Showing posts with label Paradox. Show all posts
Showing posts with label Paradox. Show all posts

Friday, September 2, 2016

Another Leftist-Created Paradox

"The 9th Circuit would probably give its judicial blessing to most any reason to stop the sale of even a single firearm, but that’s not what’s interesting about this ruling.
Smokers with a “legitimate” need for THC in California and other medical marijuana states lose their 2nd Amendment rights simply for having a doctor’s prescription. But in states like Colorado and Washington, there would seem to be no similar infringement on recreational users who just enjoy getting high."

Stephen Green, at instapundit

Tuesday, August 16, 2016

Milo On the Leftist Gay Paradox

Milo Yiannopoulis:
"I’m comfortable with people who are uncomfortable with gays, as long as they don’t want to kill us, maim us or throw us off rooftops. (Permission for lesser violence is available upon application.) For leftists, the reverse appears to be true — they’re uncomfortable with people who are uncomfortable with gays, unless they want to kill us and maim us and throw us off rooftops."

Monday, June 6, 2016

My New Favorite Paradox

"Generalizations are false".
Three words, self-referencing and internally contradictory..

Tuesday, January 19, 2016

The Paradox of the Set of All Sets

The famous Bertrand Russell paradox which destroyed the attempt by him and Whitehead to outline the totality of mathematics, was just this:
The set of all sets cannot contain itself, so it is not the set of all sets.
This brings to mind a note to myself which recently re-surfaced, which said,
All things which exist are physical;
the source of all physical things is physical.
This statement of Philosophical Materialism is just as logically incestuous as the Russell Paradox. Is it actually the case that the source of all physical things is a physical thing which created itself, ex nihilo? And of course, subsequently created all other physical things?

In other words, all other physical things couldn't exist until and unless the first, creating physical thing created itself, under Philosophical Materialism and Atheism.

Where in nature do we see something come into physical existence without an identifiable prior causal existence? Even a quantum field is required in order to produce particle pairs, according to the Copenhagen understanding of quantum physics. Either particles are created by energy, or particles actually are energy (Quantum Field Theory). But what sort of a physical "thing" would the first, self-creating energy/particle be? What gives a probability field a positive value?

That is the paradox which surrounds the underlying theory of Philosophical Materialism, which is a necessary subset of Atheism - the rejection of a non-material creating entity. To drive the nail further home, the only valid evidence under the physicalist, Philosophical Materialism constraint is empirical data which is obtained in disciplined experimental fashion, successfully replicated, peer reviewed (for whatever that is worth), with open data for public examination of methods and results.

Can this empirical evaluation be done with regard to the "first self-creating physical thing"? Or even "any self-creating physical thing" That would require creating an absolute void containing not even any quantum field, much less radiation or outside particles. Then how, within this logically and actually empty environment could the creation, ex nihilo of course, be induced? Be replicated? It cannot be done. It is an effect without a cause outside itself, so there is no prior cause available to initiate the effect.

This seems almost too simple to avoid the truth of it. But it is not apparent to Atheists, who need the concept of physical self-creation and Philosophical Materialism in order to protect their chosen worldview. But they should have to admit that both logic and empirical evidence fail to indicate any value to support their choice. Why do they not admit to this, but rather claim the opposite: to have logic and evidence for their belief? There is only one remaining possibility, outside of insanity, and that is emotional neediness for their Atheism to be true.

Atheists have a choice:
A physical thing can and did create itself, as the source of itself, the cause of itself. (Not a property of known physical things; never observed; not inducible; a theory out of desperation).


Or,
Physical things always existed. (Infinite regression)

Or,
Physical things are illusions or delusions. (self reference).
Philosophical Materialism, and therefore Atheism, fail logically and empirically.

Saturday, November 16, 2013

The Problem of Evil and Hell, and the Problem of Evil Christians

[NOTE: the following is an article which is roughly a decade old, and which is located on the companion website: atheism-analyzed.net under Atheist Talking Points]

The Problem of Evil and Hell

Premise: “There is evil. A loving and benevolent God would not allow evil things to happen to good people. And such a God could not co-exist with evil. Therefore there is no omniscient, omnipotent, and benevolent God.”

Is this premise valid? Is the conclusion warranted, rationally and logically?

As we have already determined, in Atheism, morality is a human construct and is therefore relative. The actual moral precept of Atheism is the evolutionary “survival of the fittest” concept, under which anything that benefits my survival is proper behavior. So all other behavior is of no value.

Because "evil" is undefined in the absence of absolute ethical values, then evil cannot exist without ethics existing to define it.

If ethics came from man, then "evil" is a random and capricious concept, not an absolute, real value, and therefore evil doesn't exist in a real sense.

If ethics came from God, then "evil" has to exist as the opposite to, or absence of, positive ethics. And so it would be an absolute.

But we all agree that it is evil to torture babies, for example. So evil can and does have absolute, real existence with universally recognized (therefore absolute) tenets.

The expanded, complete concept is that, “although (this part is a hidden presumption) by definition evil doesn’t exist in an Atheistic realm of relativity, yet (here is the explicit premise) evil exists, therefore God cannot exist”. This is a self-contradiction, a Type 1 paradox. An Atheist presumption of “evil” is illogical.

Therefore the assumption that evil and God cannot co-exist is not only false, evil actually requires that God exist in order that evil be rationally defined ("to exist" in an absolute sense). Whether evil can exist in the presence of God is another, unrelated issue.

Regardless of the succinctness of the logical analysis, some will object that the problem is more complex and requires detailed characteristics of both “evil”, and the characteristics of God.

