Infinite in some aspects, on the other hand, is such that greater of it cannot be thought. Crusius continues that there are then three types of infinity, as there are three aspects involved with every existing substance. Firstly, every substance has an essence, which is ultimately based on its fundamental forces: here, infinity means that a substance is capable of all possible actions. Secondly, in addition to essence, substances exist in space and time, both of which have their own types of infinity: immeasurability, where a substance occupies all possible spaces, and eternity, where the duration of a substance has no beginning or end.
Crusius also notes that none of the three types of infinity should be confused with what could be called infinity of progression, which is no true infinity, but a mere series of ever greater things, which still always remains finite. For instance, a thing generated at some point of time could continue existing without any end and still its duration would always have been just finite. Crusius suggests that such an infinity of progression is the only way we humans can think also the infinity of the past: we set out a past moment, then a still further past moment etc.
Interestingly, while Hoffmann rejected the so-called ontological - or as he called it, Cartesian - proof of God’s existence, Crusius appears to accept it. He starts with the notion of a substance with an infinite essence, that is, with capacity to do anything - such a substance has then an infinite grade of perfection. Now, Crusius continues, if a substance should be capable of everything, it should be capable of ensuring its own existence, or existence belongs to the perfection of the infinite essence. This means, he concludes, that a substance with infinite essence must necessarily exist everywhere and at every time.
Crusius argued earlier that necessary things can only be simple - otherwise they could be broken - and this must then apply also to an infinite substance. Its simplicity then implies that an infinite substance cannot be reduced. In fact, he points out, there can be no quantitative relation between the infinite substance and finite substances. In fact, nothing could be added to a finite substance to make it infinite, and finite and infinite substances differ by their essence.
Crusius makes the remark that one might think as an infinite force a determined capacity for doing a certain type of action in as great a magnitude as possible. Force of an infinite substance is not of this sort, he clarifies, but a general capacity to do anything whatsoever, even what any of these determined infinite forces could do. Indeed, an infinite substance should have only one force, which it can then apply in different manners. Of course, Crusius admits, the infinite substance cannot do anything impossible, but this is more of a clarification than any real limitation. The infinite substance does not then need any instruments for its actions, but if it so chooses, it can use them. In fact, since no effect of the actions of the infinite substance could be the highest possible, it can freely choose the magnitude of its effects.
Infinite substance should be able to do anything that just is possible. Crusius argues that creation of all finite simple substances is one of the things the infinite substance has done. True, he admits, it is inconceivable to us mere humans how an infinite substance has done this, but as contingent they must have been created by something, and since a finite mind cannot apprehend an infinite substance, it is understandable that we cannot fathom everything it could do. Crusius notes that there is also nothing contradictory in finite substances creating finite simple substances, although it is again inconceivable how they could have done it. Still, he assures the reader, we should not assume any finite substance to have such a power, because this assumption would undermine our ability to investigate natural causality, which is based on the premiss that finite substances can only bring about something by combining existing substances or by dividing existing combinations.
Crusius also considers the question, whether there could exist at the same time an infinite amount of things. His first point is that we certainly can always think of a number greater than any given number, thus, we shouldn’t be able to think any infinite number (of course, nowadays mathematicians do think of infinite numbers or cardinalities, but since they also form a never ending series of infinities, these would not actually be infinite in the sense Crusius means; still, this is a distinction that we can ignore when speaking of what Crusius had in mind).
Now, although we cannot think of an infinite number, this might not imply anything for the possibility of an infinite amount of real things. Here the crucial question is, Crusius suggests, whether this infinite amount is meant to be added up from actually different, perfect things. If it is, Crusius insists, we should be able to divide this amount into two groups. Since neither subgroup is the greatest, they are both of a finite amount, but then an infinity would be made up of two finities, which contradicts the idea that an infinity cannot be quantitatively compared with something finite.
