Ahwl Theory and Arguments Against LNC

The Theory of Ahwl and Arguments Against the LNC Behnam Zolghadr Universit t Hamburg 27/5/2019

Outline: 1. R z s Muhassal. 2. The Theory of States (Ahw l). 3. Four Arguments against LNC. 4. Other Self-evident Assents.

Rzs Muhassal Fa r al-Din al- R z (d.1210) The Book: Mu assal afk r al-mutaqaddim n wa-'l-muta' ir n (The Compendium of the Thought of the Ancients and Moderns)

Rzs Muhassal The Structure of Muhassal: 1. On preliminaries including conception (t awur), assent (t d q), reasoning and different types of it. 2. On different types of the knowns (m l m t): existents (maw d t), non-existents (m d m t), possible objects (mumkin t) and their properties. 3. On God, namely its essence, its attributes and its acts. 4. On prophecy (nabuwat) resurrection (m d) and im ma.

Rzs Muhassal In the first part of Muhassal, concerning assents: Assents: 1. Self-evident assents: Affirmation and negation do not combine and cannot be denied. 2. Sensible assents: The fire is hot.

Rzs Muhassal With respect to which of these assents philosophers accept, there will be four groups: 1. Those who accept both sensible and self-evident assents. They are the majority. 2. Those who accept self-evident assents but deny sensible assents: Plato, Aristotle, Ptolemy and Galen. 3. Those who deny self-evident assents but accept sensible assents. 4. Those who deny both self-evident assents and sensible assents: The Sophists.

Rzs Muhassal Self-evident assents: 1. Affirmation and negation do not combine and cannot be denied. 2. Identity is transitive. 3. The whole is bigger than its parts. 4. An object cannot be in two different places at the same time.

Rzs Muhassal Avicenna: if both [affirmation and negation] together are false with respect to one thing, then that thing would, for example, be not man and also not not man . Hence, the thing which is not man and its negation (which is not not man ) would have been combined. (Avicenna, Metaphysics, I, V) ?? ( ??)

The Theory of States Ab H im al- ubb (d.933) Metaphysical categories: God, Atoms, Accidents and States. States explain the ontological status of Sif t (Properties).

The Theory of States States: 1. The attribute of essence: this is the self-identity of things. (? = ?) 2. Essential attributes: These are the attributes which are entailed, as soon as objects become existent, by the attribute of essence. 3. Existence. 4. Properties which are grounded in accidents. 5. Intentionality.

The Theory of States States are neither existent nor non-existent. States are not objects.

Arguments against LNC First argument. This assent is based on conceptualizing the nonexistence by which people are perplexed. Because that which is conceptualized must be distinguished from other things, and that which is distinguished from something else is specific by virtue of itself. And that which is specific in virtue of itself is real. Since the affirmation [of the law of non-contradiction] is based on this conceptualization, and this conceptualization is impossible, so, that affirmation is also impossible. (Muhassal, p.30)

Arguments against LNC First argument. This assent is based on conceptualizing the nonexistence by which people are perplexed. Because that which is conceptualized must be distinguished from other things, and that which is distinguished from something else is specific by virtue of itself. And that which is specific in virtue of itself is real. Since the affirmation [of the law of non-contradiction] is based on this conceptualization, and this conceptualization is impossible, so, that affirmation is also impossible. (Muhassal, p.30) Affirming the LNC is self-refuting.

Arguments against LNC Second argument. The assent, that negation and affirmation do not combine, implies a distinction between existence and nonexistence, and this distinction implies that the referent of nonexistence has a distinct essence from that of existence, but it is impossible. Because every entity which the mind intends, can also be removed by the mind; otherwise it doesn t have an opposite. Therefore, nonexistence does not have an opposite and it implies the denial of existence, but it is false. Thus the removal of that which is the referent of nonexistence is coherent. However, this removal is a specific one, and is counted as a case of absolute nonexistence, and it means that the complement of nonexistence is a part of it, which is impossible. (Muhassal, p.30)

Arguments against LNC Second argument. The assent, that negation and affirmation do not combine, implies a distinction between existence and nonexistence, and this distinction implies that the referent of nonexistence has a distinct essence from that of existence, but it is impossible. Because every entity which the mind intends, can also be removed by the mind; otherwise it doesn t have an opposite. Therefore, nonexistence does not have an opposite and it implies the denial of existence, but it is false. Thus the removal of that which is the referent of nonexistence is coherent. However, this removal is a specific one, and is counted as a case of absolute nonexistence, and it means that the complement of nonexistence is a part of it, which is impossible. (Muhassal, p.30) Nonexistence is not the complement of existence!