Here is a more detailed statement of the issue[1]:

“Bad things sometimes happen. Whether they are taken to flow from the operation of the world ("natural evil"), to result from deliberate human cruelty ("moral evil"), or simply to correlate poorly with what seems to be deserved ("non-karmic evil"), such events give rise to basic questions about whether or not life is fair.

“The presence of evil in the world poses a special difficulty for traditional theists, as both Epicurus and Hume pointed out. Since an omniscient god must be aware of evil, an omnipotent god could prevent evil, and a benevolent god would not tolerate evil, it should follow that there is no evil. Yet there is evil, from which atheists conclude that there is no omniscient, omnipotent, and benevolent god. The most common theistic defense against the problem, propounded (in different forms) by both Augustine and Leibniz, is to deny the reality of evil by claiming that apparent cases of evil are merely parts of a larger whole that embodies greater good. More recently, some have questioned whether the traditional notions of omnipotence and omniscience are coherent”.
The problem arises out of the simplistic definitions and logically erroneous conclusions of the definitions of omnipotent, and benevolent. Omniscience is granted.

Most frequently the concepts of omnipotent and omnibenevolent decisions are made from a human viewpoint, drenched in cultural bias, not from the viewpoint of a functional, real deity existing in unknown dimensions.

Omnipotence, Choice, and Entropy
Omnipotence is typically over-played in arguments about God: “Can God create a rock so big that even He can’t lift it?” These nonsense word-plays are usually violations of the First Principles (Non-contradiction paradoxes), and so have no meaning: would God contradict himself? And having no meaning, no truth value can be, or needs to be, assigned to them. They are exercises in triviality.

Some things that an omnipotent being could not do: (a) Subdivide himself; (b) contradict himself; (c) deny his own existence; (d) lie; (e) be deceived; (f) die.

There are things that an omnipotent deity would not do, especially if he were also benevolent: he would not violate the First Principles (very often, or on demand). He would not require repentance; he would not require worship. He would wish for them to occur voluntarily, without coercion.

In other words, he would allow humans to choose.

The fact of “choice” requires once again the presence of entropy. Choice is easy but without value if it only is between good, pleasant alternatives. Choice is of value only if it is between good alternatives and bad alternatives. Entropy is the natural placement into our universe of both stress on humans, and bad alternatives. For example, natural disasters are entropic; they place on us stress, and the need for humans to choose between the alternatives of assisting or ignoring. Entropy is necessary, if choice is to have value. The consequences of natural disasters are not the same to a deity as they would be to us. Pain and suffering are severe to us; how would they appear to an eternal being? And how about death? It might seem permanent, severe, and the end to us. To an eternal being, it might seem as just a move to a different level, or a different set of dimensions.

Benevolence vs. Sentiment
Would the human concept of benevolence play well in the dimensions of a deity? The human concept of benevolence is sometimes confused with sentimentality. A human might wish to prevent all natural disasters. Would a deity? Why would a benevolent deity remove the precious gift of choice, in order to satisfy a sentimental need to eliminate bad things such as natural disasters from the universe? Benevolence and sentimentality should never, ever be confused.

Deformed Children, Suffering and Premature Death in the Dimensions of a Deity
From a human’s perspective, these are terrible things. Again, how would the human concept of “deploring suffering” work in the dimensions of a deity? Would a deformed child be considered defective by a deity, which sees its unbroken spirit, it’s influence on the world around it? Would suffering be deplored by a deity, when suffering is known to strengthen, to be the fire that forges character? And who is to say that any death is premature, in the dimensions of a deity, which would welcome the essence, the spirit back home?

Omnibenevolence vs. Justice
A deity is “omni” everything, right? This is a tacit assumption in the argument, yet there is no basis for assuming that a deity would be “omnibenevolent”. Were it so, it would preclude justice, which would then preclude love. So the concept of omnibenevolence in the argument produces a paradox, and destroys its own credibility. But without the concept of benevolence beyond justice, beyond love, the argument fails.

A God of justice and love would not allow suffering, would not allow people to languish eternally in Hell? Suffering (God’s megaphone, according to C.S. Lewis) gets our attention on the fact of our own non-divinity. It is part of living in an entropic universe. It part of the mechanism that allows for freedom of choice. Personal non-divinity is a universal feature of human existence.

Hell
Premise: I’m a good person. A loving God would not send me to Hell. Therefore there is no God.

Again, the Atheist has no benchmark for declaring himself to be a morally “good” person. Because of the acceptance of evolution as the only natural truth, Atheism’s concept of “good” would be to do what it takes to perpetuate your own genes. So Atheism’s evolutionary “good” would contradict God’s moral “good”, creating a paradox, Type 1. This is logically unavoidable; Atheism has no rational (non-rationalized) claim on moral “good”.

As for Hell, we know how to stay out. If we put ourselves there, it is our own doing. Some Atheists love the comparison between Hell and Hitler’s torture and death camps. But they ignore the differentiating facts: None of Hitler’s victims chose to be there, to be tortured or to be gassed or shot, and by Nietzschean Atheists no less. On the contrary, everyone, including Satan and his angels, that goes to Hell CHOOSES to do so, according to Christian Theology. Chooses to Deny God. Chooses to elevate himself to the point of self-Godhood and separate from the actual God. Hell is a CHOICE! And a loving, just, benevolent God allows that individual to complete his choice of separation.

The concept of “omnibenevolence” is now firmly entrenched in our culture, where many children are totally indulged and as a result are without fear of any consequence for the their actions or inactions. If one is totally indulged, one would expect to continue to be so treated. So omnibenevolence has become an expectation, a right, despite its destructive and paradoxical nature.

