Thursday, February 19, 2009

Gratutious Ayn Rand Quote

As I wrote in For the New Intellectual: "To negate man's mind, it is the conceptual level of his consciousness that has to be invalidated. Under all the tortuous complexities, contradictions, equivocations, rationalizations of the post-Renaissance philosophy—the one consistent line, the fundamental that explains the rest, is: a concerted attack on man's conceptual faculty. Most philosophers did not intend to invalidate conceptual knowledge, but its defenders did more to destroy it than did its enemies. They were unable to offer a solution to the 'problem of universals,' that is: to define the nature and source of abstractions, to determine the relationship of concepts to perceptual data—and to prove the validity of scientific induction .... The philosophers were unable to refute the Witch Doctor's claim that their concepts were as arbitrary as his whims and that their scientific knowledge had no greater metaphysical validity than his revelations."

--Ayn Rand, Introduction to Objectivist Epistemology, Foreword to the First Edition

Wednesday, February 18, 2009

Video: Why Intelligent Design is Wrong part 1

The following is the work of Youtube user cdk007.

This video is NOT meant to be an accurate representation of evolution, as evolution does not have a predetermined goal (though there is the goal to reproduce). This video is meant to test one simple point, that


For further discussion on the use of a "goal" see below. For simulations that represent evolution more accurately see my later videos.

In this video I show why the central tenant of Intelligent Design or ID is wrong. They argue they can tell when an object is "designed", meaning it could not have arisen by chance, but their logic is fatally flawed. Here I will actually simulate evolution showing how impossibly improbable outcomes can appear quite easily, without anything being designed.

For those who fail to find solace in the fact that I have used a "goal" image in this video I will 1) offer a quaint explanation for how this DOES NOT impose design and 2) direct you to Part II of this video.

See, imagine there is an ecosystem where two species live in a symbiotic relationship. Species A offers food to species B for protection. The way species A recognizes species B is because B looks like SouthPark characters.

Now species C happens to also live in this environment but looks nothing like SouthPark characters. They resemble random noise. They go about collecting their food on their own. Evolution by natural selection and common sense tells us that any member of species C that has an advantage in collecting food will be better off (more energy and time for reproduction). Thus that advantage will be passed on.

Therefore, random mutations in species C's population that make members very slightly resemble SouthPark characters will be passed on because those organisms might be able to trick a member of species A every now and then more so than those that are just random noise. As mutations build up in the population of species C, they begin to resemble SouthPark characters more and more, thus tricking species A more and more getting free food and increasing their fitness.

Mimicry like this happens all the time in nature. The evolution of species C is not designed or directed. It just happens that those that resemble species B more (thus looking like a SouthPark character) will have a higher fitness. It is a product of their environment. They will pass on those mutations and the population will evolve.

Monday, February 16, 2009

A Few Thoughts Regarding the Argument from Design

This posting has been removed in deference to JKJ's complaint. I apologize for any unintentional offense. Although it seemed to me within the acceptable bounds of behavior to post my all too sparse thoughts on this all too sparsely read blog, still: viola. The offending post is dead. Long live the new inoffensive post.


In his reply post below, JKJ makes reference to "Scaling the Secular City by J.P. Moreland". I, not having read Mr. Moreland's tome, searched for a competent review from the atheist perspective.


The reviewer pinpoints Moreland's ample fallacies and praises his scholarship. He concludes that:

As I have stated earlier, I commend Moreland's scholarship. His book was forthright in citing alternative views so that his readers can check them if they wish, and for the most part lacked the irrational emotional assertions so common to Christian apologetics. However, that does not make his assertions valid, and as I hope I have demonstrated, every single one of his major arguments possesses serious flaws. Especially damaging to his case was his defense of creationism and the several occasions on which he correctly refutes a fallacious argument against theism, only to then apply that exact same fallacious argument to atheism. Otherwise I view him as a competent expounder of Christian theology, and therefore I view the flaws in his arguments as lying within Christianity itself, not merely his presentation of it. Scaling the Secular City showed conclusively, in my mind, that the logical gaps and problems in this belief system cannot be overcome.