Arguments against LNC Third argument. By accepting bivalence, existence and non-existence cannot be ascribed to an object. (1) Blackness is either existent or nonexistent.

Arguments against LNC Third argument. By accepting bivalence, existence and non-existence cannot be ascribed to an object. (1) Blackness is either existent or nonexistent. By accepting bivalence, we cannot have a metaphysical explanation of properties. (2) A body is either black or not.

Arguments against LNC (1) Blackness is either existent or nonexistent. (1.1) Blackness is existent. (1.2) Blackness is nonexistent. Consider (1.1) This is not an identity sentence. Because (1.1) is informative.

Arguments against LNC If blackness and existent are distinct, (1.1) is absurd for two reasons: One of them: that is, if existence subsists through blackness, then blackness is not, as such, existent. Because otherwise the question arises again. But the same object cannot be existent for a second time. And if so, existence subsists through that which is not existent. But existence is the property of existent. Otherwise, we should accept the middle between existence and nonexistence but you deny that. (Muhassal, p. 31)

Arguments against LNC ? is existent. ?_ , ? Existence subsists through ? ? is nonexistent. (Because it is impossible for an object to become existent for the second time) ? is nonexistent Existence cannot be ascribed to ?. (Because existence is the property of existents)

Arguments against LNC The second reason: If existence is distinct from quiddity, the referent of our saying blackness is different from the referent of our saying existent . Then, if we say that blackness is existent and by this we mean that blackness is that which is existent, it is asserting the oneness of the two [non-identicals] which is impossible. (Muhassal, p. 31)

Arguments against LNC (1.2) Blackness is nonexistent. The problem of negative existential.

Arguments against LNC (2) A body is either black or not. (2.1) A body is black. First, it cannot be an identity statement. Otherwise, it is asserting the oneness of two distinct entities which is impossible. Second, since it is not an identity statement, it has the form of a subject-predicate sentence in which the subject is described by the predicate. Now, the property of being black is either existent or nonexistent.

Arguments against LNC If it exists, then it is either the same as the existence of the body and blackness or distinct from them. The former is impossible, because it is not the case that whenever one conceives the existence of the body and the existence of blackness, one also conceives that the body is described by blackness. The latter is also impossible, because if the property of being black were superadded to the body, then the property of having that property would also be superadded to the body. But this [leads to regress and thus] is impossible. (Muhassal, p.33)

Arguments against LNC ? is black. ? has the property of being black. ? has the property of having the property of being black. ? has the property of having the property of having the property of being black.

Arguments against LNC Fourth argument. Becoming. According to bivalence, it is either existent or nonexistent. But both are false. If it was existent, it would be true of the existent that it is coming out of non-existence into existence and if it is so it is like to say that the existent is coming out towards existence and thus the object is being existent twice and it is impossible. (Muhassal, p.34)

Arguments against LNC If it is non-existent the original non-existence endures and as long as the original non- existence endures, no change from non-existence occurs. (Muhassal, p.34)

Other Self-evident Assents 1. The whole is bigger than its parts. The whole is bigger than its part, because, otherwise, the existence of the other part and its non- existence would be the same. Thus, being existent and being non-existent is combined, at the same time, in the other part. (Muhassal, p.29)

Other Self-evident Assents 1. The whole is bigger than its parts. The whole is bigger than its part, because, otherwise, the existence of the other part and its non- existence would be the same. Thus, being existent and being non-existent is combined, at the same time, in the other part. (Muhassal, p.29)

Other Self-evident Assents , ? < ? ? < ? (? ?) (? ?) 1 ?( ? ? ? ? ) if ? was not bigger than ?, we would have ? = ?, which follows: 2 ?( ? ? ? ? ) (1) And (2) are contradictories.

Other Self-evident Assents 2. Identity is transitive. [Two] objects that are identical with a third object, are identical. Because, otherwise, [an object, namely] a which is identical with blackness is blackness. And since it is identical with that which is not blackness it is not blackness. Hence, if a is identical with these two different things, it follows that a is in itself blackness and a is not in itself blackness. Thus, the affirmation and the negation are combined . (Muhassal, p.29)

Other Self-evident Assents ?1 ?2 ? = ? ? = ? ? + + ?1? ?1? ? + ? +

Other Self-evident Assents 3. An object cannot be in two different places at the same time. One single object cannot be in two different places at the same time, because if it was possible there would be no difference between an object being in two places or two objects being so, and meanwhile, the existence of the other object would be the same as its non-existence, and it would be true to say that it is both existent and non-existent. (Muhassal, p.29)

These objections are only a drop of the sea of objections which have been raised against our saying that an object either is or is not. And if this is the state of the strongest self-evident [assent], what do you think about the weaker ones? (Muhassal, p.35)

Thank You!