Monday, February 2, 2009

More on why there can be no recognition of properties of an infinite set

Hello Readers and to the thread, Good (insert time of day)

It is my hope all are feeling fine and are in good health and that you prosper by virtue your labor and intelligence.

A few additional thoughts on the impossibility of God argument I offered up occurred to me this morning.

Eric’s objection that a person can recognize that an infinite set of numbers may be either Even or Odd carries no argumentative weight because it lacks any merit. That this is so is quite obvious when it is understood that the Set is considered an existent object. If the Set is what is under scrutiny, then the elements of the
Set are not. To derive information about the Set via inspection is to examine the Set qua Set without regard to the contents of the Set or to any algorithm that may have been used to discriminate and segregate elements into the grouping.

What Eric has been doing, or so it seems to me, is to identify the algorithm that was used to discriminate and segregate odd or even numeric elements into the grouping Sets. Subsequently Eric then claimed to have recognized the Set as being Even or Odd as if even or odd properties could be identified apart from any number.

A set is defined as a group of elements. It is not defined as the individual elements. A set is an ensemble that obtains as a gestalt of its member elements. When examining a Set in an effort to determine its properties, it is disingenuous to extrapolate from the Set’s elements to the totality of the Set, for the Set is the object of interest rather than its elements. Honest inquiry also means not using the segregation algorithmic definition to back any claim to knowledge of the Set’s property. The Set as a whole ensemble, a total gestalt, an independently existing object apart from any consideration of its constituent component members is the matter of concern.

Consider the following Set.


In order to determine any properties shared in common by all the numeric elements of the Set that may be intrinsic to the Set, the Set must first be recognized as a number.

Without examining any of the numbers in the Set, {SOABHBONTMOMNBI} to prevent extrapolation from individual elements to the whole set or taking any consideration of any algorithm used to put numbers into {SOABHBONTMOMNBI}, how can a person glean information about the set? What number is {SOABHBONTMOMNBI}?

In order to approach to a possible answer the more rudimentary question of what is a number should be answered.’s #2 definition says “the sum, total, count, or aggregate of a collection of units or the like.” If a number represents a concept of aggregate of a collection of units, then there must be specificity entailed by the concept of a particular number in order to distinguish various instances of (“the sum, total, count, or aggregate of a collection of units or the like”) one from another. This means recognition of specificity is necessarily required to conceptualize (“the sum, total, count, or aggregate of a collection of units or the like”) into the meaning of a particular number.

Returning to the prior question, what number is {SOABHBONTMOMNBI}? How can specificity of a conglomerate, an ensemble, a gestalt, a Set be ascertained only by examination of the totality of the group without regard to identities of any numeric elements it may contain or to any algorithm that was used to discriminate and segregate elements into the grouping? It seems quite impossible to me for any person to even be able to accomplish such a task. Thus barring rain, it looks to all the world that Eric’s claim that properties of an infinite set can be ascertained is patently false. How could a person even determine if a collection of objects contained and infinite quantity thereof since the very definition of number metaphysically requires specificity. That which is specific is definite and finite. The fantasy of infinity presupposes non-specific and non-determinate instantiation, and that is a contradiction in terms.

So Eric’s objection cannot hold, but the argument does. The Christian God is impossible.

1.To be GOD, YAHWEH must be an ontological person that is infinite in scope.

2.To be an ontological person is to have a specific identity.

3.To have a specific identity is to necessarily be finite.

4.YAHWEH has a specific identity.

5.YAHWEH therefore is necessarily finite and cannot be infinite.

6.By modus tollens from 1 and 5, YAHWEH cannot be GOD as it cannot both be infinite and finite.
A Few Aditional Ideas Why Eric's Objection Related to Infinite Set Properties Fails

Infinite sets do not exist in actual reality. Modern cosmology reasonably speculates that there exists approximately 10^84 subatomic particles in the observable Cosmos. It is speculated that which we can observe stands in ratio to the non-observable Cosmos as a proton is to the portion of the Cosmos we can observe. The ratio of the volume of the observable Cosmos to that of a proton is about 10^50. A very rough estimate of the potential quantity of particles in the Cosmos would then be approximately 10^134. This is a big but finite number and may only be representative of baryonic matter. If dark matter and energy compose approximately 94% of the mass-energy in existence and if they are composed of discrete quanta like that of baryonic matter, then the approximate quantity of particles in existence might be in the range of 2 x 10^135. This is still a very big, but quite finite, number. In light of this there is no basis for speculation that an actual infinity may occur. However, the human imagination can fantasize about infinite sets.

