
And before that I discovered the modal fallacy, which occurs when people confuse the scope of the possibility used. It may be about a single proposition or an entire implication.ii
Versions: Hypothetical and absolute
And then I discovered that even a single type (and pay close attention to the words used) of possibility is used in multiple ways. Let’s call these versions. There is the absolute version and then there is the hypothetical version. I did not invest these terms; Liebniz did.iii
Since I have already written of the aforementioned let me skip them and proceed on defining absolute and hypothetical modaly. Absolute modality is the one I’ve always been talking about and hypothetical is the one that others often talk about, which confuses matters a lot, and ultimately ends up wasting a lot of time.iv
But that is not clear enough, so let me define the first. A proposition is absolutely necessary iff the negation is a contradiction (which has the form [p∧¬p]). A hypothetical impossibility is a proposition which if added to a set of propositions would result in a contradiction. This is the kind of impossibility that we’re talking about when making reductio arguments: “If something, then some contradiction, but that it impossible, so something can’t be true.” Yes, it can in the absolute sense. We ought not to confuse them.
In a later article I attacked a hypothetical impossibility for being an absolute impossibility.v
The value of the hypothetical impossibility term?
I ask now what value we have of this term. What need do we get covered by accepting this term into our collection of words? None but confusions as far as I can tell. We might as well stop called the hypothetical impossibility for an impossibility at all, and then while we’re at it, we should be very careful in our usage of the necessarily-operator when writing conditionals, so we don’t commit the modal fallacy. It doesn’t matter if we call it ‘must’, ‘cannot’ ‘has to be’ or something else. We must be very clear in our language about this matter, for if anything is certain (meant non-literally), it is that the plain English language is not at all good enough for handling modalities. Clarity is the way forward.
iiiIt is discussed here: http://maverickphilosopher.powerblogs.com/posts/1159490720.shtml but originally from here: http://www.class.uidaho.edu/mickelsen/texts/Leibniz%20-%20Correspondence.htm