So, I want to get a bit more clear on what the grounding objection to Molinism is saying. As far as I can tell at this moment, the grounding objection seems to go something like this.

The anti-Molinist says that some general statement about the relation between grounding and truth such as the following holds:

(A) If some proposition is true then there is an entity which grounds its truth.

It seems in this context 'grounds the truth of p' just means 'is the truthmaker of p'. The objector to Molinism then proposes:

(B) There could be no entity to ground the truth of CCF's.

Of course from A and B it follows that all CCF's, if they are meaningful, are necessarily false. Hopefully this is all a correct representation of the objection.

## Sunday, August 25, 2013

## Wednesday, July 3, 2013

### Essence and Ontological Dependence

This is my term paper from my independent study last quarter on ontological dependence. I will say beforehand that I did not have enough time to make it great, and there is a lot more I could have said. However, I believe it contains a relatively good summary of Kit Fine's position, and I think the stuff toward the end about causation is somewhat original (albeit sketchy). So hopefully someone will find it interesting and useful.

I. Introduction – Examples and What We Want

In many areas of philosophy, as well as common discourse, it is normal to say that one thing depends on another. Moreoever, one of these uses of the word 'depends' is a distinctly ontological sense, as opposed to, say, a notion of epistemological dependence or logical dependence. I will use the term 'dependence' throughout this essay to stand for this particularly ontological notion, unless otherwise stated. So for instance, we might say that a composite depends on its constituents. Or we might say a smile depends on the mouth of which it is a smile. Or that a hole depends on the thing which it is a hole in. This is a philosophical datum and the only reason one would deny it or feign incomprehension seems to be hard-headedness.

I. Introduction – Examples and What We Want

In many areas of philosophy, as well as common discourse, it is normal to say that one thing depends on another. Moreoever, one of these uses of the word 'depends' is a distinctly ontological sense, as opposed to, say, a notion of epistemological dependence or logical dependence. I will use the term 'dependence' throughout this essay to stand for this particularly ontological notion, unless otherwise stated. So for instance, we might say that a composite depends on its constituents. Or we might say a smile depends on the mouth of which it is a smile. Or that a hole depends on the thing which it is a hole in. This is a philosophical datum and the only reason one would deny it or feign incomprehension seems to be hard-headedness.

## Wednesday, June 19, 2013

### Two Inadequate Arguments for a Finite Past

In this post I will consider two arguments which have at times been brought up in connection with the Kalam Cosmological Argument (KCA), which I will call the "subtraction argument" and the "argument from traversing an infinite," the former of which I have heard from Dr. William Lane Craig. The KCA goes as follows:

1. Whatever begins to exist has a cause.

2. The universe began to exist.

3. So the universe has a cause.

The arguments in question are designed to defend the second premise, which is presumably implied by the past's being finite. I should note that I think the second premise is true and there is strong evidence in favor of its truth. Alexander Pruss has given an excellent argument here, to which I have heard no compelling reply. I also think there is very strong scientific indication of the premise's truth, which Craig has adequately demonstrated. I just don't think these two arguments demonstrate its truth.

The "argument from traversing an infinite" goes something like this:

1*. If the past were infinite, one would have to cross an infinite temporal distance to get to the present moment.

2*. If one had to cross an infinite temporal distance to get to the present moment, then one could not get to the present moment.

3*. So if the past were infinite, then one could not get to the present moment.

4*. But we are at the present moment.

5*. So the past is not infinite.

The argument requires some unpacking. First of all, to say the past is finite is to say there was a beginning of time, and to say the past is infinite is to say there was no beginning of time. Second, 'temporal distance' means the length of time between one moment and another. There is a perfectly good way to define finite temporal distance. If we take our measure of time as a second, we can assign the current time the number 0, the time one second ago -1, the time two seconds ago -2, and so forth. To find the temporal distance from one time t1 to another t2, we take the number assigned to t1 and the number assigned to t2, and take the absolute value of the difference between the two. For instance, take the time 1000 seconds ago. To find the temporal distance from that time to the present time you take the absolute value of -1000 minus 0, which is of course 1000 seconds. Pretty simple.

However, problems begin to arise when we start to talk about an "infinite temporal distance." This phrase is ambiguous, and depending on which interpretation of this phrase we take it will either cause problems for premise 1* or for premise 2*. First, the phrase could mean something analogous to the way finite temporal distance has been defined above. However, infinity is not a real number, so you simply cannot define an infinite temporal distance the same way as above. There is no number "-infinity" from which you can subtract, say, -5. So if this is what is meant, then premise 1* appears to be false, since no real sense can be given to an infinite distance in this way.

