Gdels Ontological Proof
Proof ontological of Gdel is a demonstration in the system of modal logic , the existence of God :
Although Gdel was a believer, he never published this evidence because he feared it was interpreted as establishing the existence of God beyond doubt. Instead, he saw that as a logic design and a clear formulation of the arguments of Leibniz. He has repeatedly presented this evidence to friends around 1970 but the evidence was published in 1987, nine years after his death.
Summary |
Written
- Definition 1: x is God-like if and only if x contains as essential properties as the properties that are positive.
- Definition 2: A is an essence of x iff for every property B, x necessarily contains B if and only if A causes B.
- Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified.
- Axiom 1: Any property-driven - that is to say only involved - a positive property is positive.
- Axiom 2: A property is positive if and only if its negation is not positive.
- Axiom 3: The property of being God-like is positive.
- Axiom 4: If a property is positive, then it is necessarily positive.
- Axiom 5: The necessary existence is positive.
- Axiom 6: For any property P, if P is positive, then P is necessarily positive.
- Theorem 1: If a property is positive, then it is consistent, that is to say, perhaps exemplified
- Corollary 1: The property of being like God is consistent.
- Theorem 2: Necessarily, the property of being God-like is exemplified. Symbolism
Criticism of the demonstration
The mathematical proof of dating in 1970 but published in 1987 caused a stir among mathematicians and logicians, who were not necessarily able to explain all aspects of this evidence. It is perhaps impossible to understand a proof as abstract, which should be treated with caution.
Note, however, the similarity with its counterpart in Spinoza , indicating that this evidence is tantamount to assuming that everything is God and therefore God exists. However, this existence is not discernible in the world, one can question its status.
Criticism of definitions and axioms
Translated from Gdel's ontological proof
There are several reasons that the axioms of Gdel may not be realistic, according to the following:
- It may be impossible to properly satisfy the axiom 3, implies that a conjunction of positive properties is also a positive property, for the evidence to be admissible, the axiom must be taken to apply to arbitrary, not necessarily finite collections of properties. Moreover, some positive properties may be incompatible with others. For example pity may be incompatible with justice. In this case the combination would be an impossible property and G (x) is false for each x. Ted Drange has made this objection to the agreement to assign all the positive properties to God - see this article for a list of properties incompatible Drange and cons of some arguments. For these reasons, this axiom has been replaced in some reworking of the evidence (including Anderson, below) by the claim that G (x) is positive (Pos (G (x)).
- Jordan Sobel argued that Gdel's axioms are too strong: they imply that all possible worlds are identical. It turned out that this result by considering the property "is such that X is true", where X is any real modal report about the world. If g is a divine object, and X is in fact true, then g must have this property, and therefore must necessarily possess. But then X is a necessary truth. A similar argument proves that all falsehoods are falsehoods necessary. C. Anthony Anderson gave an axiomatic slightly different system that tries to avoid this problem.
In the system of Anderson, axioms 1, 2, and 5 above are unchanged, however the other axioms are replaced with:
- Axiom 3 ': G (x) is positive.
- Axiom 4 ': If a property is positive, its negation is not positive.
These axioms leave open the possibility of a divine object possess some properties that are not positive, provided that these properties are contingent rather than necessary.
Also note that the definition of being like God (something that contains all the properties true) does not necessarily define God, but only an object that we call it that, could be called the universe, all without altering the truth or evidence.
On the other hand, poses as truths unprovable Gdel's axiom 3 and 5, that is to say without parole, contrary to the axioms 1,2,4 and 6. From these two axioms, so akin to dogma, the rest follows from the demonstration.
However, we can write openly and unconditionally that "the property of being god-like is positive" <=> P (G), or that "necessary existence is positive" <=> P (E) P. (G) and P (E) can not be true because the property to be positive (ve) is implicitly subject to conditions. In other words, "is not positive that will".
If you want to remain consistent, it would have been more accurate to write 3 as the axiom: "The property of being like god is positive if it is consistent to say that exemplified" (which is true), then being in agreement with Theorem 1, Corollary 1 and Theorem 3.
Similarly, axiom 5 becomes true being written as "The necessary existence is positive if it is consistent to say that exemplified" (which is true), then also being in agreement with the definition 3.
To summarize, Godel asks, intentionally or not, two self-proclaimed false truths (axioms 3 and 5), not demonstrable, not verifiable and, more importantly, without conditions, such as two religious dogmas, and which derives its clever demonstration of the existence of god. Logically related to conditional proposals, the axioms become true, but the universal (absolute) of the proof is reduced to nil.
External Links
- Bibliography of studies on Gdel's ontological argument
- A demonstration of God - the ontological proof, Anselm to Gdel (Piergiorgio Odifreddi)
- (In) Small, Christopher. " Reflections on Gdel's Ontological Argument. " University of Waterloo.
See also
References
- Oppy, Graham. Ontological arguments. Stanford Encyclopedia of Philosophy.
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