THE ONE-ARGUMENT INTERPRETATION

3. I begin by translating the relevant text that presents what I am calling the main argument. I translate only the argumentative steps, ignoring illustrations and explanatory discussion.

For the sake of argument, we will assume that at this stage the philosophers are entitled to the supposition that there is a necessary existent. In the Fifth through Ninth Discussions of the Tahāfut al-Ġazālī does not challenge the philosophers' proof for the existence of God. He takes issue with their demonstration in the Tenth Discussion.Footnote ⁹ Our interest here lies not with the Islamic philosophers' version of the cosmological argument, but with the Tahāfut arguments for the NP conception of the divine unity.

THE MAIN ARGUMENT

4. First I reproduce this argument as a demonstration and then I give its general form.

1. 1. There is a necessary existent.

2. 2. Assume that there are two or more necessary existents.Footnote ¹⁰

3. 3. Since they are two or more existents and not one, they cannot be similar in all respects.

4. 4. Hence, they must differ in some respects.

5. 5. They cannot differ in all respects, for, from 2, they are at least similar in their having necessary existence.

6. 6. From 4 and 5: they must have at least an aspect that they share and an aspect in which they differ.

7. 7. Therefore, each one of these necessary existents has at least two aspects: one that it shares with the other necessary existents, and one in which it differs from the other necessary existents.

8. 8. Thus, it is clear that these aspects, described in 7, are not identical.

9. 9. From 7 and 8: each of the necessary existents is composed of at least two aspects.

10. 10. By conditional proof, from 2–9: if there are two or more necessary existents, then each existent admits composition.

11. 11. But no necessary existent admits composition.

12. 12. From 10 and 11: there is no more than one necessary existent.

13. 13. Given 1 and 12, it follows that there is only one necessary existent.

The general form of the argument is this.

1. P1. There is a necessary existent.

2. P2. If there are two or more necessary existents, then each necessary existent admits composition.

3. P3. No necessary existent admits composition.

4. C1. There is only one necessary existent.

5. Al-Ġazālī challenges the third premise (P3).Footnote ¹¹ He writes:

The charge of arbitrariness, according to the one-argument interpretation, may seem premature, but in fact it anticipates what is to come. Al-Ġazālī will offer, on behalf of the philosophers, five subarguments that collectively lend support to P3. In essence, these arguments will constitute the proof that he asks for at the end of the passage above – a proof that he will argue is unsatisfactory.

The second premise (P2) is an inferential premise. It is the conclusion of the conditional proof, which occupies steps 2 through 9 of the demonstration above. Al-Ġazālī does not take issue with P2. His statement about the identity of indiscernibles seems to suggest that he accepts the reasoning of the conditional proof. I think this is right. Steps 2 through 9 appear to be sufficiently benign. Now, since the general form of the argument is valid and since P1 is presupposed, this leaves P3 as the controversial premise.

Let us discuss P3 and its scope in order to see why an Ashʿarite theologian, such as al-Ġazālī, would find it objectionable and in need of a proof. P3 rules out any composition in a necessary existent. One can imagine two types of composition: quantitative and qualitative. In the words of al-Ġazālī's philosophers, “as it does not divide in terms of quantity (bi-al-kammiyya), it does not divide in terms of explanatory description (bi-al-qawl al-šāriḥ).” I take qualitative composition to be a composition that lends itself to explanatory description, and vice versa. An example might clarify the idea. The pen in my hand is hollow and it has a nib. It divides quantitatively into a nib and a body. They are two quantitative parts that make the larger mass of the pen. But they are also qualitative parts and so is the hollowness of its barrel. Presumably their terms are all parts of an explanatory description of the pen. However, while it makes sense to say that the nib and the body are quantitative parts of the pen, it does not seem to make much sense to say that the hollowness is a quantitative part of the pen. Similarly, one can think of quantitative parts that are not easily thought of qualitatively. For example, the body of my pen could be broken into two equal parts in shape and mass – a division that does not seem to lend itself to an explanatory description of my pen.