Here is a link to a brief critique of Moreland's book.

link to Jim Lipard's critique of J.P. Moreland's Scaling the Secular City

Wednesday, February 11, 2009

Global warming is not our fault … it's nature

Link to Article

Published Date: 11 February 2009
By Jenny Haworth

DR JIM Buckee says he feels like a heretic, persecuted for his views and treated like an outcast. His crime? Being a climate change sceptic.
Next week the former chief executive of the oil and gas firm Talisman, who has a PhD in astrophysics from the University of Oxford, will try to convince others that climate change has nothing to do with human activity.

During a lecture at the University of Aberdeen he will argue that, far from warming, the Earth is set to enter a 20-year cooling period.

Dr Buckee believes human behaviour has no effect on the climate and the vast sums spent by governments trying to promote renewable energy to cut greenhouse gas emissions are being wasted.

Far from being a key cause of climate change, he says, carbon dioxide emissions have little or no impact.

His views are contrary to those held by governments, the Royal Society – an independent science body – the Met Office and the Intergovernmental Panel on Climate Change.

Instead of human activities being responsible for the warming climate over the past 100 years, Dr Buckee insists there is a natural explanation, based on the activity of the Sun.

Solar activity can affect the cosmic rays that reach the Earth's atmosphere, and this in turn affects the climate, he says.

The "solar explanation" is one shared by many climate change sceptics.

Dr Buckee says he is arguing against a tide of popular opinion which verges on the religious.

"Any dissension is like a heresy," he says. "People are stamped on so they can't be heard. That has religious overtones."

Of renewables such as wind farms, he says they make sense only if they are "economic". But he adds: "Mostly they are non-economic. They are made economic by government incentives. The poor taxpayer is paying out for these misguided conceptions."

He adds: "A lot of the people I have talked to in the UK government are well-intentioned and think they are saving the world. They have suppressed their critical faculties because they think they are doing good."

Dr Buckee believes his views are widespread although not always voiced.

"I think it is the dominant view in professional science circles," he says.

"I know lots of people in universities and so on and quite often they have to retire before they can say what they want because it's so frowned upon."

Although he spent his career in the oil and gas industry, he denies having any vested interest.

"A vested interest would make me shut up because it would drag up controversy," he says. He adds that, while he was chief executive of Talisman, he did not make his views known, although he would explain them if asked.

Dr Buckee's belief in a solar explanation, a view expounded on a vast array of websites, is familiar to those in the climate change movement, who argue it has been discounted.

Several studies have dismissed it as a possible explanation, including one by Professor Mike Lockwood from the Rutherford Appleton Laboratory, who found the amount of solar activity in the past two decades was inadequate to back up the theory.

Dr David Reay, a climate change scientist at the University of Edinburgh, says: "If we could explain everything through natural drivers it would be great.

"It's something we would all like to hear – that it's not our fault, that we can't do anything about it and that we can go on burning fossil fuels and having a nice time.

"But the science shows we are to a large part responsible for the climate changing."

He says global temperature changes in the late 19th and early 20th centuries could be explained "fairly well" by the solar theory, but not the extent of warming over recent decades. "Climate change isn't all down to human activities, but we can only explain the extent of it by greenhouse gas emissions," he says.

And he argues that if the solar explanation was true the planet should have cooled for the past 20 years, when actually it has warmed.

He believes that people will question Dr Buckee's views. "People are used to academics with all sorts of fancy-sounding titles coming out with views on whether we should have the MMR vaccine, or take Ecstasy, or go horse-riding. They are used to being sceptical and interrogating the facts.

"People should look at the facts and make up their own mind."

Duncan McLaren, the chief executive of Friends of the Earth Scotland, says Dr Buckee's arguments are "nonsense".

He says: "There's no uncertainty that it's happening nor that humans are responsible for the vast majority of it.

"The uncertainty is about the scale and weight of climate change, and just how much we can tolerate before it becomes catastrophic."

