“Say what you are thinking. My heart urges me on to accomplish it, if I can accomplish it and if it is accomplishable” (Iliad 14, l. 196 and 18, l. 427, Odyssey 5, l. 90)
1. Introduction
The Impossible represents the Idea of that which cannot be, and yet is. It is the simultaneity of that which ought to lack existence, and is yet supposed to have it. The Impossible is supposed to be, on the one hand, possible so as to be negated or made exclusive of reality, and impossible so as to not be real or realizable. So we are forced to realize the Paradoxical nature of Impossibility, as a Impossibility. There is first, the direction towards being possible, in impossibility, and then there is a direction toward being Im-possible, in Impossibility. Such that two opposed directions come about at once in the Impossible.
In brief, in predicating Impossibility of any proposition, we make two assertions simultaneously.
Y = "X is Impossible"
1. X is not a property/part of anything.
2. X is a property/part of Y.
2. Examples
Take for example the Laws of Thought, or Being (as they are sometimes called) i.e. LNC and LEM, that are supposed to delineate Impossibility and therefore Possibility at it's roots.
LNC (Law of Non-Contradiction)"We have next to state what principle this is. For
the same thing to hold good and not to hold good simultaneously of the same thing and in the same respect is impossible (given any further
specifications which might be added against the dialectical
difficulties)." (Metaphysics Gamma, 1005
b
18)
Now, this statement as given, has been taken for a long time, and still is today as exemplary of what it is for a thing to be impossible, and primary in showing such. So something is impossible, if and only if (IFF)
"A predicate X and it's negation (Not-X) are simultaneously said of the same thing, in the same respect."
Examples being, "This apple is red, and not red", or that "Aristotle is the father of logic, and not the father of logic".
Now, given such, we are told that this concept is Impossible. Which isn't confusing, until we think about the fact that in saying such, we have already given an example of it being possible. Possible in our thoughts, for us to think and speak about it. But given such, we are only more confused how this is supposed to not be applicable to reality then. Clearly, the proposition which claims contradictions to be exclusive to reality, is real.
For if X wasn't real,
X = "An apple is green, and not green."
Then how could one predicate of X, that it is Impossible.
"X is Impossible."
Since, what one will predicate Impossible of will be nothing, and therefore would be equivalent to.
"---- is Impossible" or "( ) is Impossible"
Given such, we have therefore required to assume that there's at least one entity (i.e. Our Thoughts) which holds the Impossible Possibly, and therefore renders it Impossible for others.
Now, the reader might feel that given we have delineated which entities contradiction are a part of, no more troubles remain. But, a closer inspection of the delineation reveals certain problems.
I. Arbitrary
Given that we have delineated one entity from another, to which contradiction might be a part of. One question that may be asked is: What discriminates which entities contradictions are a part of, and which are not? Similar to how contradictions traditionally considered, are the criterion by which we differentiate Possibilities from Impossibilities. What property (X) of Non-Ideal entities is it that renders them incapable of having a contradiction as part of it's identity? Clearly, saying that they are impossible won't be a satisfying answer, since we are now no longer dealing with the distinction btw possibilities and impossibilities. But with different possibilities of different entities, namely that of Ideal, and Non Ideal entities.
"Ideal Entities are (X), in virtue of which they can contain contradictions as part of there Identity."
Now, someone might, expectably, posit them to be brute properties of Ideal entities. Properties that are not (explained by)/(composed of) any more basic property. Now, by nature, brute-ness is arbitrary. That is to say, it allows for it's contrary to be equally predicated of the subject, of which it itself is a predicate.
"X is arbitrary, if and only if X is a property/predicate that can be, and not-be predicated of a subject."
Exempla Gratia,
Red is an arbitrary predicate, if and only if it allows for the following claims to be true.
a. An apple is Red.
b. An apple is not Red.
Now, given such, any arbitrary predicate cannot be used to differentiate a Subject (i.e. Ideal Entity), from a Non Ideal entity, since it simultaneously allows it to be same as that Entity, and different from it. Put precisely, it allows both of these claims to be true
Contradictive: Capable of containing a contradiction, as part of there Identity.
1. Ideal entities are Contradictive, and Non Ideal Entities are Not Contradictive. (They are different)
2. Ideal Entities are Non Contradictive, and Non Ideal are Not Contradictive. (They are the same)
Therefore, arbitrary predicates cannot be used to differentiate "Ideal Entities", from "Non-Ideal Entities".
II. Thought-Thing
Now, Thought is something that is all consuming. Since, whatever proposition I make, I am thinking about, and it is therefore included in my thought. There is nothing that can be excluded from it, since in thinking of what is being excluded, we have already included it in Thought. For suppose I say that there is a property X, such that this property X is not a part of Thought. I put this in the propositional form
Y = "Thought is not X"
Now, either I am thinking Y or not thinking Y, such that
a. Thinking Y
If I am thinking Y, then (Not-X) is a part of my Thought. Therefore, X is a part of my Thought.
b. Not Thinking Y
If I am not thinking Y, then (Not-X) is not a part of Thought. Such that
"Thought is not (not-X)"
Since,
Not-Not-X = X (Logical Equivalence)
Therefore,
"Thought is X"
From this we can conclude that no property X can be invoked to differentiate Thought from Thing. Contradiction is potentially possessed by Thought, and not Thing, therefore it is a means by which Thought can be differentiated from Thing. Since, this is Impossible, therefore Thought and Thing both can possess contradiction.