As we will see later, al-Ġazālī does not dispute the claim that a necessary existent cannot admit quantitative composition. It is fair to assume that he sees as sound the argument, which I will reconstruct shortly, against the possibility of quantitative composition. He never explicitly says this in the Tahāfut, but he also never engages the argument critically. There are also passages in al-Iqtiṣād fī al-Iʿtiqād that suggest that this type of composition is specific to (extended) bodies, and, of course, the necessary existent, according to the Ashʿarites, is not a body.Footnote ¹⁵ So the types of composition that al-Ġazālī thinks to be appropriate for the necessary existent are qualitative in nature – compositions that can be utilized in explanatory descriptions of the necessary existent. Not all qualitative compositions are appropriate for a necessary existent according to al-Ġazālī. For example, the composition of form and matter is not possible for a necessary existent.Footnote ¹⁶ However, there are other qualitative compositions that al-Ġazālī thinks are true of a necessary existent, and which the philosophers deny are possible for a necessary existent. Examples of such compositions are the division into essence and attributes, into genus and species, and into quiddity and existence.Footnote ¹⁷ For each of these sorts of composition, there will be a subargument, attributed to the philosophers, denying the possibility of that composition.

6. The passage that follows al-Ġazālī's question, “What is its proof?”, is pivotal for my interpretation. There is clear evidence in it that, for al-Ġazālī, the lack of compositionality in the First Principle is what the philosophers believe establishes His oneness. We have already seen in the general form of the main argument that P3 (the lack of compositionality in the necessary existent) is sufficient to establish its oneness, and that is because neither the validity of the main argument, nor P1, nor P2 is disputed. Thus if the philosophers can establish that the necessary existent is simple, then they would obtain both oneness (i.e., no external plurality) and simplicity (i.e., no internal plurality), which together constitute the NP conception of the divine unity.

Here is al-Ġazālī's transitional (and pivotal) passage.

He then proceeds by presenting five subarguments that are supposed to demonstrate that a necessary existent does not admit any of these five forms of plurality.

I believe that the best reconstruction of these arguments is to connect them logically to the main argument via a secondary, transitional argument that supports P3 of the main argument. I am not claiming that this argument is stated explicitly in al-Ġazālī's text. But there is good textual evidence for it in the passage above. His remarks about how the oneness of the First Principle is proved on the basis of His simplicity and how the unity is not fully established unless all five forms of plurality are refuted are very suggestive as to what this argument might be. Here is what I think is a plausible reconstruction of this (secondary) argument.

1. P4. If there is composition in a necessary existent, then this composition must consist of one or more of the following five types of plurality.Footnote ¹⁹

   1. (a) An actual or conceptual quantitative plurality.

   2. (b) A conceptual qualitative plurality, such as of matter and form.

   3. (c) A plurality of positive (neither relational nor negative) attributes, which are additional to the essence.

   4. (d) A conceptual plurality of genus and differentia (or species).

   5. (e) A plurality of quiddity and existence that relates to it.

2. P5. None of these types of plurality is possible for a necessary existent.

3. C2 (= P3). There is no composition in a necessary existent.

As I noted previously, these types of plurality seem to fall into two categories: quantitative plurality, which is type (a), and qualitative plurality, which includes types (b)–(e). We will find later that type (b) could also involve quantitative pluralities. There is an important observation to make here. To the best of my knowledge, no Islamic philosopher or theologian argued for or against P4. It appears that everyone accepted these five types of plurality as exhaustive. What is debated is P5. Ibn Sīnā and his followers and many of the Muʿtazilites argued for P5. Most Islamic theologians, including the Ashʿarites, argued against P5.

Immediately after the transitional passage cited above al-Ġazālī offers, on behalf of the philosophers, five subarguments, each of which is aimed at refuting one of the forms of compositions listed in P4(a) – P4(e). He accepts the subargument against P4(a) but rejects the subarguments against P4(c), P4(d), and P4(e) in the Sixth, Seventh, and Eighth Discussions of the Tahāfut, respectively. In the Ninth Discussion he argues that the philosophers are not entitled to the denial of P4(b). Although he accepts the denial of P4(b), he thinks that the philosophers' arguments against P4(b) are unsound, given their other doctrines. Some of his arguments against P5 supply us with further evidence for the one-argument interpretation.

The logical form of P5 is a conjunction. It denies each type of internal plurality listed in P4. So an adequate defense of P5 would consist of five subarguments each of which shows the impossibility of one type of internal plurality for a necessary existent. As I said above, al-Ġazālī produces these arguments immediately after the transitional passage. I will translate each of the relevant passages and then present a reconstruction of the argument summarized in the passage.

But before we discuss these subarguments, I must stress one point. A necessary condition for the cogency of these five arguments is that their premises must not invoke the claim that there is only one necessary existent. For this would render the main argument circular. The five subarguments are needed to establish P5, P5 is needed to establish P3, and P3 is needed to establish the oneness of the necessary existent (which is C1). As we will see, not every argument of these subarguments is free from this charge.