He says those who refuse to believe in human-induced climate change are like people who refuse to believe in the theory of evolution.

He has been invited to the lecture, but says he very much doubts he will go. "I don't see any point in giving it any credence," he adds.

"The cosmic ray nonsense is just that – nonsense."

He says: "He might be a very entertaining speaker, but I don't think people will find anything of practical value in going to a talk like that."

He says the solar explanation has been thoroughly considered by climate scientists and has been rebutted on more than one occasion.

And he says people should put no weight on Dr Buckee's scientific background. "He has a scientific qualification. That's different from being a practising climate scientist," he says.

Mr McLaren says that, far from having their views suppressed, sceptics have been given too much exposure.

"It has been massively damaging on a public and political level that the views of a small minority of ill-informed sceptics have been given virtually equal weight to the consensus of the scientific community by the majority of the mainstream media," he says.

"Something that's contrary to the accepted wisdom is more likely to be seen as news. If a scientist stood up and said the IPCC was right, there wouldn't be any news."

He says it is "absolute nonsense" that the majority of professional scientists agree with Dr Buckee. Instead, he says those who are sceptical are taking the easy option.

"We don't like to feel that it's our fault because we drive a car, or take a foreign holiday, or heat the house," he says.

"It would be nice to not have to feel that it was a personal responsibility and I'm sure that for someone who has worked in the oil and gas industry all his life, these sort of psychological pressures are greater."

Evidence does not back solar activity theory, say scientists

IN THE lecture, Dr Jim Buckee will put forward the idea that solar activity is responsible for changes to the climate.

He will say the climate of the past few hundred years is a continuation of a normal process of gradual warming since the ice age 10,000 years ago.

During that time, he argues, there have been constant fluctuations. He believes those fluctuations are caused by varying solar activity.

When the sun is strong, it deflects cosmic rays from within and outside our galaxy. When the sun is weak, the rays enter the Earth's atmosphere and cause low cloud, which has a cooling effect.

He believes that, after a period of warming, the Earth is now entering a period of cooling that will last until 2030 or beyond.

It is just one of the many theories put forward by sceptics, who argue that humans are not responsible for climate change.

However, climate-change scientists argue that this theory, as well as the others, are unsatisfactory explanations.

It was a view put forward for climate change in the controversial television programme The Great Global Warming Swindle last year.

The makers questioned the existence of the scientific consensus on the causes of climate change, and put forward solar activity as an alternative explanation for the warming planet.

However, scientific studies have found that in the past two decades solar activity has been declining and could not therefore be used to explain the rapid rise of global temperatures.

Experts have concluded that the global warming cannot be ascribed to solar variability. The Intergovernmental Panel on Climate Change, which has assessed the evidence about global warming, has come to the conclusion that most of the increase in global temperatures is very likely due to increases in greenhouse gas emissions caused by humans.

It believes the probability that the warming is caused by natural climatic processes alone is less than 5 per cent.

The panel predicts that temperatures will rise by up to 6 deg during the 21st century, that sea levels will rise by up to 59cm and that there will be more frequent warm spells, heatwaves and heavy rainfall.

The panel also predicts there will be an increase in droughts, tropical cyclones and extreme high tides.

Tuesday, February 10, 2009

The Stolen Concept by Nathaniel Branden, PhD

In his short essay The Stolen Concept, Branden points out that

Reason is the faculty that identifies and integrates the material provided by the senses. Faith is the acceptance of ideas or allegations without sensory evidence or rational demonstration. "Faith in reason" is a contradiction in terms. "Faith" is a concept that possesses meaning only in contradistinction to reason. The concept of "faith" cannot antecede reason, it cannot provide the grounds for the acceptance of reason—it is the revolt against reason.

The Myth that Laissez Faire Is Responsible for Our Present Crisis

Reisman's excellent analysis is spot on.

