St. Augustine with a pocket full of punches.

3. The Manichees are accustomed to find fault in the following way with the first book of the Old Testament, which is entitled, Genesis. About the words, "In the beginning God made heaven and earth," they ask, "In what beginning?" They say, "If God made heaven and earth in some beginning of time, what was he doing before he made heaven and earth? And why did he suddenly decide to make what he had not previously made through eternal time?" We answer them that God made heaven and earth in the beginning, not in the beginning of time, but in Christ. For he was the Word with the Father, through whom and in whom all things were made. For, when the Jews asked him who he was, our Lord Jesus Christ answered, "The beginning; that is why I am speaking to you."g But even if we believe that God made heaven and earth at the beginning of time, we should certainly realize that there was no time before the beginning of time. For God also made time, and thus there was no time before he made time. Hence, we cannot say that there was a time when God had not yet made anything. For how could there be a time that God had not made since he is the maker of all time? And if time began to be with heaven and earth, there cannot be found a time when God had not yet made heaven and earth.lo When they say, "Why did he suddenly decide?" they speak as if some time passed during which God produced nothing. But a time could not pass that God had not already made, because he cannot be the producer of time unless he is before time. Surely the Manichees themselves read the Apostle Paul and praise and honor him, and they mislead many by interpreting his Letters wrongly. Let them tell us what the Apostle Paul meant when he said, "The knowledge of the truth which is in accord with the goodness of God for the hope of eternal life, which God who cannot lie, promised before eternal time." For what could precede eternal time? Let them be forced to explain this. Then they will understand that they do not understand when they rashly want to find fault with what they ought to study with care.

4. Suppose, however, that they do not say, "Why did God suddenly decide to make heaven and earth?" but remove the word "suddenly" and only say, "Why did God decide to make heaven and earth?" For we do not say that this world has the same duration as God, for this world does not have the same eternity as the eternity that God has. God certainly made the world, and thus time began to be along with the creation that God made, and in this sense time is called eternal. Nonetheless, time is not eternal in the same way that God is eternal, because God who is the maker of time is before time. So too, all the things that God has made are very good, but they are not good in the same way that God is good, because he is their maker, while they are made. Nor did he give birth to them out of himself so that they are what he is; rather he made them out of nothing so that they are equal neither to him by whom they have been made nor to his Son through whom they have been made. For this is juSt. But if they say, "Why did God decide to make heaven and earth?" we should answer them that those who desire to know the will of God should first learn the power of the human will. They seek to know the causes of the will of God though the will of God is itself the cause of all that exists. For if the will of God has a cause, there is something that surpasses the will of God-and this we may not believe. Hence, one who asks, "Why did God make heaven and earth?" should be told, "Because he willed to." For the will of God is the cause of heaven and earth, and the will of God, therefore, is greater than heaven and earth. One who asks, "Why did God will to create heaven and earth?" is looking for something greater than the will of God, though nothing greater can be found. Hence, let human temerity hold itself in check, and let it not seek what is not lest it not find what is. If anyone desires to know the will of God, let him become a friend of God. For, if anyone wanted to know the will of a man of whom he was not a friend, everyone would laugh at his impudence and folly. But one becomes a friend of God only by the highest purity of morals and by that goal of the command, of which the Apostle speaks, "The goal of the command is charity from a pure heart and a good conscience and faith unfeigned," and if they had this, they would not be heretics.


St. Augustine, De Genesi contra Manichaeos 1.2.3-4.

not paradoxical.

"There is an exception to every rule."  Yes, even to that one. 

on inconceivability and impossibility.

I take it that for any proposition p, p might be inconceivable in at least two senses.  The first sense we might call inconceivable simpliciter because p is seen to be necessarily false for either logical or metaphysical reasons. Consider, for instance, that something is both red and not red^a.  I take it that the reason why something is both red and not red is inconceivable is because we simply see (with the mind’s eye, so to speak) that it is impossible in itself, and something that is impossible per se is (or can be?) ipso facto inconceivable.  Thus, that something is both red and not red is inconceivable simpliciter not because of a lack of cognitive ability on our part.  On the contrary: that something is red and not red is inconceivable simpliciter because we have the cognitive ability to see its impossibility.

Similarly, the same can be said for some metaphysical statements.  That something can be both red and green all over^b does not assert a contradiction, and hence it is logically possible^c.  Nonetheless, that something can be both red and green all over is impossible. Even though it is not contradictory per se, we see (with the mind’s eye, so to speak) that it is impossible per se. Thus, that something can be both red and green all over is impossible (though not logically so) and hence it is (or can be?) ipso facto inconceivable.  And further, as before, that something is both red and green all over is inconceivable simpliciter not because of a lack of cognitive ability on our part.  On the contrary: that something is both red and green all over is inconceivable simpliciter because we have the cognitive ability to see its impossibility.

In sum, a proposition p may inconceivable in at least one sense: a proposition p might be inconceivable simpliciter for logical or metaphysical reasons; namely, that it asserts a logical or metaphysical impossibility.

But, a proposition p might be inconceivable simply because we lack the cognitive equipment to see its possibility. We might call this sense of inconceivability lack inconceivability. A putative candidate for lack inconceivability might be that there is a color that is not red, blue, or yellow, nor some combination thereof.  I say that this proposition is merely lack inconceivable because it does not violate a law of logic nor does it seem metaphysically impossible (for it violates no law of logic nor do I see its metaphysical impossibility), but rather because I simply cannot imagine what it such a color would look like.  The only colors I can think of (conceive of) are those colors that are red, yellow, and blue, or some combination thereof.  But, it seems to me, to group the proposition that there is a color that is not red, blue, or yellow nor some combination thereof in the same class with something can be both red and not red and something can be red and green all over seems wholly unwarranted: I can see the impossibility of the latter two; the former is indeed inconceivable to me, but I just do not see its impossibility.