THE SUBARGUMENT AGAINST P4(a)

7. It is not hard to see why the philosophers and the Ashʿarites, among many other theological schools, rejected this form of plurality. The main idea of this subargument is that if a necessary existent is divisible quantitatively into parts, whether actually or conceptually, then its existence depends on these parts staying together. In other words, since it is conceivable that these parts may come apart, it is also conceivable that the necessary existent may cease to exist. But this is absurd: the existence of a necessary existent is necessary by virtue of itself; hence, it is inconceivable that it might cease to exist.

Here is the relevant passage with emphasis added.

The argument may be reconstructed as follows.

1. P6. If a necessary existent is quantitatively divisible into parts, whether actually or conceptually, then it is conceivable that the cohesion between these parts might cease to exist.

2. P7. If it is conceivable that the cohesion between the parts of a necessary existent might cease to exist, then it is conceivable that the necessary existent might cease to exist.

3. P8. It is inconceivable that anything whose existence is necessary by virtue of itself might cease to exist.

4. P9. The existence of a necessary existent is necessary by virtue of itself.

5. C3 (= not-P4(a)). A necessary existent is not quantitatively divisible into parts, whether actually or conceptually.

It is clear that this argument is valid. One can fuss about the correct relations between the concepts of actuality, necessity, and conceivability, but that does not remove the unmistakable feel of plausibility attached to these premises. Hence, it is not surprising that al-Ġazālī doesn't take issue with this argument. Of course, al-Ġazālī independently accepts, as an Ashʿarite, that God is not divisible into quantitative parts (see 5). But there are many occasions in the Tahāfut in which al-Ġazālī criticizes a philosophers' argument whose conclusion he accepts independently.Footnote ²¹

THE SUBARGUMENT AGAINST P4(b)

8. This argument begins with a general supposition but it is abruptly restricted to a single case. The general supposition is to assume that a necessary existent is divisible, in terms of description and not necessarily in terms of quantity, into two different parts. The restrictive single case is that of the divisibility of body into matter and form. The argument proceeds by denying that God is divisible into matter and form. In fact, even the general supposition is unnecessarily restricted: why two parts only? So in reconstructing this argument one should investigate if these restrictions are essential to the argument or an argument can be made without them.

Let us examine the relevant passage.

There is tension in this passage between its general inclination and specific-case discussion and also between qualitative and quantitative divisibility. The divisibility in terms of meaning or definition is qualitative. The idea is that there are two parts that are not homogenous; they differ in the definitions of their concepts or, equivalently, in the meanings of their terms.Footnote ²³ This division could be purely conceptual or conceptual and actual. If it is also actual, then it might imply a division in terms of quantity as well.

An illustration might help here. Let us reconsider our previous example: the division of my pen into a nib and a body (see 5). As explained earlier, this is a quantitative and qualitative division. I don't think this sort of division is what al-Ġazālī has in mind in the passage above. As a quantitative division, it is already within the scope of the argument against P4(a). The distinction between the body of the pen and the hollowness of its barrel is closer to the spirit of the passage. It is a conceptual and actual division (“two things different in definition and reality”). The pen is a single object that is obtained by the union of its components, including the hollowness of its barrel. But if one tries to remove the hollowness from the pen, that is, if one “decomposes” the pen, the pen breaks into quantitative components. Thus, we have a conceptual and actual qualitative divisibility that implies, under certain circumstances, quantitative divisibility (“it would be divisible in terms of quantity when it is decomposed actually or conceptually”).

The case of matter and form is similar in some respects to the case of the pen's body and hollowness. We have a single body, say a solid cube, obtained by conjoining matter and a form. In order for this cube to persist, neither its matter nor its form may stand alone independently of the other (I propose that this is the correct way to understand the clause “it is inconceivable that they would subsist independently of each other”).Footnote ²⁴ But the divisibility of the solid cube into matter and form is an actual as well as conceptual division. If one attempts to decompose the cube by separating its form from its matter, not only would the cube cease to exist, but also it would break up quantitatively (its “parts” take different shapes). The cube needs (it depends on) the existence of its form and matter in order to exist. This is why a necessary existent cannot be made of matter and form; for its existence, in this case, would be conditioned upon the existence of its matter and form in their conjoined state. Since a necessary existent cannot depend in its existence on anything other than itself, it is clear that a necessary existent cannot be the union of matter and form.

It remains to be asked, Why cannot a necessary existent be the union of matter and form in the sense that it is primarily matter and form is concomitant with it, or alternatively, it is primarily form and matter is concomitant with it? Al-Ġazālī answers this in the last part of the passage: it can be neither because each needs the other as a condition for the existence of the whole, and this produces a condition for the existence of a necessary existent, which, as we already explained, is absurd.