Then again, Crusius notes, the previous argument works only if it is really distinct things that are added up and divided into groups. Thus, God might be able to think at once an infinite amount of possible things, since these possible things are not really distinct. We finite beings cannot comprehend how God can do it, but this does not restrict God’s capacities.
A far simpler question, Crusius thinks, is that of an infinite series of causes and effects, because Crusius smells a contradiction in that notion. In a series of causes and effects, he argues, all terms are either generated or not. If not, the series has a first cause and is therefore finite. Then again, if they all are generated, then the individual members have all not existed at some point and therefore the whole series has not existed at some point and has thus a beginning. Key part of this argument is clearly the move from all parts of a whole to the whole itself. Crusius notes that this move does not work in all cases - if parts of a whole weigh 1 kg, then the whole will definitely not weigh 1 kg. He unconvincingly tries to argue that usually and in this particular case this move is guaranteed by a principle of non-contradiction, because whole just is parts taken together.
Whatever the validity of the argument, Crusius believes he has shown that a series of causes and effects cannot be really infinite. He does admit it can have an infinity of progression, that is, it could have more members. These members could also be added to the beginning of the series, that is, we could think that the series began from an earlier point than it does, but this just means that it is completely arbitrary where such a series begins.
Because all series of causes and effects are thus finite, Crusius says, the essence of an infinite substance cannot consist of such a series of changes. Even more, he insists, the infinite substance cannot go through any series of changes, because it would undermine its eternal perfection. Crusius might be arguing here against the idea that God could be persuaded by a series of reasons to do something. In any case, he notes that an infinite substance should be immediately everything it can be.
The lack of changes in the infinite substance means according to Crusius, firstly, that all the actions of the infinite substance must be fundamental, free actions. Secondly, the infinite substance cannot be affected by a finite substance, at least not directly. Crusius does admit that finite substance could hinder actions of the infinite substance by not fulfilling certain conditions the infinite substance has placed for its own action. Furthermore, finite substance could resist finite effects generated by the infinite substance.
Although Crusius speaks against the idea of an infinite series of causes and effects, his attitude toward an infinite duration is quite the opposite. Indeed, he is committed to the idea that the first, uncaused cause has existed an infinite amount of time or eternally. One might argue that Crusius’ commitment should fall to the very same argument he himself used against the infinite series of causes and effects, creating then a dilemma reminiscent of Kant’s third antinomy, where we cannot accept either that there is an uncaused cause nor that there isn’t. Crusius’ solution is once again to differentiate between actual and merely possible. A series of causes and effects involves an actual succession of things, while an infinite duration consists only of possible succession of things, whereas nothing really changes during the existence of an eternal substance.
Crusius argued earlier that necessary things can only be simple - otherwise they could be broken - and this must then apply also to an infinite substance. Its simplicity then implies that an infinite substance cannot be reduced. In fact, he points out, there can be no quantitative relation between the infinite substance and finite substances. In fact, nothing could be added to a finite substance to make it infinite, and finite and infinite substances differ by their essence.
Crusius makes the remark that one might think as an infinite force a determined capacity for doing a certain type of action in as great a magnitude as possible. Force of an infinite substance is not of this sort, he clarifies, but a general capacity to do anything whatsoever, even what any of these determined infinite forces could do. Indeed, an infinite substance should have only one force, which it can then apply in different manners. Of course, Crusius admits, the infinite substance cannot do anything impossible, but this is more of a clarification than any real limitation. The infinite substance does not then need any instruments for its actions, but if it so chooses, it can use them. In fact, since no effect of the actions of the infinite substance could be the highest possible, it can freely choose the magnitude of its effects.