In fact, omnibenevolence occurs in our culture due to fear of not being loved. Complete indulgence is an overcompensation, attempting to cause love to occur due to the showering of material items on the object of the benevolence. Total indulgence results in the destruction of the recipient. It is not a virtue. Omnibenevolence is really omniindulgence. It is pagan.

Deification of the Self
To make this claim (that the existence of evil proves there is no God) is to assume the role of deity for oneself, insisting that oneself knows what a deity would and should do (a moral judgment by the human on the deity). This is done as an artifact of declaring that one’s own mind is the actual supremacy. The worldview of the self, and one’s own personal morality is declared superior to the deity’s. So passing judgment on the deity becomes a natural emoting of the self-declared elitist.

The premise expansion would be:
“My mind is supreme, therefore it is qualified to determine what a God would or wouldn’t do, and should or shouldn’t do; thus I have determined that God wouldn’t do (X), shouldn’t allow (Y), and therefore, because (X) and (Y) exist but are not per my expectation, I declare that God does not exist, or if He does, He is evil.”

The hidden presupposition, implicit in the premise, that “My mind is supreme…” has been shown to be a Type 2 (a) Godel Paradox.

Now, if a deity did exist, then I, myself, would be the effect; the deity would be the cause. As an effect, I am less than the cause. Since, by Godel’s theorem, I cannot even fully comprehend my own mind, it is much less possible to know the mind of the deity. To assert that one knows what a deity should do is a Godel’s Paradox Type 2 (b).

And finally, the Naturalist / Materialist Atheist would actually be required to deny that evil exists, since it is neither material, nor an empirical or forensic concept. It is a moral concept, outside the realm of science and materialism. So the Atheist assumption that evil exists is self-contradictory in the environment of the Atheist. In fact, much of what is called evil would actually be the activity called “survival of the fittest”. Since man is just a “meat machine” trying to survive, any behavior is justifiable: there is no evil. So the existence of evil cannot exist for the Atheist, who nonetheless decries it’s existence; a profound paradox, which voids the argument from the beginning .

The premise that God would do “such-and-so” based on my standards for Him, is false.
The premise that evil falsifies the existence of God, is false.
The conclusion based on this premise is false.
“I think this shows that the problem is primarily emotional, not intellectual. People just don't like the idea of a God who might send them to hell, and so they choose not to believe in Him. But that kind of attitude is just suicidal. Imagine you're standing in the middle of the street, and suddenly a friend on the curb says, "Look out! Here comes a car!" Now what do you do? Do you stand there and close your eyes real tight and say, "anybody who would run over me can't be a very nice person! If I don't believe in him, then it won't affect me! I just won't believe that he exists!" And then it is too late. A lot of people look at God that way. They think that just because they don't like the idea of God sending them to hell, if they close their eyes real tight and pretend that He doesn't exist, then it doesn't affect them. And that kind of attitude is just fatal.” [2]

“Whenever, then, anything in nature seems to us ridiculous, absurd or evil, it is because we have but a partial knowledge of things, and are in the main ignorant of the order and coherence of nature as a whole, and because we want everything to be arranged according to the dictates of our own reason; although in fact, what our reason pronounces bad is not bad as regards the order and laws of universal nature, but only as regards the laws of our own nature taken separately.” [3]


“Religion, opium for the people! …A true opium for the people is a belief in nothingness after death – the huge solace of thinking that for our betrayals, greed, cowardice, murders, we are not going to be judged.”[4]



The Problem of Evil Christians

Premise: “Christians are responsible for torture and death throughout history. Therefore, Christianity is evil.”

Is this conclusion warranted, rationally and logically?

The falsification of the concept of “evil” in the Atheist lexicon was shown in the preceding text. Atheists have no rational basis for claiming anything to be “evil”, especially if it is a clear case of acting in the behavior of the ”survival of the fittest”. The crusades, the power struggles of the Roman papacies, the conquistadors, the Inquisition, all were justifiable as Darwinian behavior. This doesn’t slow down the Atheist who has had a problem with Christians. The fact that Christians do accept the moral concept of evil allows the Atheist to strike back, using a concept in which he, the Atheist, doesn’t even believe.

Due to the Atheist worldview, this proposition is logically falsified from the get-go. Within the Atheist’s evolution paradigm, all “evil” is just more survival behavior of the “fittest”, and therefore it must be valid. However, let’s follow some clear, logical thought paths to pursue the claim anyway.

Some Atheists claim to be “sickened” (a term actually used on an Atheist website) by the millions of people tortured and murdered in the name of Jesus Christ. Ignoring the fact that more people were killed in the 20th century alone by Atheists following the precepts of Darwinism, than in the prior 19 centuries by Christians, the fact remains that very many Christians did very bad things. Why? Were they really valid Christians? Or were they deviant, quasi-Christians?

But let’s start here: exactly which slaughter was caused by the essence of Christianity?
And which were caused by perversions of the essence of Christianity? Where exactly did Jesus say “slaughter millions in my name; torture heretics and apostates; murder infidels”? The essence of Christianity is directly opposed to the actions of these types of “adherents”. Shouldn’t the blame be placed on the perpetrators, who went totally against the precepts of Christ? Of course it should. This argument in no way falsifies the existence of God or Jesus, or the validity of the Bible.

It seems easy from our perspective to discern the great evil that the deviant people were doing, not only to the people subject to their horrible treatment, but also to their professed faith. Why did they not discern this?