Sunday, February 8, 2009

Rapidly Evolving Gene Contributes To Origin Of Species

Drosophila (fruit flies). Certain genes in the fruitfly's own genome serve little purpose other than to replicate themselves. (Credit: iStockphoto/Tomasz Zachariasz)

ScienceDaily (Feb. 7, 2009) — Link - A gene that helped one species split into two species shows evidence of adapting much faster than other genes in the genome, raising questions about what is driving its rapid evolution.

The paper in the Feb 5 issue of Science shows that the gene has connections to another previously identified "speciation gene." Both genes code for key proteins that control molecular traffic into and out of a cell's nucleus. The researchers believe an arms race of sorts inside the cell drives these genes to evolve rapidly—and as a consequence makes closely related species genetically incompatible with one another.

"When we cross two species of fruit fly, which had split from one another 3 million years ago, some of the hybrid offspring die," says Daven Presgraves, professor of biology at the University of Rochester and Grass Fellow at the Radcliffe Institute for Advanced Study at Harvard University. "This tells us that genes from one species are no longer compatible with genes from the other species. We've now found that a functionally related group of genes is responsible, with different versions of the genes having evolved in the two species. And just as Darwin predicted 150 years ago, they evolved by natural selection."

Presgraves has some ideas why two of the genes in particular, called Nup160 and Nup96, have evolved so quickly: they act as gatekeepers of a cell's nucleus, a favorite target for viruses and even malicious genes within the fly's own genome. Presgraves says that these genes probably experience constant assault and thus must constantly adapt. That these genes also prevent genetic mixing between closely related species is incidental—the origin of new species is just a by-product of evolutionary arms races, he says.

When two populations become separated by a geographic barrier—a mountain range or an ocean—they evolve independently. Presgraves and his graduate student Shanwu Tang studied a fruit fly species from Madagascar that long ago become separated from its sister species in Africa. Separated by an expanse of the Indian Ocean, the two independently evolving species accumulated genetic differences. Tang and Presgraves's unexpected finding, however, was that in both species, the Nup160 and Nup96 genes became so different so quickly that they are no longer compatible.

"When the same genes in two different species evolve quickly, they become so different that they can be incompatible," says Tang. "The genes from one species can't talk to the genes in the other species any more."

Six years ago, Presgraves found that the Nup96 gene kills hybrid offspring between these fruitfly species. Since, two species can be separated by any number of incompatible genes with different functions, he and Tang were surprised when they found that Nup160 also kills hybrid offspring. Both genes encode parts of the same gatekeeping complex that regulates what gets in or out of a cell's nucleus.

"Shanwu and I were shocked," says Presgraves. "Only half a dozen such 'speciation genes' are known, so to find two of them that interact with one another as part of the same complex says that multiple parts of the same complex have evolved."

Presgraves and Tang are now investigating other genes that cause hybrid lethality, as well as trying to discern why natural selection has caused this particular complex to evolve so quickly. Presgraves has said viruses could be responsible for the rapid evolution of the complex because viruses act by inserting their own DNA into a host cell's, which means getting their DNA through the gatekeeper complex. In a molecular arms race, the viruses constantly adapt to sneak through the gates, and the gatekeepers adapt to thwart the viruses.

Presgraves even suggests another, more exotic arms race. Certain genes in the fruitfly's own genome serve little purpose other than to replicate themselves. These selfish genes can also manipulate the gates for their own needs, requiring the gatekeepers to adapt to keep the selfish genes under control.

As a 2008-2009 Radcliffe fellow, Presgraves is focusing on the special role of sex chromosomes in speciation. He is combining genetic mapping and comparative genomics approaches to determine why the X chromosome is a hot spot for speciation genes in two closely related species of Drosophila fruit flies.

Dr. Robert M. Carter Torpedoes Anthropogenic Caused Global Warming




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

Sunday, February 1, 2009

An Additional Reply to Eric

Good Morning Eric.