9. Now that the argument is laid out in these terms, it is easily seen that it could be generalized beyond the case of matter and form. Any conceptual (which might also be actual) qualitative plurality of parts such that (a) by their union a single entity is obtained and (b) they mutually depend on each other in order to form the resulting entity is impossible for a necessary existent. Seeing that divisibility into matter and form satisfies the two previous conditions, we may paraphrase the conclusion of this argument compactly as follows: A necessary existent is not conceptually divisible into qualitative parts such as matter and form.

Here is a schematization of the reconstructed argument.

1. P10. If a necessary existent is conceptually divisible into qualitative parts such as matter and form, then the necessary existent is the union of these parts, which are mutually dependent on each other.

2. P11. If a necessary existent is the union of qualitative parts that are mutually dependent on each other, then its existence is conditioned on the mutual dependency that exists between these parts.

3. P12. The existence of a necessary existent is not conditioned on anything other than itself.

4. C4 (= not-P4(b)). A necessary existent is not conceptually divisible into qualitative parts such as matter and form.

While al-Ġazālī accepts the conclusion of the argument (we know this from his other works such as al-Iqtiṣād fī al-Iʿtiqād), in the Ninth Discussion of the Tahāfut he argues that the Islamic philosophers are not entitled to this argument. He argues there that the philosophers cannot establish that God is not an extended body, and of course an extended body is divisible (at least conceptually) into matter and form.

What concerns us here is the way al-Ġazālī thinks the philosophers argue against such a division. His interpretation of the philosophers' argument lends support to our reconstruction. Responding to the philosophers' argument that God cannot be a body for He is not susceptible to a conceptual division such as the division into matter and form, he writes:

The important point is that al-Ġazālī attributes to the philosophers a claim similar to P11. This coheres well with our reconstruction of the subargument against P4(b).

THE SUBARGUMENT AGAINST P4(c)

10. We previously mentioned that the medieval Islamic philosophers are willing to attribute only relations and negations to God (see 1). They considered the affirmation of any attribute that is additional to His essence (i.e., a positive attribute) a form of attributing composition to God, and this would contradict the NP conception of the divine unity. As we explained in the Introduction, according to the philosophers, it is meaningful to say that God is Eternal because this is to attribute two negations: God's existence was not preceded by nonexistence and it will not be succeeded by nonexistence; and it is meaningful to say that God is the Creator because this is to attribute a relation: every existent, other than God, emanated from God either directly or through intermediaries. In general the medieval Islamic philosophers give imaginative readings to all the attributes of God typically found in the monotheistic traditions as well as some additional attributes, such as “enjoyer” and “enjoyable” – readings that render all of these attributes relational or negative.

The Ashʿariyya and many other theological schools believe that God has positive, eternal attributes, that is, attributes that are additional to God's essence, subsist in His essence, and coexist with His essence. If this doctrine implies that there is a composition in God, as the philosophers see things, then so be it: such composition is consistent with the divine unity. Of course, this is not the philosophers' NP conception of the divine unity.

11. Al-Ġazālī presents, on behalf of the philosophers, the argument against the positive attributes in the following passage.

It is clear that this argument invokes the oneness of the necessary existent to rule out this form of composition. This is what we cautioned against earlier (see 6). Such a move renders the larger argument circular. According to the one-argument interpretation, the simplicity of the necessary existent is required in order to establish its oneness. So one is not at liberty to invoke the oneness of the necessary existent to argue for its simplicity.

To see how the supposition of the oneness of the necessary existent enters into this argument, we need to reconstruct the argument with some elaboration.Footnote ²⁷ Suppose that a necessary existent has positive attributes, that is, it has attributes that are additional to its essence and that cannot be rendered as merely relations or negations. Then, these attributes must be pre-eternal. They did not simply occur to the necessary existent at some point in time. Otherwise, the necessary existent would undergo change: it would change, e.g., from not having knowledge to being knowledgeable. By the same reasoning, the attributes are post-eternal. They don't cease to exist at some point. Otherwise change would ensue in this case too. The Islamic philosophers and most of the Islamic theologians, including the Ashʿarites, assumed an immutable conception of the necessary existent: the necessary existent does not undergo any change whatsoever. So if there were positive attributes, they would have to be eternal – they would coexist with the essence of the necessary existent. It is also thought that it is incorrect to assume that the essence caused its attributes (see al-Ġazālī's passage below). Thus we have positive, eternal, uncaused attributes, which are additional to the essence. It follows that there would be a plurality of necessary existents: the essence of the necessary existent and its positive attributes. But there is no plurality of necessary existents. Therefore, the necessary existent has no positive attributes.