On the other hand, crossing an infinite temporal distance could just mean that the set of all the numbers assigned to the seconds is infinitely large. This makes perfectly good sense of the phrase, but then in that case it is not clear why premise 2* is true. As Thomas Aquinas points out, there being an "infinite temporal distance" in this sense is perfectly consistent with all the temporal distances from the past to the present being finite, where "temporal distance" is defined as it was earlier:

"Passage is always understood as being from term to term. Whatever bygone day we choose, from it to the present day there is a finite number of days which can be passed through. The objection, however, is founded on the idea that, given two extremes, there is an infinite number of mean terms." [ST Ia q.46 a.2]

So for instance, the distance from the present to one second ago is 1 second, the distance from the present to two seconds ago is 2 seconds, etc. and so on forever and ever back into time. Hence, no matter how far you go back in time, the distance in the way I've defined above from any given past moment to the present will be finite, and thus you will only have to cross a finite number of seconds to get to the present moment. But of course any finite number of seconds can at least in principle be crossed; hence, premise 2* is false.

So much for the "traversing an infinite" argument then. The "subtraction argument" goes something like this:

1'. If the past were infinite, then an actual infinity would be possible.

2'. If an actual infinity were possible, then one could perform subtraction on infinities.

3'. But if one can perform subtraction on infinities, then one will get contradictory results.

4'. So if the past were infinite, then one would get contradictory results.

5'. So the past is not infinite.

This seems to be one of the arguments William Lane Craig gave in his debate against Peter Millican. Let me first point out an ambiguity in the phrase "actual infinity," after which I'll assess the argument under each interpretation. Here are two possible meanings of the phrase "actual infinity":

(ACT1) An actual infinity exists just in case for some time, at that time there exist distinct concrete objects such that the size of the set containing all and only them is infinite.

(ACT2) An actual infinity exists just in case there is some set containing only distinct concrete objects whose size is infinite.

Some elaboration is in order. First off, both definitions presume when speaking of actual infinities that we are dealing with concrete objects. While my understanding is that Craig does not believe there are infinitely many numbers (he is a nominalist), presumably his argument doesn't presuppose this view; Craig only wants to rule out the possibility of infinitely many concrete objects. Now as for the definitions themselves, the difference between (ACT1) and (ACT2) is that in (ACT1) you only have an actual infinity when all the concrete objects exist

Let's deal with the first definition, (ACT1). Given our definition of actual infinity in (ACT1), premise 1' does not appear to be true, or at least not obviously true. It is consistent with holding that the past is infinite that at each time there are only finitely many concrete objects. And if you believe only objects in the present moment exist, then 1' is definitely not true. The fact that there were objects at each time in the eternal past in no way implies an infinite collection of simultaneously-existing objects.

My main concern is with 2' and 3' though. Take 2', since it is also ambiguous to a certain extent. The problem is it is not immediately clear what is meant by "perform subtraction on infinities." Craig acknowledges that the ordinary operation of subtraction is not defined for "infinity". If he did mean this, i.e. the ordinary operation of subtraction, then clearly 3' would be true but 2' would have no support at all. So it cannot mean the ordinary operation of subtraction.

Now, Craig gives us an example to support 2' and 3', and this may help us understand what he means. Suppose we have an infinite number of coins. Then we can take away all the coins except three of them. And in this sense we can be said to perform subtraction on infinity, i.e. taking away some number of things from an infinitely large collection. This definition of performing subtraction on infinities makes sense. But then why is 3' true? Craig says, considering our infinite number of coins, that you can take away infinitely many coins and be left with 3 coins, and thus infinity minus infinity = 3; but you can also take away infinitely many coins and be left with 2 coins, and thus infinity minus infinity = 2; hence, 2 = 3, which is our contradiction.

The problem with this argument is that it runs on an equivocation: We agreed that we are not using "performing subtraction" or "minus" in the normal sense of the arithmetical operation, since this just makes no sense. So "infinity minus infinity = 3" must simply be shorthand for saying "taking away infinitely many objects from an infinite collection leaves us with 3", and similarly with "infinity minus infinity = 2." But then if "2 = 3" means that 2 is identical to 3, then it certainly does not follow that 2 = 3; all that follows is that you can take away an infinite number of things and be left with 3, and also take away an infinite number of things and be left with 2, and this is certainly not a contradiction! It only looks like a contradiction when we are illicitly inferring "2 = 3", as if the phrase "infinity minus infinity = 2" were using "minus" and "=" in the same way as "5 minus 3 = 2." It would be like if I had infinitely many pennies and dimes, and I said, "infinity minus infinity = a penny, infinity minus infinity = a dime, so a penny = a dime." Clearly I am making an illicit inference here, and for the same reason Craig's argument makes an illicit inference as well.