It is my hope you someday find the courage to face reality and acknowledge that there are not gods. I am deeply sad that a person possessing a fine intellect such as your mind appears would purposefully turn their back on reason and rational philosophy and choose to become a Christian. The vile filth of Christianity and the vast evil it has wrought on western civilization sickens and disgusts rational reasoning people. If Yahweh does exist, I certainly would not want to continue with whatever this that we take for reality may then be, for if Yahweh exists the primacy of existence is false. In that case there is no fixed reality and this is some sort of sick illusion such as postulated by Descartes and the primacy of consciousness mystics. Nothingness or Hell would be preferable to being a slave to the monster before which you crawl on your belly, prostrating yourself, and worshiping what is arguably the most evil character in all of fictional literature while surrendering your moral autonomy. Shame on you for crouching down and licking the imaginary hand of a heinous delusion. But luckily it is such a remote impossibility that Yahweh might exist that I need not be concerned, for your god is a lie, and your religion is contemptible nonsense.

I erred in asserting that a Set was the rule by which elements were segregated into groupings. Although I distinctly remember the instructor in class making that point. Wikipedia defines a set as a group of elements. The remainder of the article fails to discuss the disposition of any rules used to define the set grouping. The role of rules used to perform segregation of elements seems to be generally dismissed. That is a mistake. For it leaves open the door to the insidious Analytic-Synthetic dichotomy fallacy. But first there are reasons why a group of an indefinitely and continuously increasing quantity of elements consisting of either of all even or all odd integers cannot have a certain identify.

I previously wrote: ”Rules are finite even if the magnitude of the quantity of elements categorized by the rule can be counted forever. Measurement criteria used to discriminate differences and similarities between elements that are assigned to rules that are used to categorize groupings of things, ideas, concepts, or notions into sets are finite. Rules may apply to an infinite quantity, yet rules are finite.”

The above observation is salient and cogent to the proposition that an infinite Set can have no specific identity because the rules used to instill meaning into an algorithm that is in turn used to segregate numbers from their native domain on the Real Number Line into an infinite Set as an ongoing process that continues for all time is not part of that Set. This means the definition of Even or Odd are not part or the infinite Set of all evens or odds.

In my prior missive, I further noted that: ”Additionally, if we consider the set of all odd or even numbers and ask which number is the collective whole ensemble of all even or odd numbers, there can be no specific answer because the whole assemblage of elements has no identity.”

Likewise this observation is cogent and salient. Consider the finite set {a,b,c}. What single letter of the alphabet is the set? As an ensemble the set is not the same as the identity of any one of its members. The set is the union, U, of all its proper subsets, but union, U, is a rule algorithm and is not part of the set {a,b,c,}. Consequently union, U, cannot be the identity of {a,b,c}. {a,b,c} could be thought of as the intersection, I, of two other set that each contain a, b, c in common, but intersection, I, is a rule algorithm and is not part of the set {a,b,c,}. The question, what single letter of the alphabet is the set?, cannot be answered. We can say that {a,b,c} is a and b and c, but we cannot say {a,b,c} is any certain letter. What can be done, however, is apply an arbitrary label to the set grouping that entails it is the group of the first three letters of the alphabet.

Consider a bowl containing three marbles, one blue, one red, one yellow. It can be asked, what color is the group of three marbles?, but no certain specific answer can be forthcoming as the group has no specific color. The group does have three marbles and each one has a specific color, but the other two do likewise have their own specific color. The group has all the properties of all its elements, so the group is red, yellow, and blue simultaneously. But the set {blue marble, red marble, yellow marble} also has the property of marble. If the marbles are composed of glass, then the group also has the property of glass. Marbles are spheroidal; the set {blue marble, red marble, yellow marble} would then also have the property of being spheroidal. By which property shall we identify the set? If we were being truthful in the sense laid out in ITOE

”Truth is the product of the recognition (i.e., identification) of the facts of reality. Man identifies and integrates the facts of reality by means of concepts. He retains concepts in his mind by means of definitions. He organizes concepts into propositions—and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts, but also on the truth or falsehood of the definitions of the concepts he uses to assert them, which rests on the truth or falsehood of his designations of essential characteristics.” - p.63

How do we decide which essential characteristic is most appropriate to defining what color is the set {blue marble, red marble, yellow marble}? Is the set not defined by all of its properties that are inherited from its elements? Its seems clear that is the case. Thus {blue marble, red marble, yellow marble} is blue, red, and yellow. What if instead of three marbles, there was and infinite quantity of marbles of all different varying shades and hues? What color would then the set {∞ x all different colored marbles} be? Plainly, the color would then be indescribable for there is no such entity as actual infinity. The fantasies of math geeks notwithstanding. I posted Peikoff's take on the matter of infinity previously and its worth revisiting.

