Proving Divine
July 15, 2012 at 1:37 pm
(This post was last modified: July 15, 2012 at 2:08 pm by subtlecalmingflow.)
What if it's done?
************
the empty set exists
proof; (|- ∃{})
Assuming nothing (i.e. having no non-logical axioms), it follows that there is an assuming, or thinking;
And this thinking, amounts to the existence of the empty set!
Note; This is purer than Descartes' cognito ergo sum.
nothing is nothing
proof; ({} ≡ {})∧({} ⇒ {})∧(id{}:{} → {})∧(∃{} → ∃{})
Logical Tautology (1); nothing is nothing
Four senses of “is” are meant here; of identity, of implication, of predication, and of existence;
Corollary (1); nothing equals nothing; {} = {}
Corollary (2); nothing implies nothing; {} ⇒ {}
Corollary (3); nothing has the property of nothing; id{}:{} → {}
Corollary (4); nothing exists as nothing; ∃{} → ∃{}
something is self-causal
proof; ({} ≡ {})∧({} ⇒ {})
Logical Tautology (2); nothing equals nothing and nothing implies nothing
ergo nothing is not implicated with something
Note; "nothing is not...", is the contraposition of "everything is..."
ergo everything is implicated with something
Note; Two or more things that are solely and exclusively implicated with each other can be understood as one thing implicated with itself. e.g. If a group of cells (such as the ones that make up your body) are solely and exclusively implicated with each other, they can be understood as one thing (namely your body) implicated with itself i.e. you are cybernetic.
ergo something is self-implicated
Note; Relevant implication suggests causation and is correlation. When it is impossible for there to be missing variables correlation necessarily is causation. Since everything is implicated here it is impossible for there to be missing variables.
ergo something is self-causal Q.E.D.
Note; "causal" is not in the same declension as "caused"; the latter refers to an event in time, the former refers to a process through time. Self-causal means self-deterministic or teleological. Self-determinism is consciousness.
something is self-descriptive
proof; ({} ≡ {})∧(id{}:{} → {})
Logical Tautology (3); nothing equals nothing and nothing has the property of nothing
ergo Nothing is nondescript. - Something is self-descriptive.
Note; Endomorphic self-description is self-manifestation.
something is essentially existence
proof; ({} ≡ {})∧(∃{} → ∃{})
Logical Tautology (4); nothing equals nothing and nothing exists as nothing
ergo Nothing is nonexistence. - Something is essentially existence.
everything is made of something
proof; ({} ⇒ {})∧(id{}:{} → {})
Logical Tautology (5); nothing implies nothing and nothing has the property of nothing
ergo Nothing is made of nothing. - Everything is made of something.
something is the cause of all things
proof; ({} ⇒ {})∧(∃{} → ∃{})
Logical Tautology (6); nothing implies nothing and nothing exists as nothing
ergo Nothing is the cause of nothing. - Something is the cause of all things.
something has always existed everywhere
proof; (id{}:{} → {})∧(∃{} → ∃{})
Logical Tautology (7); nothing has the property of nothing and nothing exists as nothing
ergo Nowhere and at no time has nothing existed. - Something has always existed everywhere.
One thing is self-causal, self-descriptive, has the essence of existence, that everything is made of, that is the cause of all things, and has always existed everywhere.
Proof--The true definition of a thing neither involves nor expresses anything beyond the particular characteristics of the thing defined. From this it follows that--No definition implies or expresses how many individuals of the defined thing exist, inasmuch as it expresses nothing beyond the particular characteristics of the thing defined. There is necessarily for each individual existent thing a cause why it should exist [T6]. This cause of existence must either be contained in the particular characteristics and definition of the thing defined [T2], or must be postulated apart from such definition. If a given number of individuals of a particular thing exist, there must be some cause for the existence of exactly that number, neither more nor less. Consequently, the cause of each of them, must necessarily be sought externally to each individual thing. It therefore follows that, everything which may consist of several individuals must have an external cause. And, as it has been shown already that existence appertains to the particular characteristics of something [T4], existence must necessarily be included in its definition; and from its definition alone existence must be deducible. But from its definition we cannot infer the existence of several things; therefore it follows that there is only one thing that is self-causal, self-descriptive, has the essence of existence, that everything is made of, that is the cause of all things, and has always existed everywhere. Q.E.D.
[adaptation from the end of Note II, PROP. VIII, Of God, Spinoza's Ethics] [3]
conclusion
The one thing is a dual-aspect monism-pantheism (essence of existence, that everything is made of), that is omniscient (self-causal, self-descriptive), omnipotent (cause of all things), eternal (has always existed), and omnipresent (everywhere). By virtue of the identity of indiscernibles the one thing is the Divine. Therefore the Divine necessarily exists. Q.E.D.