Now, this whole time I have been working under the assumption that throughout the argument "actual infinity" is meant in the sense of (ACT1). But under interpretation (ACT2) the situation is even worse, since it is not clear 2' is true. It seems that in order to "subtract" infinitely many coins in the sense defined above, all of them must exist at the same time. But if "actual infinity" is taken in the sense of (ACT2), then it is not required that all of the infinite number of coins exist at the same time, and thus 2' has no support. And of course, with the exception of premise 1', all the same criticisms I have just given apply equally well under (ACT2). So, interpreted charitably, the argument seems to be a failure, with the primary problem being in premise 3'.

I should note one more time that, in spite of all my criticisms of these two arguments, I think there are good reasons for thinking the KCA is sound. I just don't think these are among them.

1. Whatever begins to exist has a cause.

2. The universe began to exist.

3. So the universe has a cause.

The arguments in question are designed to defend the second premise, which is presumably implied by the past's being finite. I should note that I think the second premise is true and there is strong evidence in favor of its truth. Alexander Pruss has given an excellent argument here, to which I have heard no compelling reply. I also think there is very strong scientific indication of the premise's truth, which Craig has adequately demonstrated. I just don't think these two arguments demonstrate its truth.

The "argument from traversing an infinite" goes something like this:

1*. If the past were infinite, one would have to cross an infinite temporal distance to get to the present moment.

2*. If one had to cross an infinite temporal distance to get to the present moment, then one could not get to the present moment.

3*. So if the past were infinite, then one could not get to the present moment.

4*. But we are at the present moment.

5*. So the past is not infinite.

The argument requires some unpacking. First of all, to say the past is finite is to say there was a beginning of time, and to say the past is infinite is to say there was no beginning of time. Second, 'temporal distance' means the length of time between one moment and another. There is a perfectly good way to define finite temporal distance. If we take our measure of time as a second, we can assign the current time the number 0, the time one second ago -1, the time two seconds ago -2, and so forth. To find the temporal distance from one time t1 to another t2, we take the number assigned to t1 and the number assigned to t2, and take the absolute value of the difference between the two. For instance, take the time 1000 seconds ago. To find the temporal distance from that time to the present time you take the absolute value of -1000 minus 0, which is of course 1000 seconds. Pretty simple.

However, problems begin to arise when we start to talk about an "infinite temporal distance." This phrase is ambiguous, and depending on which interpretation of this phrase we take it will either cause problems for premise 1* or for premise 2*. First, the phrase could mean something analogous to the way finite temporal distance has been defined above. However, infinity is not a real number, so you simply cannot define an infinite temporal distance the same way as above. There is no number "-infinity" from which you can subtract, say, -5. So if this is what is meant, then premise 1* appears to be false, since no real sense can be given to an infinite distance in this way.

On the other hand, crossing an infinite temporal distance could just mean that the set of all the numbers assigned to the seconds is infinitely large. This makes perfectly good sense of the phrase, but then in that case it is not clear why premise 2* is true. As Thomas Aquinas points out, there being an "infinite temporal distance" in this sense is perfectly consistent with all the temporal distances from the past to the present being finite, where "temporal distance" is defined as it was earlier:

"Passage is always understood as being from term to term. Whatever bygone day we choose, from it to the present day there is a finite number of days which can be passed through. The objection, however, is founded on the idea that, given two extremes, there is an infinite number of mean terms." [ST Ia q.46 a.2]

So for instance, the distance from the present to one second ago is 1 second, the distance from the present to two seconds ago is 2 seconds, etc. and so on forever and ever back into time. Hence, no matter how far you go back in time, the distance in the way I've defined above from any given past moment to the present will be finite, and thus you will only have to cross a finite number of seconds to get to the present moment. But of course any finite number of seconds can at least in principle be crossed; hence, premise 2* is false.

So much for the "traversing an infinite" argument then. The "subtraction argument" goes something like this:

1'. If the past were infinite, then an actual infinity would be possible.

2'. If an actual infinity were possible, then one could perform subtraction on infinities.

3'. But if one can perform subtraction on infinities, then one will get contradictory results.

4'. So if the past were infinite, then one would get contradictory results.

5'. So the past is not infinite.