Infinite substance should be able to do anything that just is possible. Crusius argues that creation of all finite simple substances is one of the things the infinite substance has done. True, he admits, it is inconceivable to us mere humans how an infinite substance has done this, but as contingent they must have been created by something, and since a finite mind cannot apprehend an infinite substance, it is understandable that we cannot fathom everything it could do. Crusius notes that there is also nothing contradictory in finite substances creating finite simple substances, although it is again inconceivable how they could have done it. Still, he assures the reader, we should not assume any finite substance to have such a power, because this assumption would undermine our ability to investigate natural causality, which is based on the premiss that finite substances can only bring about something by combining existing substances or by dividing existing combinations.
Crusius also considers the question, whether there could exist at the same time an infinite amount of things. His first point is that we certainly can always think of a number greater than any given number, thus, we shouldn’t be able to think any infinite number (of course, nowadays mathematicians do think of infinite numbers or cardinalities, but since they also form a never ending series of infinities, these would not actually be infinite in the sense Crusius means; still, this is a distinction that we can ignore when speaking of what Crusius had in mind).
Now, although we cannot think of an infinite number, this might not imply anything for the possibility of an infinite amount of real things. Here the crucial question is, Crusius suggests, whether this infinite amount is meant to be added up from actually different, perfect things. If it is, Crusius insists, we should be able to divide this amount into two groups. Since neither subgroup is the greatest, they are both of a finite amount, but then an infinity would be made up of two finities, which contradicts the idea that an infinity cannot be quantitatively compared with something finite.
Then again, Crusius notes, the previous argument works only if it is really distinct things that are added up and divided into groups. Thus, God might be able to think at once an infinite amount of possible things, since these possible things are not really distinct. We finite beings cannot comprehend how God can do it, but this does not restrict God’s capacities.
A far simpler question, Crusius thinks, is that of an infinite series of causes and effects, because Crusius smells a contradiction in that notion. In a series of causes and effects, he argues, all terms are either generated or not. If not, the series has a first cause and is therefore finite. Then again, if they all are generated, then the individual members have all not existed at some point and therefore the whole series has not existed at some point and has thus a beginning. Key part of this argument is clearly the move from all parts of a whole to the whole itself. Crusius notes that this move does not work in all cases - if parts of a whole weigh 1 kg, then the whole will definitely not weigh 1 kg. He unconvincingly tries to argue that usually and in this particular case this move is guaranteed by a principle of non-contradiction, because whole just is parts taken together.
Whatever the validity of the argument, Crusius believes he has shown that a series of causes and effects cannot be really infinite. He does admit it can have an infinity of progression, that is, it could have more members. These members could also be added to the beginning of the series, that is, we could think that the series began from an earlier point than it does, but this just means that it is completely arbitrary where such a series begins.
Because all series of causes and effects are thus finite, Crusius says, the essence of an infinite substance cannot consist of such a series of changes. Even more, he insists, the infinite substance cannot go through any series of changes, because it would undermine its eternal perfection. Crusius might be arguing here against the idea that God could be persuaded by a series of reasons to do something. In any case, he notes that an infinite substance should be immediately everything it can be.
The lack of changes in the infinite substance means according to Crusius, firstly, that all the actions of the infinite substance must be fundamental, free actions. Secondly, the infinite substance cannot be affected by a finite substance, at least not directly. Crusius does admit that finite substance could hinder actions of the infinite substance by not fulfilling certain conditions the infinite substance has placed for its own action. Furthermore, finite substance could resist finite effects generated by the infinite substance.
Although Crusius speaks against the idea of an infinite series of causes and effects, his attitude toward an infinite duration is quite the opposite. Indeed, he is committed to the idea that the first, uncaused cause has existed an infinite amount of time or eternally. One might argue that Crusius’ commitment should fall to the very same argument he himself used against the infinite series of causes and effects, creating then a dilemma reminiscent of Kant’s third antinomy, where we cannot accept either that there is an uncaused cause nor that there isn’t. Crusius’ solution is once again to differentiate between actual and merely possible. A series of causes and effects involves an actual succession of things, while an infinite duration consists only of possible succession of things, whereas nothing really changes during the existence of an eternal substance.
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