I would need to argue that that with a lower state of existence than another could not give rise to the latter. With this proposition proved, our argument has full basis.
By definition, that with a greater level of existence has greater essence, and the existence of a substance is defined to be its extent of being in the field of knowledge.
We take as an axiom, that all that exists must exist in itself as a whole or in something else as a part. For that which exists in something else is a form of its singularity. We could redefine our axiom to state that all that exists, exists as a singularity or as form. If one doubts this, conceive of something which does not fulfil such criterion. This cements my proposition that the singularity-form structures are archetypes that we use to understand being.
Now, does the form give rise to the singularity or the singularity to the form. It should make itself clear that this is the same as the initial argument. Suppose that the form gives rise to the singularity.
The form has lesser essence in our system of metaphysics. Suppose the form has a greater essence than the singularity from which it had sprung forth from. Since the singularity had produced infinite forms through its being then the form in question must also in essence be able to produce infinitely many forms and hence act as a singularity. From mathematics it is understood that a subset of a set can contain at most the number of elements of the set. And hence the latter singularity could at most contain the number of elements or the essence of the initial singularity. And two singularities with the same essence are one and the same, for their existence is defined by their inner essence. So the latter singularity, the initial form is able to produce its initial singularity. But this very clearly contradicts our definitions.
Tuesday, 8 January 2013
On the Nature of Parts and their Whole
It has occurred to me that the relevance of the part is defined by the whole. To make this more clear take, say, the set of real numbers. This must be an uncountable infinite and thus contains the essence of infinity and its attributes. To make this subject clearer proceed to the following example.
Let us say that there exists a person who has no prior knowledge of circles, but encounters a circle segment.
But can the segment lead to the circle, how could the part lead to the whole? The part of the circle is defined as such through the very being of the circle itself. So clearly our example is preposterous we could not call a segment a 'circle segment' unless we had clear knowledge of what a circle was. So the knowledge of the segment of a circle is a part of the its respective whole, complete knowledge of the circle itself.
Coming back to the matter at hand, could numbers being a part of infinity lead to infinity? Would it not be infinity which necessarily dictates the being of numbers by a similar argument; For the numerical infinity must encompass all possible numbers in its being, and we have shown that the substance of a higher level of existence, that is the singularity, gives rise to its form respective forms. We should note that from our definitions it is clear that infinity is a singularity.
It is a surprising result to conclude that numbers cannot exist independent of infinity, and hence infinity necessarily exists for numbers do also exist. This is a paradigm shift in our traditional views on metaphysics, moving away from insistence of analytic construction from the lesser to the greater, but arguing for the greater giving rise to the lesser on its own accord. This now in turn opens up an important analysis into that 'analytic construction'. Clearly it is the work of the human mind, and so some innate epistemological structure must exist within the mind.
Concluding Remarks
To the unlearned mind which insists upon materialism or empiricism, this may seem very surprising as infinity is not a material construct, nor a concept which could be understood by such means. Do not treat this as a formal argument, although I believe there to be great truth in it. In fact I would argue that formalism is a deceptive mode of inquiry, the essence of argument must be in sound logic, but all logic fundamentally reduces to the naive archetypes of intuition which are in built in the human mind. I believe that these fundamental intuitions are represented clearly in my arguments, and that the reader through their own discourse could arrive at similar conclusions, and at the very least I encourage each person to use this method of inquiry to uncover their own understanding and knowledge.
Let us say that there exists a person who has no prior knowledge of circles, but encounters a circle segment.
But can the segment lead to the circle, how could the part lead to the whole? The part of the circle is defined as such through the very being of the circle itself. So clearly our example is preposterous we could not call a segment a 'circle segment' unless we had clear knowledge of what a circle was. So the knowledge of the segment of a circle is a part of the its respective whole, complete knowledge of the circle itself.