If they had done the simple act of rational discernment, they would have realized that their behavior in no way mapped onto the teachings of Jesus, and was in fact irrational and diametrically opposed to those teachings. The church was and is inhabited by mere humans in positions of great power, some of whom are non-intuitives, others of whom might be intuitive, but not rational, others of whom, just corrupt, as well as those who accurately reflect the teachings of Christ. The great power that always corrupts came with the human cost levied by the power of the human church in the hands of non-rational, non-intuitives. The conclusion is that these people were at best deviant, quasi-Christians, and at worst manifestations of total evil, in control of the human church, sometimes for prolonged periods of time. They were in full pursuit of Darwinist “survival of the fittest” behavior, which carries no moral value in the Atheist worldview.

But they do not detract from the rational, intuitive Christians that do exist, and can be found if they are sought. To condemn all Christians, or Christianity in general, for the evil of others is a logical fallacy, Guilt by Association. As I have said elsewhere, if I assume the guilt for the massive 2 millennia of “Christian” evil, will the Atheist assume the guilt for the even more massive 20th Century Atheist evil? The question itself is nonsense. The absurdity is obvious. It is irrational and trivial.

The principles of Christianity do not support or condone the behaviors being illustrated by viewing faulty papacies, crusades run amuck, or greedy conquistadors. It is not Christianity that is at fault; it is the deviancy of human beings, especially human beings in positions of great power, that is at fault. That deviancy is found both within and without religious boundaries.

To deny the existence of a deity because of deviancy in humans is logically fallacious. The fallacy is Guilt By Association. The premise is not pertinent to the conclusion, which is false.

Also, the Atheist cannot legitimately claim to be sickened by behavior that would appear to be “survival of the fittest”, and perpetrated in spades by Atheists in modern history. Nor can the Atheist claim any moral value on behavior at all, since there is no morality in the “sciences” that are the Atheist’s complete source of truth.

So the huge paradox here is that the Atheist can make NO legitimate claim of evil, while the Christian can, and does claim that the early Roman church institution did have periods that were, indeed, evil. There is no wind left for Atheist sails on this matter.

These paradoxes falsify the premise and conclusion.
“Moral indignation is a technique to endow the idiot with dignity.” [5]
[1] philosophypages.com/dy/e9.htm#evil

[2] William Lane Craig, from his debate with Ray Bradley. (Emphasis added)

[3] Spinoza; Ethics IV. In “The Story of Philosophy” 2nd Ed, Will Durant

[4] Czeslaw Milosz, Polish Poet, Nobel Prize 1980; “The discreet Charm of Nihilism”, from McGraw, “The Twilight of Atheism”

[5] Marshall McLuhan

Tuesday, February 28, 2012

The Paradox In Hate Crime Laws

Back when living in Oregon there was a big issue generated by the paradox generated by certain laws. The issue was the protection of the salmon which come up the rivers to spawn vs. the protection of the sea lions which hang around the coast. The sea lions learned to hang around the river outlets and take a bite out of passing salmon. There were enough salmon that the sea lions took just one bite and left that salmon to die while the sea lion looked for another one.

Well, you can’t interfere with the sea lions, they are protected. But you must save the salmon, they are protected. The paradox became palpable.

Here we have another law which demonstrates its basic irrationality. Because it sets up protected classes of people which get more protection than ordinary victims, what happens when a protected person attacks a protected person?

The case involves three lesbians who attacked a homosexual man.

Now if anyone outside the protected class had done this crime, the additional punishment would be automatic, because it becomes a hate crime regardless of actual motivation. This was well established in the Matthew Shepard case, where the attackers didn’t even know that the victim was homosexual; it was a robbery gone bad. But in this case, the question arises, “can a person in Category Z hate another person in Category Z because of that person’s membership in Category Z”?

The ACLU staff attorney claims that Jews can be anti-Semitic, thereby proving that class hatred still applies, even within the class. So the paradox becomes even more bizarre, having to involve self-hatred as well as class hatred as motivators. Not that that has to be proved. All that needs to be proved is that the victim is in a protected class according to the prosecutors and the ACLU.

But wait. The lesbians charge that the homosexual man used “homophobic slurs” too. And it is the slur which is the crime, apparently. So maybe he deserves 10 years in lock down too?

And here’s the prosecutor’s actual stance:

” But Jake Wark, a spokesman for Suffolk District Attorney Daniel F. Conley, said prosecutors will have no problem proving the women committed a hate crime, even if they are lesbians.

‘The defendants’ particular orientation or alleged orientations have no bearing on our ability to prosecute for allegedly targeting a person who they believe to be different from them,’ he said.”

That sounds like every person to me. So any assault is a hate crime, because every person is different from every other person. That sort of levels it out. Or is it every assault which is accompanied with objectionable language? If that is the case, then when you assault someone, be sure to compliment that person, especially on whatever categories they might belong to. It’ll save you an extra ten years in the can.

Wednesday, July 16, 2008

Reason: Rational Thinking and Critical Thought.

[Author's note: This is the second in a series of articles concerning the process of rational thought. The first was published earlier this week and concerned the first principles. Subsequent articles will be concerned with linear thought, fallacy use and abuse, and the subversion of reason.]


Finding a Process for Locating Real Truth

Truth exists, and it can be known. Fallacy exists, and it can be known. How can I know if this is true? By questioning absolutely everything: all ideas, including existence, reality, logic, and the reasoning process itself, I can come to know whether or not truth exists. Socrates questioned everything. Descartes doubted all things, and by doubting even his own doubt, he began to peel away layers in order to get to truth. So did Hume and Locke, but others such as Bertrand Russell were so affected by previous philosophers that they themselves could not get to the basic questions.