This seems to be one of the arguments William Lane Craig gave in his debate against Peter Millican. Let me first point out an ambiguity in the phrase "actual infinity," after which I'll assess the argument under each interpretation. Here are two possible meanings of the phrase "actual infinity":

(ACT1) An actual infinity exists just in case for some time, at that time there exist distinct concrete objects such that the size of the set containing all and only them is infinite.

(ACT2) An actual infinity exists just in case there is some set containing only distinct concrete objects whose size is infinite.

Some elaboration is in order. First off, both definitions presume when speaking of actual infinities that we are dealing with concrete objects. While my understanding is that Craig does not believe there are infinitely many numbers (he is a nominalist), presumably his argument doesn't presuppose this view; Craig only wants to rule out the possibility of infinitely many concrete objects. Now as for the definitions themselves, the difference between (ACT1) and (ACT2) is that in (ACT1) you only have an actual infinity when all the concrete objects exist

*at the same time*. In (ACT2) you could have finitely many objects at t2, finitely many at t1, and so forth, yet if you take a set containing concrete objects from different times, and the times go back to infinity, you will still have an actual infinity. So both of these definitions make fine sense. However, the assessment of the argument will depend on which interpretation we take.Let's deal with the first definition, (ACT1). Given our definition of actual infinity in (ACT1), premise 1' does not appear to be true, or at least not obviously true. It is consistent with holding that the past is infinite that at each time there are only finitely many concrete objects. And if you believe only objects in the present moment exist, then 1' is definitely not true. The fact that there were objects at each time in the eternal past in no way implies an infinite collection of simultaneously-existing objects.

My main concern is with 2' and 3' though. Take 2', since it is also ambiguous to a certain extent. The problem is it is not immediately clear what is meant by "perform subtraction on infinities." Craig acknowledges that the ordinary operation of subtraction is not defined for "infinity". If he did mean this, i.e. the ordinary operation of subtraction, then clearly 3' would be true but 2' would have no support at all. So it cannot mean the ordinary operation of subtraction.

Now, Craig gives us an example to support 2' and 3', and this may help us understand what he means. Suppose we have an infinite number of coins. Then we can take away all the coins except three of them. And in this sense we can be said to perform subtraction on infinity, i.e. taking away some number of things from an infinitely large collection. This definition of performing subtraction on infinities makes sense. But then why is 3' true? Craig says, considering our infinite number of coins, that you can take away infinitely many coins and be left with 3 coins, and thus infinity minus infinity = 3; but you can also take away infinitely many coins and be left with 2 coins, and thus infinity minus infinity = 2; hence, 2 = 3, which is our contradiction.

The problem with this argument is that it runs on an equivocation: We agreed that we are not using "performing subtraction" or "minus" in the normal sense of the arithmetical operation, since this just makes no sense. So "infinity minus infinity = 3" must simply be shorthand for saying "taking away infinitely many objects from an infinite collection leaves us with 3", and similarly with "infinity minus infinity = 2." But then if "2 = 3" means that 2 is identical to 3, then it certainly does not follow that 2 = 3; all that follows is that you can take away an infinite number of things and be left with 3, and also take away an infinite number of things and be left with 2, and this is certainly not a contradiction! It only looks like a contradiction when we are illicitly inferring "2 = 3", as if the phrase "infinity minus infinity = 2" were using "minus" and "=" in the same way as "5 minus 3 = 2." It would be like if I had infinitely many pennies and dimes, and I said, "infinity minus infinity = a penny, infinity minus infinity = a dime, so a penny = a dime." Clearly I am making an illicit inference here, and for the same reason Craig's argument makes an illicit inference as well.

Now, this whole time I have been working under the assumption that throughout the argument "actual infinity" is meant in the sense of (ACT1). But under interpretation (ACT2) the situation is even worse, since it is not clear 2' is true. It seems that in order to "subtract" infinitely many coins in the sense defined above, all of them must exist at the same time. But if "actual infinity" is taken in the sense of (ACT2), then it is not required that all of the infinite number of coins exist at the same time, and thus 2' has no support. And of course, with the exception of premise 1', all the same criticisms I have just given apply equally well under (ACT2). So, interpreted charitably, the argument seems to be a failure, with the primary problem being in premise 3'.

I should note one more time that, in spite of all my criticisms of these two arguments, I think there are good reasons for thinking the KCA is sound. I just don't think these are among them.

## Tuesday, June 4, 2013

### Consequentialist 'Bajillion People' Objections and the Divine

If you are a believer, this argument

(1) It's absolutely wrong to blaspheme against God, as in swearing at God. Even if a thousand/million/bajillion people were going to die if you didn't.

(2) So there are some moral absolutes.