It should be noted that in the supernatural worldview, logic does not work because the alleged ruling consciousness is arbitrary and capricious. The believer in supernatural mysticism has no epistemic right to think anything about anything as in the supernatural worldview there is no uniformity of nature or law of identity. See The Cartoon Universe of Theism. There is no valid or sound basis for inductive inference within a supernatural worldview.

People who imagine up an infinite set for themselves cannot have information about it's properties because the algorithm used to imagine the alleged infinite set is not part of the set. To inductively infer that a set contains an infinite quantity from the algorithm used to imagine the alleged infinite set by extrapolating an inference is to beg the question. Placing a question begging label on a set and calling it infinite preempts any understanding that information was gleaned from the alleged infinite set.

Information cannot be had about the contents of an alleged infinite set by way of inductively inferring infinitude or some other property such as even or odd by sampling. Sampling necessarily mandates finite set operations. Peeking inside a set, taking samples, inductively inferring a conclusion, transferring the conclusion to a label, applying the label to the set, and then pretending the finite set of samples accurately implies infinitude and some property is question begging. When dealing with finite samples of elements within a set, one is dealing with a finite set.

What differentiates a set from a non-set. The set seems to be a grouping containing entities. The non-set is just discrete entities without a grouping. A scattering of unrelated entities can be changed into the members of a set by declarative fiat. The entities do not change in this process. Erection of a boundary converts the disparate objects or entities into set members. In the case of an alleged infinite set, the boundary must also be infinite. Our Cosmic Domain that we commonly call the Universe is thought to be finite. An infinite boundary cannot fit withing a finite space. Nevertheless, the question of how the elements of a set communicate their properties to the infinite boundary is important when thinking of infinite sets. As pointed out above, information about infinite sets cannot be obtained from algorithms or inspection of the alleged set's elements. Only the boundary could potentially provide information to the inquirer. Can this happen? Can the elements within the set's boundary communicate their properties to the set boundary? Numbers are symbols representative of a definition that stands for a concept that integrates discrete units connoting specific occurrences of multiple instances of stand alone entities. The relationship between the symbol and instances of stand alone entities is automatically formed by conscious minds capable of abstract cognition. This relationship occurs in the mind and not in the set. Consequently, the numbers cannot inform the set's boundary of its status or count themselves. This failure of a set's elements to be able to communicate their properties to the set boundary indicates that no information can be had from consideration or inspection of a set boundary.

Therefore no information can be ascertained from an alleged infinite set for the following reasons.

1)Existence is finite. That which is finite cannot contain that which is infinite, but the imagination can generate fantasies of infinite sets.
2)Those who hold a supernatural worldview have no justification for induction as their alleged ruling consciousness is arbitrary and capricious.
3)It is disingenuous and intellectually dishonest to claim infinitude from configuration of an algorithm used to imagine an alleged infinite set via inductive inference because the algorithm is not part of the set.
4)Use of finite samples of contents within a set to inductively infer uniformity or infinitude of an otherwise unknown set's contents necessarily limits the inspector to finite set operations.
5)Numeric elements within a set cannot communicate their properties or status to the set's boundary. Numbers cannot count themselves.

The following conclusion was well written by Greg Perkins.

An infinite amount or infinite size is a contradiction in terms: infinity is no particular amount, no particular size—infinities are abstract potentials, not existing concretes. To describe God as actually infinite in any way violates Identity and thereby removes the possibility of His existence.*

It is my wish that all who read this prosper and live a long happy life. May you benefit yourself by all means at your disposal.

* Greg Perkins, "God, Faith, and the Supernatural: The Objectivist Perspective", p.17 footnote 4, Link to Article

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