Here is a schematization of this argument, which isolates the supposition of the oneness of God as an explicit premise.

1. P13. If the necessary existent has positive attributes, which are additional to its essence, then these attributes cannot occur to it at some point in time or cease to exist.

2. P14. If the positive attributes cannot occur to the necessary existent or cease to exist, then they are eternal and coexist with its essence.

3. P15. The positive attributes of the necessary existent are uncaused.Footnote ²⁸

4. P16. If the positive attributes of the necessary existent are eternal, uncaused, and coexist with and additional to its essence, then they have necessary existence by virtue of themselves.Footnote ²⁹

5. P17. The essence of the necessary existent has necessary existence by virtue of itself.

6. P18. If the essence and the positive attributes of the necessary existent have necessary existence by virtue of themselves, then there is a plurality of necessary existents.

7. P19. There can be only one necessary existent.

8. C5 (= not-P4(c)). The necessary existent does not have positive attributes, which are additional to its essence.

P19 is the source of the difficulty. It is a paraphrase of the principle of the oneness of the necessary existent. Al-Ġazālī, in fact, points out this circularity in the Sixth Discussion of the Tahāfut, where he critically examines the argument above and other arguments against the positive attributes of the necessary existent. He asks the philosophers to present a more detailed proof for the claim that the necessary existent cannot have positive, eternal, necessarily existing attributes, which are additional to its essence. He answers the question and presents, on behalf of the philosophers, the following argument.

Al-Ġazālī objects to this argument. He writes:

Here is how I think the italicized sentences ought to be understood. The first ‘it’ refers to the philosophers' rejection of absolute duality (i.e., to their affirmation of the oneness of the necessary existent). So the first italicized sentence says that the philosophers' denial of absolute duality (which is the basis for their rejection of the first option) cannot be established unless internal plurality is refuted whether in this or the other cases. The phrase ‘is a branch of’ means, I believe, ‘is a consequence of’. Hence, the second italicized sentence asks how it is possible to base their rejection of the composition described in this case on the rejection of a duality of necessary existents, where the latter (i.e., the rejection of the multiplicity of necessary existents) is supposed to be a consequence of the former (i.e., the rejection of internal plurality within the necessary existent).

Because of the importance of al-Ġazālī's analysis to my one-argument interpretation, I will restate his point more conspicuously. Al-Ġazālī's charge against the philosophers is this. The philosophers are attempting to reject internal plurality on the basis of their rejection of external duality. But, the rejection of external duality requires the rejection of internal plurality. So, how can they base the rejection of internal plurality (or the affirmation of simplicity) on the rejection of external duality (or the affirmation of oneness) when the rejection of external duality is itself a consequence of the rejection of internal plurality?

12. This is exactly how the one-argument interpretation sees matters. According to this interpretation, the five subarguments, including this one (i.e., the subargument against P4(c)), aim at showing that the necessary existent is simple, and the main argument invokes the simplicity of the necessary existent to establish its oneness. In arguing, then, for the simplicity of the necessary existent, it is illegitimate to appeal to its oneness. One may legitimately appeal only to aspects that are part of the concept of necessary existent, such as its necessary existence, its eternality, its independence of all conditions outside its essence, and its constancy, all of which are part of the philosophers' conception of the necessary existent. Al-Ġazālī shows that since the subargument against P4(c) appeals to oneness to establish simplicity, it renders circular the larger argument that then appeals to simplicity to establish oneness.

THE SUBARGUMENT AGAINST P4(d)

13. The fourth type of (internal) plurality that the secondary (transitional) argument rules out is a conceptual plurality of classification. The main point is this: the necessary existent does not share a genus with any other thing from which it is differentiated by a differentia (that is, by belonging to a different species). This is because if it is possible to recognize a genus and a species in a necessary existent, then the necessary existent would be conceptually divisible into two qualitative parts. The second subargument against qualitative composition might be applicable to this case as well. Recall that the second subargument refutes the possibility of conceptual divisibility into qualitative parts by showing that these parts are in need of each other in order to maintain the existence of their union, which is the necessary existent. In such a case, the existence of the necessary existent would be conditioned upon the interdependency of these parts. Typically the differentia is a subcategory of the genus, but much more needs to be said about theses different categories in order to cash out the interdependency relations correctly.