If you don't think this works then think of some worse offense against God, maybe killing him, like they did to Our Lord. Then stipulate once more that a thousand/million/bajillion people will die if you don't.

When the divine comes in this seems

If you think the first example works, then acting contrary to other moral absolutes can be viewed as violations of God's law, and thus equally worse or bad offenses against God; after all, if saying certain words to God is absolutely wrong, then surely violating his commands about even more important things, like killing innocent humans, is also absolutely wrong.

*might*appeal to you:(1) It's absolutely wrong to blaspheme against God, as in swearing at God. Even if a thousand/million/bajillion people were going to die if you didn't.

(2) So there are some moral absolutes.

If you don't think this works then think of some worse offense against God, maybe killing him, like they did to Our Lord. Then stipulate once more that a thousand/million/bajillion people will die if you don't.

When the divine comes in this seems

*to some extent*to release us from the intuitive pull which consequentialist 'what if a bajillion people'-type objections have.If you think the first example works, then acting contrary to other moral absolutes can be viewed as violations of God's law, and thus equally worse or bad offenses against God; after all, if saying certain words to God is absolutely wrong, then surely violating his commands about even more important things, like killing innocent humans, is also absolutely wrong.

## Monday, March 4, 2013

### Suarez's Modal Distinction and the Eucharist

Sorry for the lack of posts and for being bad about approving comments. I've been very busy this quarter as I'm taking three math classes, and this consumes most of my time. Here is an explanation (albeit somewhat oversimplified) of Suarez's idea of the 'modal distinction'. Suarez is an excellent, extremely clear late medieval philosopher. I wish more of his works were in English and I hope he will be canonized some day. The reference for Suarez's theory of distinctions is his Metaphysical Disputation VII.

Suarez makes three types of metaphysical distinctions. There are two which most philosophers of his era admit to exist: the real distinction and the distinction of reason. A real distinction holds between A and B just in case A can exist without B and B can exist without A. A prime example of a real distinction is between two substances, like me and my chair. A distinction of reason on the other hand holds between A and B just in case A and B are really the same and thus mutually inseparable, yet we conceive A and B using distinct and incomplete concepts. So, one of the primary examples Suarez appeals to is the divine attributes. Given the theory of divine simplicity (the idea that God has no proper parts at all) it seems to follow that God's justice is really the same as God's mercy. They are both mutually inseparable in the sense that neither can exist without the other. However, we use different and necessarily incomplete concepts to think about each of them. This explains why it is not obviously true that God's mercy is identical to God's justice, even though both phrases and their corresponding concepts refer to the same being.

Aside from these two Suarez admits a third distinction, called a modal distinction. The motivation for this distinction comes in large part from problems about the relationship between an accident and its inherence in a substance. The problem is raised by Bl. John Duns Scotus, taking as his starting point the case of the Eucharist (though his argument doesn't really depend on this example in particular). We know in the case of the Eucharist that the accidents of the bread such as the quantity remain even though the substance of the bread does not. Hence, the accidents no longer inhere in the substance. So suppose that the quantity of the bread were not really distinct from its relation of inhering in the substance of the bread. Then since the quantity of the bread exists after transubstantiation, so would its inhering in the substance of the bread. But clearly the quantity's inhering in the bread cannot exist unless it inheres in the bread! This is a contradiction, since in the case of the Eucharist the accidents no longer inhere in the bread. Hence, it seems to follow there is a real distinction between a quantity and its relation of inhering (similar arguments can be run for other relations of union or composition).

But this leads to problems of its own. Let I be the relation of inhering between an accident a and substance b. Suppose I is really distinct from a as Scotus's argument appears to show. Then since I is an accident of a (it's a feature of a connecting it to b), it follows there must be some relation I* between I and a in virtue of which I inheres in a. But then there must be some relation I** between I* and I in virtue of which I* inheres in I, and so on. This creates an infinite regress, which is problematic to say the least. So it seems whichever way we go we have an issue. If the relation of inhering is really distinct from the accident, we have an infinite regress. If it is not really distinct from the accident, we have a contradiction.

While nominalists like Ockham have their own solution to this quandary, Suarez is a metaphysical realist, and thus unlike the nominalists he thinks as a matter of semantic principle that there must correspond to the term 'inheres' some extramental being. It is with this concern in mind that Suarez develops his notion of a modal distinction. A modal distinction is a distinction which obtains between a being and its mode. Suarez is using the word 'being' here in a strong sense, to denote a real, particular individual, in scholastic terminology a 'res' (though this need not be a substance). A mode on the other hand is just a way in which a being or 'res' can exist. So Suarez wants to say that instead of letting an accident's inhering be a really distinct relation, we let it simply be a mode or way of being of the accident. Suarez considers this modal distinction to be a distinction intermediate between a real distinction and a distinction of reason, because the accident can exist separately from its mode (at least by the power of God), but the mode cannot exist separately from the accident. Since this is the only intermediate distinction Suarez admits, he takes A and B to be modally distinct just in case A can exist without B but B cannot exist without A, or vice versa (but not both).