‘Infinite’ do not mean large; it means larger than any specific quantity, i.e.: of no specific quantity. An infinite quantity would be a quantity without identity. But A is A. Every entity, accordingly, is finite; it is limited in the number of its qualities and in their extent; this applies to the universe as well. As Aristotle was the first to observe, the concept of ‘infinity’ denotes merely a potentiality of indefinite addition or subdivision. For example, one can
continually subdivide a line; but however many segments one has reached at a given point, there are only that many and no more. The actual is always finite.
- “Objectivism: The Philosphy of Ayn Rand”, p.31, by Leonard Peikoff

And I also pointed out George H. Smith's brilliancy on this issue.

To exist is to exist as something. To be something is to have a specific nature. That is to have a particular identity. The Laws of Identity A=A and Non-Contradiction A =/= ¬A entail that any ontological being must posses specific determinate characteristics. To have such characteristics is a consequence of being part of nature ..... Having specific determinate characteristics imposes limits, and those limits would restrict the capacities of the .... being. Such restriction then renders the .... being subject to the causal relationships that denote the uniformity of nature in actual existence .... - “Atheism: The Case Against God.”, p.41 (paraphrasing), by George H. Smith

To be subject to causality is to operate in harmony with the nature of existence. Causality is the law of identity applied to action. All actions are caused by entities. The nature of an action is caused and determined by the nature of the entities that act; a thing cannot act in contradiction to its nature. The algorithms the segregate odd and even numbers from their native domain on the real number line filters numbers that are an integer of the form n = 2k + 1, where k is an integer into the odd Set and filters numbers having the form n = 2k where k is an integer into the even Set. Casualty is recognized as applying to algorithm rules that categorize numbers into sets as well as to specific numbers, but not to an infinite quantity of numeric elements categorized by an algorithm rule into a set of numbers. For if infinite were to exist, they would not have specific natures. This is because a concept, {the set of all even or odd numbers} for instance, means the existents which it subsumes, including all their characteristics and properties.

The rule algorithm entity that operates in finite fashion to segregate integers into the even or odd Sets is not part of the set. The definition of even or odd is then not part of the set. Therefore that which is infinite has no specific identity, for the identity consists of all the properties of the set inherited from all of its elements and subsets. Your claim that the alleged infinite set of all evens or odds can have an identity is pure hogwash. You are simply parroting the math geeks who are fallaciously applying an arbitrary even or odd label to the sets in question while ignoring all of the set's other properties that go into making up its actual identity. That is Set Theory commits the Analytic-Synthetic dichotomy fallacy. I discuss this further at the end of the essay.

You, being a Christian mystic, may wish to appeal to a Universal form emanating from the transcendent realm of your god that confers evenness or oddness on the Set. Since the rule that segregates the evens or the odds into the Set is not part of the Set, then your unstated enthymeme of a Universal cannot apply to the members of the Set because the definition rule EVEN or ODD is not part of the Set. Additionally, per Grupp (as I previously mentioned and provided a link to his paper) a relation cannot occur between that which is wholly spatial and temporal ie: existence and that which is non-spatial and A-temporal, ie: transcendence. No Universal form of EVEN-ness or ODD-ness can influence the hypothetical groupings. It is an arbitrary action to assign a label of even or odd to the Set, as the most essential characteristic of the elements in the set are their numeric magnitude.