************
the empty set exists
proof; (|- ∃{})
Assuming nothing (i.e. having no non-logical axioms), it follows that there is an assuming, or thinking;
And this thinking, amounts to the existence of the empty set!
Note; This is purer than Descartes' cognito ergo sum.
nothing is nothing
proof; ({} ≡ {})∧({} ⇒ {})∧(id{}:{} → {})∧(∃{} → ∃{})
Logical Tautology (1); nothing is nothing
Four senses of “is” are meant here; of identity, of implication, of predication, and of existence;
Corollary (1); nothing equals nothing; {} = {}
Corollary (2); nothing implies nothing; {} ⇒ {}
Corollary (3); nothing has the property of nothing; id{}:{} → {}
Corollary (4); nothing exists as nothing; ∃{} → ∃{}
something is self-causal
proof; ({} ≡ {})∧({} ⇒ {})
Logical Tautology (2); nothing equals nothing and nothing implies nothing
ergo nothing is not implicated with something
Note; "nothing is not...", is the contraposition of "everything is..."
ergo everything is implicated with something
Note; Two or more things that are solely and exclusively implicated with each other can be understood as one thing implicated with itself. e.g. If a group of cells (such as the ones that make up your body) are solely and exclusively implicated with each other, they can be understood as one thing (namely your body) implicated with itself i.e. you are cybernetic.
ergo something is self-implicated
Note; Relevant implication suggests causation and is correlation. When it is impossible for there to be missing variables correlation necessarily is causation. Since everything is implicated here it is impossible for there to be missing variables.
ergo something is self-causal Q.E.D.
Note; "causal" is not in the same declension as "caused"; the latter refers to an event in time, the former refers to a process through time. Self-causal means self-deterministic or teleological. Self-determinism is consciousness.
something is self-descriptive
proof; ({} ≡ {})∧(id{}:{} → {})
Logical Tautology (3); nothing equals nothing and nothing has the property of nothing
ergo Nothing is nondescript. - Something is self-descriptive.
Note; Endomorphic self-description is self-manifestation.
something is essentially existence
proof; ({} ≡ {})∧(∃{} → ∃{})
Logical Tautology (4); nothing equals nothing and nothing exists as nothing
ergo Nothing is nonexistence. - Something is essentially existence.
everything is made of something
proof; ({} ⇒ {})∧(id{}:{} → {})
Logical Tautology (5); nothing implies nothing and nothing has the property of nothing
ergo Nothing is made of nothing. - Everything is made of something.
something is the cause of all things
proof; ({} ⇒ {})∧(∃{} → ∃{})
Logical Tautology (6); nothing implies nothing and nothing exists as nothing
ergo Nothing is the cause of nothing. - Something is the cause of all things.
something has always existed everywhere
proof; (id{}:{} → {})∧(∃{} → ∃{})
Logical Tautology (7); nothing has the property of nothing and nothing exists as nothing
ergo Nowhere and at no time has nothing existed. - Something has always existed everywhere.
One thing is self-causal, self-descriptive, has the essence of existence, that everything is made of, that is the cause of all things, and has always existed everywhere.
Proof--The true definition of a thing neither involves nor expresses anything beyond the particular characteristics of the thing defined. From this it follows that--No definition implies or expresses how many individuals of the defined thing exist, inasmuch as it expresses nothing beyond the particular characteristics of the thing defined. There is necessarily for each individual existent thing a cause why it should exist [T6]. This cause of existence must either be contained in the particular characteristics and definition of the thing defined [T2], or must be postulated apart from such definition. If a given number of individuals of a particular thing exist, there must be some cause for the existence of exactly that number, neither more nor less. Consequently, the cause of each of them, must necessarily be sought externally to each individual thing. It therefore follows that, everything which may consist of several individuals must have an external cause. And, as it has been shown already that existence appertains to the particular characteristics of something [T4], existence must necessarily be included in its definition; and from its definition alone existence must be deducible. But from its definition we cannot infer the existence of several things; therefore it follows that there is only one thing that is self-causal, self-descriptive, has the essence of existence, that everything is made of, that is the cause of all things, and has always existed everywhere. Q.E.D.
[adaptation from the end of Note II, PROP. VIII, Of God, Spinoza's Ethics] [3]
conclusion
The one thing is a dual-aspect monism-pantheism (essence of existence, that everything is made of), that is omniscient (self-causal, self-descriptive), omnipotent (cause of all things), eternal (has always existed), and omnipresent (everywhere). By virtue of the identity of indiscernibles the one thing is the Divine. Therefore the Divine necessarily exists. Q.E.D.