Consider the relevant passage.

If this argument is meant to show that a necessary existent is not conceptually composed of genus and differentia, then it fails miserably. It presupposes the negation of P4(d), which is the goal of the argument.

The argument seems to run as follows.

1. P20. If it is possible to classify a necessary existent into genus and differentia, then it is possible to conceive of a necessary existent as a composite of a genus and a differentia.

2. P21. If it is possible to conceive of a necessary existent as a composite of a genus and a differentia, then it is possible for a necessary existent to admit a conceptual plurality of genus and differentia.

3. P22. It is not possible for a necessary existent to admit a conceptual plurality of genus and differentia.

4. C6 (= not-P4(d)). It is not possible to classify a necessary existent into genus and differentia

This is not really an argument for the simplicity of a necessary existent, though it does avoid the circularity of the preceding argument inasmuch as it does not invoke the oneness of the necessary existent. Nevertheless, it is question begging in a strong sense. This argument is one of a collection of subarguments that are jointly supposed to show that a necessary existent admits no type of internal plurality. Each subargument aims at refuting one type of plurality. This argument aims at refuting the possibility of having a conceptual plurality of genus and differentia in a necessary existent. But this is P22. The argument, instead of arguing for this form of simplicity, invokes it to conclude that a necessary existent is not subject to classification of genus and species.

Al-Ġazālī disputes the conclusion of this argument in the Seventh Discussion of the Tahāfut. As I said earlier, our interest in al-Ġazālī's polemics is solely focused on corroborating our one-argument interpretation. In a few places he indicates that the philosophers invoke the simplicity of the necessary existent to infer its oneness. This is the central idea of the one-argument interpretation. This interpretation sees the five subarguments as aiming, through the transitional secondary argument, at establishing the simplicity of the necessary existent, which is invoked in the main argument to establish the oneness of the necessary existent. Al-Ġazālī asserts this central idea in the following passages of the Seventh Discussion. Responding to the philosophers' claim that the First Principle cannot be composed of a genus and a differentia, he writes:

In another passage he makes it clear that the philosophers' burden is to show that a necessary existent is simple and one.

14. Our reconstruction of the argument against P4(d) makes it hopeless. Could we be more charitable? Is there textual evidence to suggest a better reconstruction of this argument? Al-Ġazālī presents a more elaborate argument against P4(d) in the Seventh Discussion of the Tahāfut. Let us examine the passage with some care. Again, he is challenging the philosophers to advance an argument for the impossibility for a necessary existent to be a composite of genus and differentia.

The argument here seems to be this. Suppose that a necessary existent is a composite of genus and differentia. This means that the necessary existent is the union of the two, which are its components. Now, what is the relation between the whole and the components? If it is a relation of mutual dependency, then none of them is a necessary existent, including the necessary existent, which is absurd. The other possibility is that the whole or at least one of the components is independent of the rest. In this case, what is independent is the necessary existent and everything else that is not fully independent is not a necessary existent.

What the argument does not articulate is which one of these possibilities is applicable to the genus-differentia composition. It is very likely the second possibility is the relevant one. For example, being human is conditioned upon being an animal and being rational. Being rational is a species of being an animal. This leaves being an animal as the most likely candidate to be the one aspect that is independent of the other two. If it is permissible to carry this analysis to the case of the necessary existent, then it would follow that the necessary existent, which is the union of genus and differentia, is not the necessary existent, but most likely the genus is. This is absurd too.

If this is correct, we obtain a reconstruction of the argument that is not subject to the charge of question begging.

1. P23. If a necessary existent is conceptually divisible into genus and differentia, then the necessary existent is the union of components.

2. P24. If the necessary existent is the union of components, then either the whole and the components are all dependent for their existence on each other or one of them is independent of the rest.

3. P25. If they are all dependent for their existence on each other, then none of them, including the necessary existent, has necessary existence by virtue of itself.

4. P26. If one of them, call it x, is independent of the rest of them, then the necessary existent, which is the union of the components, is not x.

5. P27. If the necessary existent is not independent for its existence of all the components, then it cannot have necessary existence by virtue of itself.

6. P28. A necessary existent has necessary existence by virtue of itself.

7. C7 (= not-P4(d)). A necessary existent is not conceptually divisible into genus and differentia.

This argument is far more elaborate than the original short passage from the Fifth Discussion. But there is no reason why we shouldn't avail ourselves of the elaborate analysis in the Seventh Discussion. Note that we didn't do the same for the argument against the positive attributes (P4(c)). The longer passage we cited from the Sixth Discussion did not improve the situation. The argument there was based on refuting three options. One of those refutations invoked the oneness of the necessary existent – a point that al-Ġazālī makes explicit, as we have seen.