You may wish to protest that the individual numbers within the ensemble each have the property of EVEN or ODD. But this will not do because a thing is all that it is. The Set is all its elements, then it must also be all of its element's properties and all of its subsets. Each number can be considered a proper subset of the main set. Not only is then each number different, but it is composed of an infinite number of fractional rational and irrational divisions and summation sequences each of which is a proper subset of its integer. All of the numbers within the main Set are also members of other Sets that can be defined and that are proper subsets of the main Set. An infinite number of encapsulated Sets occurs within any give sequence of numbers, and since Sets are defined as objects by Set theory, they must exist. If they exist they have properties even if we do not know what they are. Thus there is a vast multiplicity of Sets with their own properties within the main Set. The main Set's identity must include all its properties and those of all its proper subsets and not just EVEN or ODD. That math geeks wrongfully and arbitrarily apply the EVEN or ODD rule labels to these imaginary structures does not actually identify the Set any more than calling me Robert identifies me. I am all that I am and the arbitrarily applied label stuck on me by my parents is not my identity. It is my label. The Sets identity is like mixing all colors of the marbles together. What color then results? Why, no color at all, for black is not a color. What magnitude of quantity is the ensemble of the main Set?, why no specific magnitude of quantity at all for all numbers taken together in a group cannot be any certain number.

Consider Pure Sets. A set is pure if all of its members are sets, all members of its members are sets, and so on. For example, the set containing only the empty or Null Set is a non-empty pure Set. If the Set containing the Null Set is non-empty, then the Null set must be something according to Set theory. But the Null Set is the grouping of its members. In the Null set resides its member, nothingness. A grouping of nothingness is nothingness. Yet Set Theory reifies nothingness into somethingness. Let W = a Pure Set that is an sequential encapsulation of an infinite quantity of instances of Null Sets like Russian Babushka dolls. Each order of successively encapsulated Null Sets is assigned a ranking with its ordinal number. As the sets are encapsulated each set will contain its own powerset. The main Set will then have cardinality greater than Aleph 0. Now imagine, (F), a one-to-one injective function correspondence between W and the Set of all evens. Since W contains its own powerset, it has 2^(Aleph 0) more elements than does a non-Babushka doll-sequentially-encapsulated Pure Set containing an Aleph 0 quantity of Null Sets. After (F) is applied, then the remaining |2^(Aleph 0)- Aleph 0| Russian Babushka doll Null Sets in W will still be uncountable and still be equivalent to nothingness. Yet the remnant of W will have a greater quantity of elements than the Set of all Evens. This is absurd. How can nothingness be greater than infinity? It can't be. But it is indicative of a basic contradiction that renders the notion of an infinite Sets incomprehensible and incoherent and thus non-identifiable, but math geeks can arbitrarily apply those EVEN or ODD labels to the indeterminate groupings so stipulated by way of the Analytic-Synthetic Dichotomy fallacy.

Consider a Set of all even numbers {E} that results from a bijective functional mapping, f, such that each element is the product of {N}={2,4,6,....,n(sub ∞)} and (Aleph 0^(Aleph 0)) as follows: {E}=f(n)=n * (Aleph 0^(Aleph 0)). Each element in {E} is the product of one of the even natural numbers X (Aleph 0^(Aleph 0)). Plotted on a number line each element of {E} would be separated by (Aleph 0 raised to the (Aleph 0) exponential power) quantity of numeric points. The reciprocal of (Aleph 0^(Aleph 0)) or 1/(Aleph 0^(Aleph 0)) is the LIM of x as x→0 . The cardinality of the total number of elements of in {E} would then be the (LIM of x as x→0) * (The cardinality of the total number of elements of {N}). The cardinality of {E} then would be very much like zero, But a bijective functional mapping of a one-to-one correspondence between elements of {N} and {E} was established. Both sets are countable, but {E} has Aleph 0 cardinality while {N} has LIM of x as x→0 cardinality. Here is a definite relationship between Zero and ∞. But zero is nothingness, and a definite relationship between nothingness and somethingness cannot occur. (See Grupp.) The concept of infinity (or eternity) is incoherent and incomprehensible and cannot actually exist.