“Men become civilized, not in proportion to their willingness to believe, but in proportion to their readiness to doubt.”
H. L. Mencken [1]

We need tools to help us peel away the layers to get to truth. This section gives the skeleton of the process of producing rational thoughts about truth. It’s simple and straightforward; think of it as a handbook for the pursuit of truth.

Notice that every segment is framed as a question to be examined. No viewpoint is immune to being questioned and tested for validity. This is the Socratic method. Some might find it annoying; after all it cost Socrates his life. Yet, as Socrates knew, it is the way to truth.

What is Rational Thought?
Rational thought is the cognitive process used to identify concepts that are true and slice away any parts that are false. It is a sequence of logical propositions leading to a valid conclusion.

Ontologically (for existence) the process of rational thought proceeds along the First Principle of Cause and Effect:

Cause A + Cause B, taken together: exist; are necessary; are sufficient to produce Effect AB. (Empirical Process)

Epistemologically (for truth) the process of rational thought again proceeds along the First Principle of Cause and Effect:

Premise J + Premise K, taken together: are true; are necessary; are sufficient to produce Conclusion JK. (Rational or Logical Process; not Empirical).

Critical thinking is a further organization of rational thought.

Critical (reflective) reasoning is “active, persistent, and careful consideration of a belief or supposed form of knowledge in the light of the grounds which support it and the further conclusions to which it tends.”

John Dewey[2]

What is Logic?

Logic is merely an organizing of the thought processes, so that truth might be extracted systematically from a group of premises containing facts and fallacies. There are two categories, Deductive and Inductive logic.

Deductive logic generally resolves toward a specific. It tends to be absolute.

Inductive logic generally resolves toward a generality (such as a natural law). It tends to be probabilistic.

The propositional logical process starts with premises that might or might not be valid, and results in a conclusion based on those premises. The premises must be knowable, stated completely, and tested for validity. And the ordering of the premises within the proposition can influence the truth of the conclusion.

There are more than 100 documented informal logic fallacies. A working knowledge of the basis for falsity is essential for winnowing truth from any claim.

Inductive Reasoning, Deductive Reasoning, and Falsification

Induction, Premises and Conclusion:

Inductive conclusions are not absolute, but are probabilistic. Induction usually resolves from specifics toward generalities.

Example:
Fred is mortal and human.

Ethel is mortal and human.

Lucy is mortal and human.

Therefore, probably all mortals are human.

(True in a probabilistic manner?).

This example has three valid premises, but the conclusion is false. It shows how susceptible induction can be to false conclusions when based upon a sample size too small to find a falsifier, or when the data gathering is restricted to one population, ignoring other possible populations. In this case, “Rover is mortal and a dog” would falsify the conclusion.

Another way to write the above is as follows:

X is A and B;

Y is A and B;

Z is A and B;

Conclusion 1: Therefore, all A is B; (A is completely contained inside B)

Conclusion 2: Therefore, all B is A; (B is completely contained inside A)

Both conclusions assume that there is no population that is outside the boundaries, based on the sample size of three. So the accuracy of this type of logical process depends upon the quality of the sampling process, the sample size, and possibly the ability of the sampler to objectively locate all the populations involved. This illustrates the probabilistic nature of the inductive process.

Inductive reasoning is used in defining scientific principles, where a series of isolated facts “induce” a conclusion that is “probably” true. Ironically, the so-called “laws” of science are at best only “probably” true, because there can never be enough verification to prove them for all conceivable cases, or absolutely. Keep this in mind!

Deduction, Propositions and Syllogism

Deductive conclusions absolutely draw from the premises without depending upon anything else. Deduction generally resolves toward the specific.

Deductive “categorical propositions”, invented by Aristotle and called “syllogisms”, are formed by two premises, and a conclusion.

Example 1:

All humans are mortal.

Fred is human.

Therefore, Fred is mortal.

(True, because Fred is a valid subset of humans,
and human mortality is well established)

Example 2:
All humans are mortal.

Fred is mortal.

Therefore, Fred is human.

(False, Fred is my dog, which is mortal but not human)

Deductive reasoning is used to “deduce” a specific truth from general truths and other specific, related truths. In example 1, a general set (mortal) and subset (all humans) are established. Then a member of that subset (Fred, a human) is identified. When done properly, a correct (true) conclusion can be drawn.

In example 2, the second premise does not establish membership in a valid subset, so the logic has the ability to be incorrect even though the premises are true.

Premises can be written in the following forms, which are given letters (A,E,I,O) for names which identify each one:

A: All S is P

E: No S is P

I: Some S is P

O: Some S is not P

Deductive Categorical Syllogisms have three terms, two are premises and one is the conclusion. P is the major term, located in the predicate of the conclusion, and in the first term. The minor term, S, is in the second premise only. The middle term, M, is in both the premises, and at least one use must be “distributed” (contain all the members of its class). These look like this example:

All P is M (A)

Some S is all M (I)

-----------------

:. Some S is P (I)


This particular example is an A-I-I Syllogism. A syllogism category can be from AAA to OOO, and some are never valid while others are always valid. Since the Middle term can occur in four locations in the premises, there are four “figures”, or combinations of configuration. This leads to 256 combinations that form Syllogisms.

A simple way to view the syllogism is with the Venn diagram (intersecting circles denoting sets), which allows us to visualize the content and conjunctions of S, P, and M. If S, P and M are each sets, then basic set theory takes hold.