It might seem that P26 above is too convenient. This might be true, but it is not unreasonable for a reconstruction of the argument against P4(d) to include such a premise. Although the passage we cited does not state P26 or a paraphrase of it, the analysis we gave of the example of humanity, animality, and rationality is quite plausible. In fact, al-Ġazālī, too, gives a similar analysis in the Seventh Discussion shortly after he presents, on behalf of the philosophers, the argument we reconstructed above.

Even though al-Ġazālī does not say that the genus is the independent factor among the triad of genus, species, and their composite, the important point that is relevant to P26 is that the composite is not independent of the genus and species. Al-Ġazālī's analysis lends support to our analysis.

THE SUBARGUMENT AGAINST P4(e)

15. As explained in note 17, the Islamic philosophers and theologians frequently (but not always) distinguished between māhiyya, which is usually translated as ‘quiddity’, and ḏāt, which is typically translated as ‘essence’. The distinction, when maintained, is that the māhiyya of something is its true nature without the supposition of existence. When existence is added to the māhiyya (whether existence is necessary or contingent for the māhiyya), the resulting combination is ḏāt. Hence, a nonexistent thing might have a māhiyya but not a ḏāt. Henceforth, I shall use ‘quiddity’ and ‘essence’ instead of māhiyya and ḏāt, but the distinction must be borne in mind for the following discussion to make sense.

The relevant passage is somewhat long. Only part of it contains the argument; the other part explains that existence is additional to the quiddity. I will translate the argumentative statements fully and the explanatory ones selectively.

The gist of the argument is condensed in the second paragraph. Let us unpack it. If a necessary existent is divisible into quiddity and existence, then it seems that it is possible to conceive of its quiddity without its existence. But the philosophers believe this to be obviously false. For in this case, it would be possible to conceive of a necessary existent as nonexistent. The philosophers think that since the existence of a necessary existent is necessary, it is not possible to conceive of it as nonexistent. So, it must be the case that when the quiddity of a necessary existent is conceived of, the existence of the necessary existent is conceived of as well. How could this be? By definition, existence is not part of the quiddity. This leaves us with one option: the existence of a necessary existent is an immediate consequence of its quiddity. The consequence must be so immediate that as soon as one thinks of the quiddity of a necessary existent, he has also to think of its existence. It is akin to a triangle's being three-sided and its being three-angled. But now the existence of a necessary existent is conditioned upon its quiddity: if the quiddity is removed, existence ceases. This contradicts the philosophers' conception of a necessary existent as an existent independent of all conditions.

Below is a schematization of the reconstructed argument.

1. P29. If a necessary existent is divisible into quiddity and an existence that relates to it, then the existence of the necessary existent is not an immediate consequence of its quiddity only if it is possible to conceive of its quiddity without conceiving of its existence.

2. P30. If it is possible to conceive of the quiddity of a necessary existent without conceiving of its existence, then it is possible to conceive of a necessary existent as nonexistent.

3. P31. It is not possible to conceive of a necessary existent as nonexistent.

4. P32. If the existence of a necessary existent is an immediate consequence of its quiddity, then its existence is conditioned on its quiddity.

5. P33. The existence of a necessary existent is not conditioned on anything.

6. C8 (= not-P(e)). A necessary existent is not divisible into quiddity and existence.

16. We now reach the end of the one-argument interpretation of al-Ġazalī's argument, on behalf of the philosophers, for the NP conception of the divine unity. I did not discuss the cogency of this multi-faceted argument or the plausibility of its many premises. That is beyond the scope of this paper. My interest here is to understand the logical structure of this argument and the logical forms of its various parts, and to give faithful reconstructions of these parts in order to identify their premises and conclusions.

We observed that all of these reconstructions are valid, yet there is one serious problem: the third subargument, against the positive attribute of the necessary existent, begs the question against the main argument. The subargument invokes the oneness of the necessary existent in order to conclude that the necessary existent is not composed of essence and attributes, which in turn is needed to establish the absolute simplicity of the necessary existent. The main argument relies on the simplicity of the necessary existent to demonstrate its oneness. Al-Ġazālī devotes a whole Discussion to refute the philosophers' doctrine against the positive attributes of God. The discussion there is not helpful to remove the circularity. Indeed, I cited a fairly long passage in which al-Ġazālī presents an elaboration of the philosophers' argument against the positive attributes (see 11). As noted there, the elaborate argument is still circular, and al-Ġazalī points this out.