Coming back to the matter at hand, could numbers being a part of infinity lead to infinity? Would it not be infinity which necessarily dictates the being of numbers by a similar argument; For the numerical infinity must encompass all possible numbers in its being, and we have shown that the substance of a higher level of existence, that is the singularity, gives rise to its form respective forms. We should note that from our definitions it is clear that infinity is a singularity.
It is a surprising result to conclude that numbers cannot exist independent of infinity, and hence infinity necessarily exists for numbers do also exist. This is a paradigm shift in our traditional views on metaphysics, moving away from insistence of analytic construction from the lesser to the greater, but arguing for the greater giving rise to the lesser on its own accord. This now in turn opens up an important analysis into that 'analytic construction'. Clearly it is the work of the human mind, and so some innate epistemological structure must exist within the mind.
Concluding Remarks
To the unlearned mind which insists upon materialism or empiricism, this may seem very surprising as infinity is not a material construct, nor a concept which could be understood by such means. Do not treat this as a formal argument, although I believe there to be great truth in it. In fact I would argue that formalism is a deceptive mode of inquiry, the essence of argument must be in sound logic, but all logic fundamentally reduces to the naive archetypes of intuition which are in built in the human mind. I believe that these fundamental intuitions are represented clearly in my arguments, and that the reader through their own discourse could arrive at similar conclusions, and at the very least I encourage each person to use this method of inquiry to uncover their own understanding and knowledge.
Monday, 7 January 2013
On the States of Existence Regarding Knowledge
This proceeding may not take a systematic fashion which I concede, but all gaps in time will be eradicated as the thirst of the mind is quenched at the will of the beholder. I shall speak of how some substance could differ in its state of existence by recollecting a philosophical excerpt of mine.
That which gives rise to less knowledge than other is of a lower state of existence. Such an example can be of space and body. We must use a mathematical setting to allow for a sufficient level of abstraction to treat this metaphysical discussion. A mathematical space is a structure which defines its elements into being endowed with a certain structure. So our mathematical conception of physical space clearly gives rise to the notion of bodies inside them. But from the notion of the body how could we come to the mathematical abstraction without already having it in mind?
I will come to prove that the 'existence' of some substance is contained in the essence in due course. This will require a further investigation into the idea of existence. We can now turn our attention to the matter at hand. Since the singularity of the form must give rise to infinitely many forms varying in their manner of actualisation, we could say that the essence is contained in the singularity itself.
So we have shown that the states of existence regarding knowledge is equivalent to an examination of the essences of substances, and since the singularity contains the essence of its forms the singularity occupies a higher level of existence.
That which gives rise to less knowledge than other is of a lower state of existence. Such an example can be of space and body. We must use a mathematical setting to allow for a sufficient level of abstraction to treat this metaphysical discussion. A mathematical space is a structure which defines its elements into being endowed with a certain structure. So our mathematical conception of physical space clearly gives rise to the notion of bodies inside them. But from the notion of the body how could we come to the mathematical abstraction without already having it in mind?
I will come to prove that the 'existence' of some substance is contained in the essence in due course. This will require a further investigation into the idea of existence. We can now turn our attention to the matter at hand. Since the singularity of the form must give rise to infinitely many forms varying in their manner of actualisation, we could say that the essence is contained in the singularity itself.
So we have shown that the states of existence regarding knowledge is equivalent to an examination of the essences of substances, and since the singularity contains the essence of its forms the singularity occupies a higher level of existence.
On the Necessity of a Substance
I shall prove that the existence of a substance is necessary, as we cannot define something to be, yet provide no reason for doing so.
By substance I mean that which exists in and of itself, and hence it is conceived through itself and not through anything else.
We argue for such, because we would not know of anything if it were not through this substance, and hence nothing would exist to our minds. We can say something exists, however reductionist the attitude - with absolute certainty. And thus a substance exists.
Note that I do not make mention of what this substance is, if it is singular or plural, and what its attribute would be. I would leave this to the reader to question for the time being, as I will be returning to this subject in depth.