Clearly then Scotus's problem was with his first argument; Scotus assumed that if the quantity of the bread and its inhering are not really distinct then it follows they are both mutually inseparable. Suarez on the other hand allows that it is possible for a being to be separable from its mode even though they are not really distinct; after all, a being's mode is not in itself a 'being' in the strong sense, so it is not some separate 'being', and thus it is not really distinct. With his modal distinction laid out Suarez has the tools to give a very nice solution to the problem of the Eucharist. The accidents of the bread and wine can continue to exist even without the substance because it is not part of their essence that they inhere in something; inhering is only one of their modes. While it is obviously not a natural occurrence that an accident exist without its mode of inhering, it is not metaphysically impossible, and thus God can bring it about by his power.

While Suarez's account seems secure there is one objection. Someone like St. Thomas Aquinas might object that the essence of an accident includes mention of the substance of which it is a part. However, at least in the case of the Eucharist, even Aquinas makes exceptions, and thus this account must obviously be modified. And Suarez can easily modify it by saying that accidents are beings whose definition include that it is metaphysically possible that they inhere in a subject. Substances by contrast are beings for which it is metaphysically impossible that they possess the mode of inhering. So it seems Suarez's modal distinction provides a coherent solution to all the puzzles set out above.

Suarez makes three types of metaphysical distinctions. There are two which most philosophers of his era admit to exist: the real distinction and the distinction of reason. A real distinction holds between A and B just in case A can exist without B and B can exist without A. A prime example of a real distinction is between two substances, like me and my chair. A distinction of reason on the other hand holds between A and B just in case A and B are really the same and thus mutually inseparable, yet we conceive A and B using distinct and incomplete concepts. So, one of the primary examples Suarez appeals to is the divine attributes. Given the theory of divine simplicity (the idea that God has no proper parts at all) it seems to follow that God's justice is really the same as God's mercy. They are both mutually inseparable in the sense that neither can exist without the other. However, we use different and necessarily incomplete concepts to think about each of them. This explains why it is not obviously true that God's mercy is identical to God's justice, even though both phrases and their corresponding concepts refer to the same being.

Aside from these two Suarez admits a third distinction, called a modal distinction. The motivation for this distinction comes in large part from problems about the relationship between an accident and its inherence in a substance. The problem is raised by Bl. John Duns Scotus, taking as his starting point the case of the Eucharist (though his argument doesn't really depend on this example in particular). We know in the case of the Eucharist that the accidents of the bread such as the quantity remain even though the substance of the bread does not. Hence, the accidents no longer inhere in the substance. So suppose that the quantity of the bread were not really distinct from its relation of inhering in the substance of the bread. Then since the quantity of the bread exists after transubstantiation, so would its inhering in the substance of the bread. But clearly the quantity's inhering in the bread cannot exist unless it inheres in the bread! This is a contradiction, since in the case of the Eucharist the accidents no longer inhere in the bread. Hence, it seems to follow there is a real distinction between a quantity and its relation of inhering (similar arguments can be run for other relations of union or composition).

But this leads to problems of its own. Let I be the relation of inhering between an accident a and substance b. Suppose I is really distinct from a as Scotus's argument appears to show. Then since I is an accident of a (it's a feature of a connecting it to b), it follows there must be some relation I* between I and a in virtue of which I inheres in a. But then there must be some relation I** between I* and I in virtue of which I* inheres in I, and so on. This creates an infinite regress, which is problematic to say the least. So it seems whichever way we go we have an issue. If the relation of inhering is really distinct from the accident, we have an infinite regress. If it is not really distinct from the accident, we have a contradiction.