THE MANY-ARGUMENT INTERPRETATION

17. There is a way of understanding these arguments that does not render the argument for the oneness of the necessary existent as a main argument and the five arguments for the simplicity of the necessary existent as tributary arguments feeding into the main argument via the secondary, transitional argument. This interpretation sees the relation between these two categories of arguments as making converse points. In the argument for the oneness of the necessary existent, we show that simplicity leads to oneness; in the arguments for the simplicity of the necessary existent, we show that oneness leads to simplicity – they are not subarguments that are meant to establish the simplicity of the necessary existent independently of the supposition of its oneness. So the many-argument interpretation runs as follows: if God is simple, He is one; and if He is one, He is simple. There is one revision to this formula. The second part is best understood in the contrapositive form: if God is not simple, He is not one.Footnote ⁴⁰

This interpretation does not offer new reconstructions of the arguments. After all, our reconstructions were guided by careful examination of the textual evidence. There is, however, one clear advantage to this interpretation. The charge of circularity is no longer applicable to the argument against the positive attributes of God. There would be no modification to the argument. The oneness of the necessary existent is still a premise of the argument, but the argument is no longer circular because it is not supposed to be employed to prove the oneness of God.

According to the many-argument interpretation, there are six independent arguments. The first argument presupposes the simplicity of the necessary existent and delivers its oneness. Each one of the other five arguments may presuppose the oneness of the necessary existent in order to establish one type of its simplicity – except that it does it in the contrapositive form. In a sense, the last five arguments are not fully independent of each other because they collectively aim at establishing the absolute simplicity of the necessary existent. Thus, on this interpretation, the six arguments are not meant as a multi-faceted argument for the NP conception of the divine unity. All that they show is that each component of this conception entails the other: simplicity entails oneness and oneness entails simplicity.

18. If the many-argument interpretation solves the circularity problem, why then do I prefer the one-argument interpretation? There are three reasons for my preference. First, there is something attractive about saying that there is an argument for the philosophers' extreme conception of the divine unity. It is not simply that its two senses (namely, oneness and simplicity) entail one another, but actually one can give a proof for the whole conception. The “proof” for it is meant to be based on the philosophers' basic conception of the necessary existent. For the philosophers, the essence of a necessary existent is necessary existence. They understood this to mean that it is inconceivable and impossible for the necessary existent to be nonexistent at any point in time, that it is uncaused temporally or essentially,Footnote ⁴¹ and that its existence is independent of all things and conditions. They also believed that the necessary existent is unchanging: it is not susceptible to occurrences and cessations. It is not clear why they thought that this immutable conception is part of the essence of the necessary existent,Footnote ⁴² but there is no question that they held such a view.

Second, the structure of the five arguments for the simplicity of the necessary existent lends significant support to the one-argument interpretation. Except for the argument against the positive attributes, all the arguments rely on the philosophers' basic conception of the necessary existent. These arguments do not show that oneness entails simplicity; rather they show that necessary existence entails simplicity. While the many-argument interpretation makes sense of the argument against the positive attributes, its explanation is irrelevant to the other four arguments.

Third, there is the textual evidence, of course. We have seen that al-Ġazālī's comments about some of these arguments fit nicely with the one-argument interpretation. In the transitional passage and other passages (see 6, 11, and 13), he indicates that the denial of the various forms of compositionality in the necessary existent is employed by the philosophers to argue for its oneness (or, equivalently, for the denial of duality). Add to this, his recognition of the circularity of the argument against the positive attributes – a feature that fits the one-argument interpretation but not the many-argument interpretation. If one supposes that the many-argument interpretation is the correct reading of these arguments, then much of al-Ġazālī's analysis makes little sense. Al-Ġazālī argues that four of the five arguments for the simplicity of the necessary existent fail, and he takes this failure as showing the philosophers' inability to prove that the oneness of God follows from the basic concept of necessary existent. The Sixth through Ninth Discussions of the Tahāfut are devoted to showing that the philosophers are unable to refute P4(b) – P4(e). His central claim is that if the philosophers are shown to be unable to establish that there is no plurality within a necessary existent, then they are shown to be unable to prove that there is no plurality of necessary existents, and this shows, he argues, that the philosophers cannot establish the doctrine of divine unity. He doesn't argue that they fail to show that the two senses of the divine unity entail one another, but that they fail to show that God is one, that is, they fail to show that the oneness of the necessary existent follows from the concept of necessary existent.