Syllogisms are arguments in basic natural language. They can be formalized into truth tables and into more formal “predicate logic” language specifically for logic. These formal methods are usually not needed for informal logic analysis, and won’t be addressed here.

Falsification Process:

An argument cannot be true if any one of the necessary premises can be shown to be false. One way to test this is give values of “T” and “F” to the conclusion, then find the corresponding requirements of the premises. A false premise will show up as a contradiction. This is a “falsification” of the argument. If a premise is not falsifiable, there is doubt as to its validity. Should such a premise be used?

Falsification is the first and most positive test that can be performed on a hypothesis. Because of the limitations of science, a hypothesis can never be 100% verified (Discussion of science is coming up). Many verifications can point to the probability of being correct. But just one falsification serves to disprove the entire theory. So falsification is a very powerful detector for the process of finding truth.

The verification or falsification of premises is a technique that will be used throughout this work to determine the credibility of the claims of Atheism.

Informal Logical Fallacies; Definition and Examples

Fallacies are pieces of erroneous reasoning or tactics that lead away from valid conclusions rather than toward them. Knowledge of fallacies is an essential part of detecting departures from valid reasoning. Some common examples are:

Ad Hominem (Abusive): attacking the attacker.

Ad Baculum: appeal to force the acceptance of a proposition.

Ad Ignorantiam: It’s true because it hasn’t been proven false. Appeal to Pity.

Begging the question.

False Cause Fallacy.

Hasty Generalization.

Appeal to Fear.

Appeal to Authority.

Circular Reasoning.

Guilt by Association.

Red Herring.

Genetic Fallacy.

Rationalization.

Post Hoc Ergo Propter Hoc (Just So Stories)

Ad Hominem Abusive
One of the most pervasive fallacies is the Ad Hominem Abusive. The Ad Hominem Abusive is a direct attack on the opposing debater, deflecting the debate away from logic and reason. This has been a common tactic in the makeover of our society from one of absolutes to one of relativism and secular humanism. It involves the use of ridicule to debase the beliefs of others, while maintaining a call for tolerance of one’s own behaviors, as shown here:

On July 19, 2006 President George W. Bush vetoed the Embryonic Stem Cell Bill. Senator Tom Harkin had this Ad Hominem Abusive reaction: “George Bush is an embarrassment to His Science teacher; he is acting as the Moral Pope, the Moral Ayatollah”. “This veto is a shameful display of cruelty and hypocrisy.” [3]


The name-calling attack has nothing to do with logic, and everything to do with emotional force. These attacks can actually be preemptive in that the attacks are made even before a counter argument is made. The Ad Hominem Abusive attempts to place the victim on the defensive immediately by forcing a denial (which is attacked), then forcing proof of the denial (which is also attacked), and so on. It is a tactic to jerk the debate focus away from controlled logic into angry, defensive, prideful retaliation, thereby resolving in the favor of the attacker who remains cool and collected. It can also force the withdrawal of the timid. Ad Hominem Abusive is a favored attack in the political arena.

Here is an Ad Absurdum (taken to an absurd extreme for demonstration purposes) example of the Ad Hominem Abusive Fallacy:

“In the Monty Python ‘Argument’ sketch, a man enters an office and says to the receptionist: ‘Good morning. I’d like to have an argument please.” She directs the man to Mr. Barnhart in room 12. When he opens the door to room 12 the following dialog takes place [4]:

Barnhart (angrily): Whaddayouwant?

Man: Well, well, I was told outside that…

Barnhart (shouting): Don’t give me that you snotty faced heap of parrot droppings!

Man: What?

Barnhart: Shut your festering Gob, you tit! Your type makes me puke! You vacuous stuffy nosed malodorous pervert!!!

Man: Yes, but I came here for an argument!!”


Non Sequitur

Some have pointed out that all fallacies are really “non sequitur” (does not follow) in the sense that the conclusion doesn’t follow the premises. The point is that fallacies derive from improper logic, or a lack of logic at all. There are appeals to fear, to patriotism, to all sorts of emotions. There is outright deception, diversion, and bad evidence. There are mathematical errors, misunderstanding of probabilities, confusion of cause and effect. By some counts the list is over 100 documented informal fallacies. There are many unnamed informal fallacies as well.



Classification

T. Edward Damer, in “Attacking Faulty Reasoning” , classifies fallacies into four groups: Irrelevance; Unacceptability, Insufficiency; and Ineffective Rebuttal. The titles of the groups are descriptions of the general defects found in the reasoning process. For example, the Ad Hominem Abusive fallacy falls into the Ineffective Rebuttal category, because it doesn’t rebut an argument. Rather it deflects the argument off the logical path, onto an emotional one.

But there are also undocumented fallacies. It is not necessary to know the names and particulars of every known informal fallacy. All one needs is the ability to discern erroneous or insufficient premises, or failure to form a conclusion that follows from the premises . Watch for emotion, deceit, and fear as well as tangled logic. For me, a slow and determined analysis is required (not available in a hot debate!).

1.7 What is a Paradox?

The most potent detector of non-valid propositions is the self-contradiction. Any statement that contradicts itself in any way can’t be valid. A great many of the premises under which our society is operating are in fact self-contradictory, in other words, illogical. Paradox abounds, and once one trains oneself to see them, they are easily found.

Paradox is a violation of the second “First Principle”, the Principle of Non-Contradiction. A paradox can’t be established as true or false because it is self-contradictory.