While nominalists like Ockham have their own solution to this quandary, Suarez is a metaphysical realist, and thus unlike the nominalists he thinks as a matter of semantic principle that there must correspond to the term 'inheres' some extramental being. It is with this concern in mind that Suarez develops his notion of a modal distinction. A modal distinction is a distinction which obtains between a being and its mode. Suarez is using the word 'being' here in a strong sense, to denote a real, particular individual, in scholastic terminology a 'res' (though this need not be a substance). A mode on the other hand is just a way in which a being or 'res' can exist. So Suarez wants to say that instead of letting an accident's inhering be a really distinct relation, we let it simply be a mode or way of being of the accident. Suarez considers this modal distinction to be a distinction intermediate between a real distinction and a distinction of reason, because the accident can exist separately from its mode (at least by the power of God), but the mode cannot exist separately from the accident. Since this is the only intermediate distinction Suarez admits, he takes A and B to be modally distinct just in case A can exist without B but B cannot exist without A, or vice versa (but not both).

Clearly then Scotus's problem was with his first argument; Scotus assumed that if the quantity of the bread and its inhering are not really distinct then it follows they are both mutually inseparable. Suarez on the other hand allows that it is possible for a being to be separable from its mode even though they are not really distinct; after all, a being's mode is not in itself a 'being' in the strong sense, so it is not some separate 'being', and thus it is not really distinct. With his modal distinction laid out Suarez has the tools to give a very nice solution to the problem of the Eucharist. The accidents of the bread and wine can continue to exist even without the substance because it is not part of their essence that they inhere in something; inhering is only one of their modes. While it is obviously not a natural occurrence that an accident exist without its mode of inhering, it is not metaphysically impossible, and thus God can bring it about by his power.

While Suarez's account seems secure there is one objection. Someone like St. Thomas Aquinas might object that the essence of an accident includes mention of the substance of which it is a part. However, at least in the case of the Eucharist, even Aquinas makes exceptions, and thus this account must obviously be modified. And Suarez can easily modify it by saying that accidents are beings whose definition include that it is metaphysically possible that they inhere in a subject. Substances by contrast are beings for which it is metaphysically impossible that they possess the mode of inhering. So it seems Suarez's modal distinction provides a coherent solution to all the puzzles set out above.

## Thursday, January 10, 2013

### New Natural Law and Deriving an 'Ought' from an 'Is'

Many people have said that we cannot derive an 'ought' statement from an 'is' statement. In one sense this is trivially true, in another it is straightforwardly a mistake in logic. I'll discuss this in relation to new natural law theory and the grounding of morality in metaphysics.

First the sense in which it is true. Obviously if the premises of your argument contain no 'ought' statements then you can't logically derive an 'ought' from them. At best you can conclude from the premises that some ought statement is plausible. However, I think most people who want to say we can derive an ought from an is would all agree with this rather trivial observation.

Now some discussion of natural law: On new natural law theory we immediately perceive certain states of affairs as to be pursued, and from this we determine what we ought to do; the states of affairs to be pursued are instances of the 'basic goods', which are immediately recognizable aspects of human flourishing. Now, new natural law theorists say we cannot derive an ought from an is. However, they also say that new natural law theory does not carry any commitments one way or the other as to what, metaphysically speaking, human flourishing consists in or is grounded in. After all, everyone can know the natural law in their hearts, and you do not need to be a metaphysician to gain insight into what's right and wrong. But by the same token on new natural law theory, it should be consistent with the theory to say the human flourishing is grounded or consists in something like, say, the perfection of the human form. New natural law should not rule this out.

What follows from this? Well, if this type of theory is possible on new natural law, then supposing it is true, every aspect of human flourishing will at the very least coincide with some aspect of the perfection of the human form. The details of this perfection aren't that important, since the main point of this post is supposed to be logical. So just take some arbitrary aspect of human flourishing A and some arbitrary aspect of the perfection of the human form P. A and P coincide just means that if one exists then so does the other. Now we can launch an argument:

(1) If P and A coincide then P is an aspect of the perfection of the human form if and only if A is an aspect of human flourishing. [by def.]

(2) P and A coincide [prem]

It follows logically that

(3) P is an aspect of the perfection of the human form if and only if A is an aspect of human flourishing. [from 1 and 2]

From this we can infer by the rules of logic that

(4) If P is an aspect of the perfection of the human form, then A is an aspect of human flourishing. [from 3]

(5) P is an aspect of the perfection of the human form. [prem]

Again by the rules of logic:

(6) Therefore, A is an aspect of human flourishing. [from 4 and 5]

(7) If A is an aspect of human flourishing, then instances of A are states of affairs that ought to be pursued. [by NNL]

(8) Therefore, instances of A are states of affairs that ought to be pursued. [by 6 and 7]

(1) just follows from the definition of 'coincide'. (7) is just what new natural law says. Given the premises the rest follows by the incontestable rules of logic. Now, one might question premise (2) and (5). However, it is at least possible for them to be true given new natural law theory. And if they are true then this argument shows one can derive an ought from an is.