Whoever asserts that the fantasy of an infinite set (Yes, it is a fantasy as there can be no actual infinity.) of even or odd numbers to have the identity of even or odd is committing the Analytic-Synthetic Dichotomy fallacy.

An analytic proposition is defined as one which can be validated merely by an analysis of the meaning of its constituent concepts. The critical question is: What is included in “the meaning of a concept”? Does a concept mean the existents which it subsumes, including all their characteristics? Or does it mean only certain aspects of these existents, designating some of their characteristics but excluding others?
The latter viewpoint is fundamental to every version of the analytic-synthetic dichotomy. The advocates of this dichotomy divide the characteristics of the existents subsumed under a concept into two groups: those which are included in the meaning of the concept, and those—the great majority—which, they claim, are excluded from its meaning. The dichotomy among propositions follows directly. If a proposition links the “included” characteristics with the concept, it can be validated merely by an “analysis” of the concept; if it links the “excluded” characteristics with the concept, it represents an act of “synthesis.”
- ITOE, p.127 Peikoff

The Objectivist theory of concepts undercuts the theory of the analytic-synthetic dichotomy at its root .... Since a concept is an integration of units, it has no content or meaning apart from its units. The meaning of a concept consists of the units—the existents—which it integrates, including all the characteristics of these units. Observe that concepts mean existents, not arbitrarily selected portions of existents. There is no basis whatever—neither metaphysical nor epistemological, neither in the nature of reality nor of a conceptual consciousness—for a division of the characteristics of a concept’s units into two groups, one of which is excluded from the concept’s meaning ....The fact that certain characteristics are, at a given time, unknown to man, does not indicate that these characteristics are excluded from the entity—or from the concept. A is A; existents are what they are, independent of the state of human knowledge; and a concept means the existents which it integrates. Thus, a concept subsumes and includes all the characteristics of its referents, known and not-yet-known. - ITOE, p.131 Peikoff

On pages 98-101 of Introduction to Objectivist Epistemology Expanded 2nd Edition, Meridian Penguin Books, April 1990, Leonard Peikoff demonstrate how the Objectivist theory of concepts defangs and neuters the Analytic-Synthetic Dichotomy. By a fine example of reasoning Peikoff notes the following:

I)Metaphysically, and entity is: all of the things which it is. Each of its characteristics has the same metaphysical status: each constitutes a part of the entity's identity.

II)Epistemologically, all the characteristics of the entities subsumed under a concept are discovered by the same basic method: by observation of these entities.

III)... a concept subsumes and includes all the characteristics of its referents, known and not-yet-known.

IV)....a concept is an open-end classification which includes the yet-to-be discovered characteristics of a given group of existents. All of man's knowledge rest on that fact.

V)Whatever is true of the entity, is meant by the concept.

VI)It follows that there are no grounds on which to distinguish “analytic” from “synthetic” propositions. Whether on state that “A man is a rational animal” or that “A man has only two eyes” - in both cases, the predicated characteristics are true of man and are, therefore, included in the concept “man”. The meaning of the first statement is: “A certain type of entity , including all its characteristics (among which are rationality and animality) is: a rational animal.” The meaning of the second is: “A certain type of entity, including all of its characteristics (among which is the possession of only two eyes) has: only two eyes.” Each of these statements is an instance of the Law of Identity; each is a “tautology”: to deny either is to contradict the meaning of the concept “man,” and thus to endorse a self-contradiction.

When someone labels a so-called infinite Set defined by the rules EVEN or ODD they are denying that the sequence of numbers is all that it actually is. Placing a label on something that is incomprehensible, incoherent and which does not actually exist is to deny (I-VI). By assuming that a Universal transcendence form of Even or Odd somehow crosses from a transcendence to our reality, the delusional believer violates (III). No certain identity can be ascertained from an infinite set. An arbitrarily applied label can be suck on it to give an impression of an identity, but such labels are no more identity than is my name, my identity. But labeling an infinite set with one of its characteristics while ignoring the remaining characteristics is constructively a lie, a falsehood, a deceit.