The usual examples of a posteriori necessities are identities between kinds and objects under two descriptions, at least one of which involves a contingent mode of presentation, such as water (presented as “the stuff in this pond”, say) and H2O.
Such a posteriori necessities are certainly interesting. But we should not assume that these exhaust the scope of all a posteriori necessities.
For instance, Thomas Aquinas was committed to the existence of God being an a posteriori necessity: he held that necessarily God existed, but that all a priori arguments for the existence of God failed, while some a posteriori ones, like the Five Ways, succeeded.
For another theistic example, let p be an unprovable mathematical truth. Then p is, presumably, not a priori knowable. But God could reveal the truth of p, in which case we would know it a posteriori, via observation of God’s revelation. And, plausibly, mathematical truths are necessary.
For a third example, we could imagine a world where there is an odd law of nature: if anyone asserts a false mathematical statement, they immediately acquire hideous warts. In that world, all mathematical truths, including the unprovable ones, would be knowable a posteriori.
10 comments:
And if God doesn't exist, the thesis that God doesn't exist is a necessary truth. The main argument against the existence of God is _a posteriori_ (the argument from evil). Much fewer people think the _a priori_ arguments against the existence of God (the stone argument, the modal argument from evil) succeed.
Alex
Why does the distinction between a priori and a posterior necessity even matter.
To me, something is either necessary or it isn't.
BTW, to me, the non-existence of God is an a priori necessary truth based on the utter absurdity of God's existence. The concept of God juqst doesn't make any sort of sense to me.
The distinction is important though, for a posteriori necessities you need empirical observations. At the face of it an omnipotent, omniscient, perfectly good (any kind of goodness can be applied here) being is a perfectly coherent concept. Only due to a posteriori considerations of evil, or supposed paradoxes for the other attributes does the concept need to be readjusted, or the attributes be understood differently. And some other concepts get thrown over board. The point is though that considered in a vacuum the concept is coherent, which gives a priori evidence for its possibility. The a priori impossibility can be deduced from incompatible attributes of known concepts, e.g. a rational stone or concepts that violate the laws of logic
Dominik
Complete nothingness is, at the face of it, also a perfectly coherent concept. An omnipotent being that can create things from absolutely nothing, however, is, at the face of it, not a coherent concept at all.
Moreover, an omnipotent, omniscient, perfectly good being may be possible, but that does not make it a priori necessary. It is only necessary of all other conceivable alternatives are impossible.
A priori and a posteriori are epistemological concepts, necessary beings either exist or they don't. How we come to know them has no bearing on their (non-) existence.
Sure, but note that the concept above didn't include necessary existence, it was purposely formulated to include the Richard Swinburnes and the Basill Mitchells of this world.
Note also that the commitment to the possibility of the empty world alongside "ex nihilo nihil fit" entails the denial of S5.
Also if your definition of creatio ex nihilo requires the involvement of literal nothingness, this is a you-problem, not a problem for the Christian or other adherents of abrahamic faiths. Traditionally the doctrine has been construed as a creation from nothing outside of God, meaning the created world is an outflow exclusively from the divine essence and not e.g. additional abstracta in Plato's realm conceived like mathematical Platonists do it post-Frege. So if the assertion of impossibility were based upon that conception, then yes, this kind of theism were impossible, but who adhered to that one in the first place?
To the second paragraph, the first sentence is true, the second gets it the wrong way around. Patching together different attributes, even to maximal degrees (a limit simpliciter as opposed to limit case, following Miller) wouldn't entail anything. This is btw also why the real distinction is implicit in modern modal metaphysics, but I digress. The second sentence however hits in the exact same space that philosophers arguing about necessary beings, e.g. Craig, Oppy, Hale have hit in way too often and to no avail. It's true that on pain of absurdity only one absolutely necessary being is possible, given the priority of existence to nature. However we absolutely don't have to eliminate all other conceivable possibilities, for this gets the issue backwards. We rather have to ask what nature necessary existence might entail. This is the only intelligible way to approach that question, otherwise we'd once again try to discern necessary existence from the attributes that need to presuppose their existence however. That's also why Plantingas argument isn't convincing, or why Descartes ontological argument is the worst.
Your third paragraph is true, but then I don't understand why youquestion how the two types of necessities matter. True, ontologically the distinction adds nothing, but you recognize their usefulness in epistemology. Why assume Pruss wanted to make a point relevant to the former?
Walter:
One reason the distinction between _a priori_ and _a posteriori_ necessities matters is that it undercuts some old theories about the nature of necessity. Thus, until Kripke, a lot of people were happy to say that necessity = provability = aprioricity. You can see that going back to Leibniz at least: the possible is what does not involve a contradiction.
Even with Kripke, we still have people like Swinburne who think necessity = provability after expansion of definitions and resolution of natural kind and individual identity claims. So it's useful to be able to see that there are necessities that are not a priori and that are not of the Kripkean sort.
Interestingly, though, to refute those like Swinburne, we don't need the necessities I gave examples of to be _a posteriori_. We only need them not to be _a priori_.
Alex
I don't dispute that there are necessities that can be known a priori and necessities that can only be known a posteriori, but I don't accept that this has anything to do with the nature of necessities. Something is necessary if its negation entails a contradiction. That's the only nature of necessities that really matters.
Dominik
I only mentioned the possibility of an empty world to show that on the face of it lots of things can seem coherent concept, but in order to really claim they are coherent, much more is needed.
Like I told Alex, something is necessary if its negation entails a contradiction. If there is a possible alternative for N, then obviously the non-existence of N does not lead to a contradiction.
As to your claim that traditionally the doctrine of creatio ex nihilo has been construed as a creation from nothing outside of God, meaning the created world is exclusively from the divine essence, I am arguing from the claim that God is absolutely simple and immutable. It is obvious that something absolutely simple and immutable can have no outflow.
It is obvious that something absolutely simple and immutable can have no outflow.
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No? How is that supposed to follow? Simplicity merely states the identity of is-ness and that-ness, immutability states that nothing external to it can act upon it. Unless you assume that there mere fact of being is abstract, thus making the absolutely simple being an abstract object you don't have a reason for its inactivity. It's merely a lack of passive potencies. And this lack entails immutability, for there is nothing in the absolute simple to be actualized. Inactivity doesn't follow however. What follows is that the act it undergoes is necessarily unchangeable, meaning that the absolute simple can never stop to act upon itself, it's not possible for it to be static or inactive. So your assertion has a few hidden premises, it doesn't follow from simplicity nor immutability.
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