In sum, a proposition p is inconceivable simpliciter just in case we see the impossibility of p.  On the other hand, a proposition p is merely lack inconceivable if we cannot think of p but yet do not see its utter impossibility.

Now, with which kind of inconceivability should we tag the following proposition?

There is some hotel with an actually infinite number of rooms and guests such that if you were to add one more guest to it then there would be the same number of guests before the guest arrived as there was after the guest arrived.

I take it that this (unwieldy) proposition is inconceivable.  But is it inconceivable simpliciter? Not by my lights: it does not violate a law of logic, nor do I see its per se metaphysical impossibility.  (It may be metaphysically impossible, though, but I do not see its metaphysical impossibility.)

At best it seems lack inconceivable:  I simply cannot comprehend it.  But, the mere fact that it is lack inconceivable is not enough for us to think it is inconceivable simpliciter. As such, we are not warranted in saying that it is impossible; it could be impossible, but we do not seem to be in a position to know. 

_____________________

 

  ^a If you want to be fussy, add at the same time.                                                ^b If you want to be fussy, add at the same time.                                                ^c For you naysayers:  that two contraries are true of same subject is indeed logically impossible, but that red and green are contraries is not a tautology. You could stipulate that red and green are contraries, but good luck proving that they are with the mere use of tautologies and the rules governing logical syntax. 

The Peripatetic on unactualized possibilities.

I once wrote a whole paper on a single, seemingly innocuous, line from Aristotle:

"For example, it is possible for this cloak to be cut up, and yet it will not be cut up but it will wear out first. (De Int. 9)"



Not only is the truth of this proposition deeply perplexing from the point of view of trying to understand Aristotle's modal thought, it's deeply perplexing tout court.

(im)possible colors.

Suppose that the primary theory of colors is merely contingently true (i.e., that it just so happens that every color we've experienced so far is either red, blue, and yellow or some combination thereof). Could God make a color that cannot be derived by the three primary colors? If your answer is "yes", then it seems to me that you're committed to the thesis that it's actually possible that God make the actually inconceivable.

Or, to put it more poignantly: the inconceivable is possible.

In Swingroverian terms: the actually inconceivable is actually possible.

on the necessity of necessity.

I take it that all true conditional statements express a necessary connection between the antecedent and the consequent. Put slightly different: all true conditional statements are true because they express a necessary connection between the antecedent and the consequent, and all false conditional statements are false because they fail to express a necessary connection between the antecedent and the consequent.

Consider, for instance, the standard conditional form: if p then q (symbolically: p ⊃ q). Quite ordinarily, we express things in the standard conditional form to express sufficient conditions, whereby in saying p ⊃ q we mean p is sufficient for q. How is it that in saying p is sufficient for q we are expressing a necessary connection between p and q? At least in this sense: to say that p is sufficient for q is to say q is a necessary condition for p. For example, consider the following true conditional: if there is life then there is water. I take it that this conditional, if true, is true because water is a necessary condition for life, and hence, this is why the antecedent’s being true (that there is life) is sufficient for the truth of the consequent (that there is water).

Another way to say the same thing is to say that the standard conditional expresses natural dependencies. Again, to say that p is sufficient for q is to say that q is a necessary condition for p, and it seems to me that this second statement (and thereby the first) is another way of saying that p depends upon q. In the same way that someone might say that water is necessary for life, someone might equally say that the possibility of life depends upon the existence of water.

As such, all conditional statements that fail to express necessary conditions or dependency relations between the antecedent and the consequent are false, even if the antecedent and consequent are true. For instance, the following antecedents and consequents for the following conditionals are all true:

If Louis lives in Idaho then I am an uncle

If Soren is a person then Jon is a budding logician

If Max is Max then Max kissed a girl

If Max kissed a girl then Max kissed Brianna.

But alas, all of these conditionals are false, for the truth of each antecedent is neither sufficient nor dependent on the truth of each consequent, and neither is each consequent necessary for the truth of each antecedent.

According to the truth functional interpretation of the conditional, all these conditionals are true. By modus tollens, etc.

.:addendum:.

Here’s my modal interpretation of the truth functional interpretation of the material conditional:

p        q         p ⊃ q

T        T         ◊T
T        F        ~◊T
F        T         ◊T
F        F         ◊T

Since, on my view, p ⊃ q is true if and only if p depends upon the truth of q, the second row is sufficient to show that the corresponding material conditional is necessarily false. However, rows 1, 3, and 4 merely assert necessary (but not sufficient) conditions for the corresponding material conditional to be true. That is:

If p is true and q is true, then p ⊃ q is possibly true.
If p is true and q is true, then it is impossible that p ⊃ q is true.
If p is false and q is true, then p ⊃ q is possibly true.
If both p and q are false, then p ⊃ q is possibly true.

Another way to put it:

If p is true and q is true, then p might depend upon the truth of q to be true.  If p is true and q is false, then p does not depend upon the truth of q to be true.  If p is false and q is true, then p might depend upon the truth of q to be true.  If p is false and q is false, then p might depend upon the truth of q to be true.