Basically, to say we can derive some statement Q from some set S of premises {P1, P2, ... , Pn} just means that there is a proof of Q from S. This is Logic 101 stuff. Given all the premises and definition in our argument we can derive an ought, namely (8). Our premises, (2) and (5) are paradigm 'is' statements. This is why it is false to say we cannot derive an 'ought' from an 'is' statement.

Here's the upshot for natural law theory: If NNL is true, then it is possible for (2) and (5) to be true. If (2) and (5) are true there's a perfectly good sense in which we can derive an 'ought' statement from a set of 'is' statements. Hence, even if NNL is true, it is possible to derive an 'ought' from an 'is' in the precise logical sense of 'derive' above. The only other possibility is to either say aspects of human flourishing can't coincide with anything, which basically means NNL is inconsistent with certain metaphysical theories of flourishing (viz. all of them), or else we are using some other sense of 'derived' in saying an 'ought' can never be derived from an 'is'. As a person sympathetic to NNL myself I think we should go with the latter (or possibly drop the use of the phrase altogether).

First the sense in which it is true. Obviously if the premises of your argument contain no 'ought' statements then you can't logically derive an 'ought' from them. At best you can conclude from the premises that some ought statement is plausible. However, I think most people who want to say we can derive an ought from an is would all agree with this rather trivial observation.

Now some discussion of natural law: On new natural law theory we immediately perceive certain states of affairs as to be pursued, and from this we determine what we ought to do; the states of affairs to be pursued are instances of the 'basic goods', which are immediately recognizable aspects of human flourishing. Now, new natural law theorists say we cannot derive an ought from an is. However, they also say that new natural law theory does not carry any commitments one way or the other as to what, metaphysically speaking, human flourishing consists in or is grounded in. After all, everyone can know the natural law in their hearts, and you do not need to be a metaphysician to gain insight into what's right and wrong. But by the same token on new natural law theory, it should be consistent with the theory to say the human flourishing is grounded or consists in something like, say, the perfection of the human form. New natural law should not rule this out.

What follows from this? Well, if this type of theory is possible on new natural law, then supposing it is true, every aspect of human flourishing will at the very least coincide with some aspect of the perfection of the human form. The details of this perfection aren't that important, since the main point of this post is supposed to be logical. So just take some arbitrary aspect of human flourishing A and some arbitrary aspect of the perfection of the human form P. A and P coincide just means that if one exists then so does the other. Now we can launch an argument:

(1) If P and A coincide then P is an aspect of the perfection of the human form if and only if A is an aspect of human flourishing. [by def.]

(2) P and A coincide [prem]

It follows logically that

(3) P is an aspect of the perfection of the human form if and only if A is an aspect of human flourishing. [from 1 and 2]

From this we can infer by the rules of logic that

(4) If P is an aspect of the perfection of the human form, then A is an aspect of human flourishing. [from 3]

(5) P is an aspect of the perfection of the human form. [prem]

Again by the rules of logic:

(6) Therefore, A is an aspect of human flourishing. [from 4 and 5]

(7) If A is an aspect of human flourishing, then instances of A are states of affairs that ought to be pursued. [by NNL]

(8) Therefore, instances of A are states of affairs that ought to be pursued. [by 6 and 7]

(1) just follows from the definition of 'coincide'. (7) is just what new natural law says. Given the premises the rest follows by the incontestable rules of logic. Now, one might question premise (2) and (5). However, it is at least possible for them to be true given new natural law theory. And if they are true then this argument shows one can derive an ought from an is.

Basically, to say we can derive some statement Q from some set S of premises {P1, P2, ... , Pn} just means that there is a proof of Q from S. This is Logic 101 stuff. Given all the premises and definition in our argument we can derive an ought, namely (8). Our premises, (2) and (5) are paradigm 'is' statements. This is why it is false to say we cannot derive an 'ought' from an 'is' statement.

Here's the upshot for natural law theory: If NNL is true, then it is possible for (2) and (5) to be true. If (2) and (5) are true there's a perfectly good sense in which we can derive an 'ought' statement from a set of 'is' statements. Hence, even if NNL is true, it is possible to derive an 'ought' from an 'is' in the precise logical sense of 'derive' above. The only other possibility is to either say aspects of human flourishing can't coincide with anything, which basically means NNL is inconsistent with certain metaphysical theories of flourishing (viz. all of them), or else we are using some other sense of 'derived' in saying an 'ought' can never be derived from an 'is'. As a person sympathetic to NNL myself I think we should go with the latter (or possibly drop the use of the phrase altogether).

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