Paradox in a logic statement or premise automatically falsifies it. However, in secular, neo-pagan, auto-pagan, postmodernism, the Worldview trumps logic every time, despite any and all paradoxes involved in the worldview. Some worldviews and eastern philosophies consider “either / or” logic too restrictive, and believe that “both / and” logic is correct. ‘Both / and” logic embraces both of the contradictory statements as true, and rejects the concept of contradiction. This produces another paradox, the “Both / And” paradox (See Appendix for Paradoxes, Conundrums and Hoaxes). So in such a logic system, truth can be two contradictory concepts simultaneously…in other words, there would be no absolute truth.

Western rationalist logic, on the other hand, requires that no contradiction exist if a set of premises is to be true and produce a true conclusion. So the falsification that paradoxes provide is one of the surest routes to finding truth.

Anatomy of a Paradox

There are two issues to be considered. Self-reference, and ever rising systems.

Self-Referencing Contradictions

Here is a statement that references itself, and contradicts itself:

“The truth is that there is no truth.”

If there is, in fact, “no truth”, then the statement cannot be true. So it is a contradiction, a paradox. Another example:

“This statement is false.”

If this statement is true, then it is false. Self-contradiction, a paradox.

Double self-referencing:

>“The following statement is true.

The previous statement is false.”

Standing alone, each statement is OK. Together they form a two-sentence, self-referencing paradox.

Ever Rising Systems: Godel’s Theorem

Kurt Godel developed two theorems of undecidability that rocked the mathematics world. The second theorem shook the bedrock under Bertrand Russell’s “Principia Mathematica”, and influences science, mathematics and culture today. It goes like this (approximately):

“A system of number theory cannot be consistent if it can validate itself; it requires validation at a higher level, a “meta-theory”, in order to be consistent. The meta-theory requires a meta-meta-theory, and so on.

This translates to: System “A” needs validation by a higher system, “meta-A”, and “meta-A“ needs validation by yet higher system “meta-meta-A”, and meta-meta-A requires validation by still higher system “meta-meta-meta-A”, ad infinitum. So the validation of system A can never be reached due to the infinite spiraling hierarchy of validation requirements.

System A might be consistently valid (i.e. true), but it also might be false, which we can’t know for certain without complete validation. But if System A does, in fact, validate itself, then it is definitely inconsistent (contains false statements).

“The implication [of Godel’s 2nd theorem] is that all logical systems of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.” [5]

So, is any system true? The point is that there is a requirement for meta-mathematical thought, and truth is more closely approximated with the amount of hierarchical thought given it. If one stays locked inside a specific system level, the probability of validity is undecidable. For an idea of the paradox, see the Godel Paradox, below.

Where does this apply? Some critics want to believe that it has a restricted range of mathematical application. However, can these critics prove that their own system of restrictive reasoning is valid, without a hierarchical proof? This is the point. Denying the hierarchical requirement places one in a position of potential fallacy: “I validate myself”. Or, “My postulate validates itself”. So the denial is actually an example of the undecidability propositions of Godel. Here are some “common sense” Godel exchanges:

Salesman: “I am honest”.

Me: “Why should I believe that?”

Salesman: “because I say so.”

The salesman has made a self-referenced, self-validated assertion. Is that good enough?

Salesman: “This data is valid.”

Me: “Why should I believe that?”

Salesman: “Because the data says so.”

Another self-referencing, self-validating assertion. Is it good enough? Is self-validation ever good enough to conclusively confirm the accuracy of an assertion? We intuit that the answer is “no”.

“And it [Godel’s 2nd theorem] has been taken to imply that you'll never entirely understand yourself, since your mind, like any other closed system, can only be sure of what it knows about itself by relying on what it knows about itself.” [6]

(For an interesting twist, ask the question: “is Godel’s 2nd theorem hierarchically validated? Or did it validate itself? Or is it possibly immune to validation, as in a First Principle? Or maybe it is “undecidable” also? And if so, does that not allow for a release from paradox, by creating a different paradox?).

“It is not certain that everything is uncertain”.
Blaise Pascal

OK, then.

Type 1 Paradox: Epimenides.

Since “undecidability” does not mean partly true, partly false, violating Godel’s Undecidability theorem is not a violation of the first or third “First Principles”. It is (a) self-referencing, (b) of the kind “if it is true then it is false; if it is false then it is true”, which makes it a paradox. But there are also non-Godel self-contradictions, which are simpler because they completely exist at one level. These are of the Epimenides (“Liars”) type, which I call Type 1 paradoxes. Here are some characteristics and examples of this type of paradox:

Characteristics of a Type 1 Paradox:

a. Self-referencing

b. Self-negating or self-denying. (Internally inconsistent).

c. The negation of the statement is generally true (internally consistent).

Examples of a Type 1 Paradox: (Epimenides and variants):

1. “I am Lying.” (Epimenides classic statement)

2. “This sentence is false”.

3. “I do not exist”.

4. “This valid statement cannot be validated at this level”. (Yes, the Godel statement is a Type 1 paradox).


Type 2 (a) Paradox: Godel’s Explicit.

Characteristics of a Type 2 (a) Paradox:

1. Self-referencing.

2. Explicit external inconsistency or denial. Attempted self-validation while denying the Godel requirement for higher order validation: contradiction, a paradox.

3. The negation of the statement is generally true.

Self validation, because it can’t be verified at it’s own level, has no truth value.

Let Q be an unvalidated proposition with no truth value;

For Q to claim Q is absolutely true….is false.

For Q to claim Q is absolutely false…is false.