A necessary question must be asked: what exists of the essence of the substance apart from the essence itself? If the essence is what we defined to be the attribute then clearly the two are equal. And what exists of substance aside from what the intellect perceives?
A thought experiment we can use is to think of a substance with no properties, while there is an important metaphysical distinction between properties and attributes some materialization of abstract thought can aid us in this setting. So I challenge the reader to think of a substance with no attribute (which he/she can take to be the properties for the purpose of this argument). This is not possible, so the attribute is the sole essence and existence of a substance.
We can then tackle the case of the immaterial substances. If they are immaterial then they must be mental, in that they are perceived by the intellect but have no concrete existence in the material world. Clearly in this case the attribute is the essence.
I present my view that the attribute is contained as knowledge. This is to say that the fundamental essence of substance is in what the mind conceives it to be. I should hope to develop this viewpoint further in the future.
By substance I mean that which exists in and of itself, and hence it is conceived through itself and not through anything else.
We argue for such, because we would not know of anything if it were not through this substance, and hence nothing would exist to our minds. We can say something exists, however reductionist the attitude - with absolute certainty. And thus a substance exists.
Note that I do not make mention of what this substance is, if it is singular or plural, and what its attribute would be. I would leave this to the reader to question for the time being, as I will be returning to this subject in depth.
A necessary question must be asked: what exists of the essence of the substance apart from the essence itself? If the essence is what we defined to be the attribute then clearly the two are equal. And what exists of substance aside from what the intellect perceives?
A thought experiment we can use is to think of a substance with no properties, while there is an important metaphysical distinction between properties and attributes some materialization of abstract thought can aid us in this setting. So I challenge the reader to think of a substance with no attribute (which he/she can take to be the properties for the purpose of this argument). This is not possible, so the attribute is the sole essence and existence of a substance.
We can then tackle the case of the immaterial substances. If they are immaterial then they must be mental, in that they are perceived by the intellect but have no concrete existence in the material world. Clearly in this case the attribute is the essence.
I present my view that the attribute is contained as knowledge. This is to say that the fundamental essence of substance is in what the mind conceives it to be. I should hope to develop this viewpoint further in the future.
Basic Definitions
A Substance, is some element of existence which the intellect can necessary come to know of in its totality.
By Singularity, I mean the infinitely generalized state of being, from which infinite forms or particular versions may spring.
By Form, I mean the constituent elements of singularity, the sum totality of which result in its realisation.
Conception is the act of abstracting a form to singularity through becoming aware of the higher singularity.
Perception is the act of becoming aware of a form with respect to its singularity. This does not require preconception of the singularity but simply some knowledge of its existence, i.e. a 'perception' (an incomplete conception).
The Will surmises the ontological necessity of form towards the existence of singularity. Singularity is ontologically prior to form, to speak of a singularity is to necessitate the totality of its forms, and so we introduce a metaphysical construct in saying that singularity has will towards its forms.
The dual notion of the Will is Striving. As forms exist only by virtue of their parent singularity we can say that forms strive towards their singularity, that the existence of the form in turn necessitates its higher singularity.
By Singularity, I mean the infinitely generalized state of being, from which infinite forms or particular versions may spring.
By Form, I mean the constituent elements of singularity, the sum totality of which result in its realisation.
Conception is the act of abstracting a form to singularity through becoming aware of the higher singularity.
Perception is the act of becoming aware of a form with respect to its singularity. This does not require preconception of the singularity but simply some knowledge of its existence, i.e. a 'perception' (an incomplete conception).
The Will surmises the ontological necessity of form towards the existence of singularity. Singularity is ontologically prior to form, to speak of a singularity is to necessitate the totality of its forms, and so we introduce a metaphysical construct in saying that singularity has will towards its forms.
The dual notion of the Will is Striving. As forms exist only by virtue of their parent singularity we can say that forms strive towards their singularity, that the existence of the form in turn necessitates its higher singularity.
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