The Impossible represents the Idea of that which cannot be, and yet is. It is the simultaneity of that which ought to lack existence, and is yet supposed to have it. The Impossible is supposed to be, on the one hand, possible so as to be negated or made exclusive of reality, and impossible so as to not be real or realizable. So we are forced to realize the Paradoxical nature of Impossibility, as a Impossibility. There is first, the direction towards being possible, in impossibility, and then there is a direction toward being Im-possible, in Impossibility. Such that two opposed directions come about at once in the Impossible.
In brief, in predicating Impossibility of any proposition, we make two assertions simultaneously.
Y = "X is Impossible"
1. X is not a property/part of anything.
2. X is a property/part of Y.
2. Examples
Take for example the Laws of Thought, or Being (as they are sometimes called) i.e. LNC and LEM, that are supposed to delineate Impossibility and therefore Possibility at it's roots.
LNC (Law of Non-Contradiction)
"We have next to state what principle this is. For
the same thing to hold good and not to hold good simultaneously of the same thing and in the same respect is impossible (given any further
specifications which might be added against the dialectical
difficulties)." (Metaphysics Gamma, 1005
b
18)
Now, this statement as given, has been taken for a long time, and still is today as exemplary of what it is for a thing to be impossible, and primary in showing such. So something is impossible, if and only if (IFF)
"A predicate X and it's negation (Not-X) are simultaneously said of the same thing, in the same respect."
Examples being, "This apple is red, and not red", or that "Aristotle is the father of logic, and not the father of logic".
Now, given such, we are told that this concept is Impossible. Which isn't confusing, until we think about the fact that in saying such, we have already given an example of it being possible. Possible in our thoughts, for us to think and speak about it. But given such, we are only more confused how this is supposed to not be applicable to reality then. Clearly, the proposition which claims contradictions to be exclusive to reality, is real.
For if X wasn't real,
X = "An apple is green, and not green."
Then how could one predicate of X, that it is Impossible."X is Impossible."
Since, what one will predicate Impossible of will be nothing, and therefore would be equivalent to.
"---- is Impossible" or "( ) is Impossible"
Given such, we have therefore required to assume that there's at least one entity (i.e. Our Thoughts) which holds the Impossible Possibly, and therefore renders it Impossible for others.
Now, the reader might feel that given we have delineated which entities contradiction are a part of, no more troubles remain. But, a closer inspection of the delineation reveals certain problems.
I. Arbitrary
Given that we have delineated one entity from another, to which contradiction might be a part of. One question that may be asked is: What discriminates which entities contradictions are a part of, and which are not? Similar to how contradictions traditionally considered, are the criterion by which we differentiate Possibilities from Impossibilities. What property (X) of Non-Ideal entities is it that renders them incapable of having a contradiction as part of it's identity? Clearly, saying that they are impossible won't be a satisfying answer, since we are now no longer dealing with the distinction btw possibilities and impossibilities. But with different possibilities of different entities, namely that of Ideal, and Non Ideal entities.
"Ideal Entities are (X), in virtue of which they can contain contradictions as part of there Identity."
Now, someone might, expectably, posit them to be brute properties of Ideal entities. Properties that are not (explained by)/(composed of) any more basic property. Now, by nature, brute-ness is arbitrary. That is to say, it allows for it's contrary to be equally predicated of the subject, of which it itself is a predicate."X is arbitrary, if and only if X is a property/predicate that can be, and not-be predicated of a subject."
Exempla Gratia,
Red is an arbitrary predicate, if and only if it allows for the following claims to be true.
a. An apple is Red.
b. An apple is not Red.
a. An apple is Red.
b. An apple is not Red.
Now, given such, any arbitrary predicate cannot be used to differentiate a Subject (i.e. Ideal Entity), from a Non Ideal entity, since it simultaneously allows it to be same as that Entity, and different from it. Put precisely, it allows both of these claims to be true
Contradictive: Capable of containing a contradiction, as part of there Identity.
1. Ideal entities are Contradictive, and Non Ideal Entities are Not Contradictive. (They are different)
2. Ideal Entities are Non Contradictive, and Non Ideal are Not Contradictive. (They are the same)
Therefore, arbitrary predicates cannot be used to differentiate "Ideal Entities", from "Non-Ideal Entities".
Contradictive: Capable of containing a contradiction, as part of there Identity.
1. Ideal entities are Contradictive, and Non Ideal Entities are Not Contradictive. (They are different)
2. Ideal Entities are Non Contradictive, and Non Ideal are Not Contradictive. (They are the same)
Therefore, arbitrary predicates cannot be used to differentiate "Ideal Entities", from "Non-Ideal Entities".
II. Thought-Thing
Now, Thought is something that is all consuming. Since, whatever proposition I make, I am thinking about, and it is therefore included in my thought. There is nothing that can be excluded from it, since in thinking of what is being excluded, we have already included it in Thought. For suppose I say that there is a property X, such that this property X is not a part of Thought. I put this in the propositional form
Y = "Thought is not X"
Now, either I am thinking Y or not thinking Y, such that
a. Thinking Y
If I am thinking Y, then (Not-X) is a part of my Thought. Therefore, X is a part of my Thought.
b. Not Thinking Y
If I am not thinking Y, then (Not-X) is not a part of Thought. Such that
a. Thinking Y
If I am thinking Y, then (Not-X) is a part of my Thought. Therefore, X is a part of my Thought.
b. Not Thinking Y
If I am not thinking Y, then (Not-X) is not a part of Thought. Such that
"Thought is not (not-X)"
Since,
Not-Not-X = X (Logical Equivalence)
Therefore,
"Thought is X"
From this we can conclude that no property X can be invoked to differentiate Thought from Thing. Contradiction is potentially possessed by Thought, and not Thing, therefore it is a means by which Thought can be differentiated from Thing. Since, this is Impossible, therefore Thought and Thing both can possess contradiction.