A proposition (that has no truth value) claiming that itself (a proposition that has no truth value), does, in fact, have a specific truth value, is contradictory. (The process is paradoxical). Moreover, result of the paradox is falsity.



Examples of a Type 2 (a) Paradox:

1. “My mind is supreme.” (Denies higher order Godel requirement for validation; self-validated).

2. “We are all god.” (Denies higher order Godel requirement for validation; self-validated).

Type 2 (b) Paradox: Godel’s Implicit.

Characteristics of a Type 2 (b) Paradox:


1. Self-referencing.

2. Implicit external inconsistency or denial. Attempted self-validation while denying the Godel requirement for higher order validation: contradiction, a paradox.

3. The negation of the statement is generally true.

4. Truncated statement, concealing implicit or embedded presuppositions.


Example of a Type 2 (b) Paradox:

1. “There is no (Necessary Cause, Deity, Supreme Intelligence).”

This is an example of a truncated statement, with possible implicit and embedded components that are in play, but not stated. The complete statement might be:

“{My mind is supreme and has the capacity to determine all matters, and because of worldview presuppositions A through Z(z) (unstated, and unknown validity), has determined categorically that} there is no (Necessary Cause, Deity, Supreme Intelligence).”

This shows the possibility of embedding several fallacies and worldview self-limitations within an implied-but-not-stated framework, including the obvious implied Type 2a paradox, “My mind is supreme”. This type of paradox is found implicitly embedded inside many worldviews, and is the basis for certain irrational approaches to the problems of life. A paradox inside a worldview directs the holder of the worldview away from truth, not toward it. For this reason understanding the nature of paradox is crucial.

Paradox Examples

Here are some of the most well known and some of my favorite paradoxes:

1. Epimenides (“Liars”) Paradox (Type 1).

Epimenides, a Cretan, said, “All Cretans are liars’.

Statement: “I am Lying.”

Or,

“This statement is false”.

Is this statement true or is it false?

I don’t know, but it definitely is a paradox.

2. Bertrand Russell’s “Set of all sets” Paradox (Type 2).

Statement: “There exists a set of all sets, which of necessity contains itself”. Can a set contain itself and all others, or does that produce yet a larger set? This was a direct result of Godel’s theorem. After 7 years looking for a resolution to this paradox, Russell reputedly gave up declaring it a waste of his time.

3. The Infinity Paradox #1.

Given an infinite chain of pop-beads, I break the chain at the point where I exist. Then I have two infinite chains of pop-beads. This proves that one equals two, which is a paradox.

The infinity Paradox #2.

Given that there are an infinite number of numbers, there are also an infinite number of even numbers. This is because for every number there exists a double of that number (an even number). So every number produces a corresponding even number, making the even numbers the same quantity as the total number. The concept of infinity produces lots of paradoxes.

4. The Zero Paradox.

If there are any two equations:

A+B = C and X+Y = Z,

Then,

A+B-C = 0 and X+Y-Z = 0

So,

A+B-C = X+Y-Z.

Therefore all variables in the universe can be mathematically equated. (Inches can be made to relate to lumens or kilograms, for example).

This seeming paradox is actually just an exercise in triviality: the “=0” is a trivial solution to all equations. Setting trivial solutions equal to each other is meaningless.

5. The Relativist’s Paradox.

Premise: “All truth is relative.”

Premise expansion: “(It is absolutely true that) All truth is relative (not absolute).”

Is this statement absolutely true? Or is it a relative truth? If it is true, then it is false. It is a paradox.

6. The Escher 2-D Paradoxes.

The drawings of Escher show people walking upward on an infinite staircase yet winding up where they started, producing an infinite loop. Paradox in picture form.

7. The Godel Paradox: Questioning the Undecidable.

Godel’s theorem now is being applied to all things, including worldviews. Undecidability is popular because it seems to deny that any absolute knowledge can exist. This of course eliminates absolutes such as moral statements.

But is Godel’s theorem absolutely true? Is the system in which the theorem exists self-validating, or does the hierarchy requirement apply, making the validity of the theorem itself questionable? If it’s own validity is undecidable, can the theory be used to question the validity of other premises? Here we go:

(a) If Godel’s theorem (GT), applies to all things, including worldviews, then it must also apply to itself, meaning that it’s own validity is undecidable… thereby opening the door to the possibility of absolute truths, since the GT might not be valid.

(b) If GT does not apply to all things, then it still opens the door to the possibility of absolute truths.

(c) If GT exists as a singular exception to the hierarchical validation requirement, it is therefore a paradox, contradicting it’s own premise.

So the Undecidability of GT is not absolute. And other absolutes are not precluded.

8. The Empiricism Paradox.

Empirical analysis depends upon the ontological form of the First Principles of both Cause and Effect, and the principle of Identity. Both of these are intuited to be valid, which of course requires intuition, a transcendent entity. If the Principle of Identity is not valid, then the “cause” does not exist (exist != exist) and rational thought collapses into irrationality. So empiricism demands that the First Principle of Identity be valid / true, in order for itself, empiricism to exist.

Thus a discipline that excludes transcendence is dependent on transcendence for its existence, a paradox.
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[1] H. L. Mencken [Atheist], from George Seldes, ed., The Great Quotations, quoted from James A. Haught, ed., 2000 Years of Disbelief

[2] John Dewey, “How We Think”, 1909; from “Critical Thinking”, A. Fisher.

[3] (Televised and Print Media interviews with Sen. Harkin).

[4] From Fisher, Critical Thinking, An Introduction; Cambridge.

[5] From Jones and Wilson; An Incomplete Education, on miskatonic.org

[6] Ibid.