Proving A Universal Negative: An Omniscient AND Free-willed God?

 "Fight and kill the disbelievers wherever you find them, take them captive, harass them, lie in wait and ambush them using every stratagem of war."
-(Qur'an) Sura 9:5

P1: Assume there exists an entity X which has the property of total omniscience.

P2: Total omniscience is the property by which an entity knows all things that are true, ever were true and ever will be true.

C1: If entity X believed something in the future to be true, it would necessarily be true (from P1 and P2).
P3: Assume there exists a being B.
C2: If entity X believed that being B would take some specific action, it would necessarily be true that this being would take this action (from C1 and P3).
P4: Free-will requires having the ability to choose options other than the one actually chosen.
C3: If entity X believed that being B would take some specific action, this being would have no choice but to take that action, as it must satisfy the prediction of entity X (from C2).
C4: Being B does not have the ability to make another choice, as this would contradict the necessarily true knowledge that entity X has (from C1 and C3).
C5: No being has free-will (from P4 and C4).
P6: All persons are beings.
C6: No person has free-will (from C5 and P6).
P7: God is a being.
C7: God does not have free will (from C5 and P7).
C8: If entity X exists, no beings, including God, can have free will (from P1, C5 and C7).
C9: If there exists any being B which has free-will, entity X cannot exist (contrapositive of C8).
C10: There cannot exist both a being with free-will and a being with total omniscience (from C8 and C9).

This means that even if we are to assume the existence of a god, we are left with only three possibilities for our world: a world in which there are no beings with omniscience or free-will, one in which there is an omniscient being but no free-will, or one in which one or more beings have free-will, but there are no omniscient beings.

Case 1: God is omniscient, but there is no free-will


If this is true, then God doesn't really control his own actions, nor does anyone else. There are many implications to this; for one, if God isn't truly making the decisions to do anything, does he really deserve to be worshiped? If no one has control over their actions, is is morally just to punish to reward anyone based on actions when they could not choose to do otherwise?

Case 2: There is free-will in the world


In this case, God cannot be omniscient, and therefore he can make mistakes. He could've made mistake upon mistake, because he may have the same amount of information as we do. In this case, God cannot know the future, and therefore every time he created something or did something on Earth, he very possibly screwed a lot up. In fact, perhaps the idea of "Intelligent Design" should be re-named "Unintelligent Design." If this god exists, he made it so we breathe through the same tube we eat with, giving us the ability to choke. He combined muskrats and ducks to give us the platypus, the most awkward animal ever and the only non-echidna mammal that lays eggs, and he gave humans the appendix, an organ which serves humans absolutely no purpose. Additionally, this means that what this god declares may be wrong, so the things he orders are quite possibly very wrong.

Case 3: Their is neither free-will nor and omniscient being


See above

Conclusion


There is, of course, the very real possibility that no god exists, in which case free-will seems likely. Regardless  of whether or not a god exists, however, this holds true. A universe which contains an omniscient being cannot also have beings with free-will. Next time you hear someone say that their god is omniscient, ask them if they think he can even choose his own actions!

russellsteapot.com

Proving a Universal Negative: Aristotle's Principle of Non-contradiction and Transcendence vs. Omnipresence

"If a damsel that is a virgin be betrothed unto an husband, and a man find her in the city, and lie with her; Then ye shall bring them both out unto the gate of that city, and ye shall stone them with stones that they die; the damsel, because she cried not, being in the city." (If a woman does not cry out loud enough for someone to hear her while she is being raped, she is to be stoned to death.)

-Deuteronomy 22:23-24

This should hopefully be a short post. A long time ago, back before disco was popular, there was this dude named Aristotle. He figured out that you can't both be something and not be that same something at the same time, meaning the properties you have can't contradict themselves. For example, you can't be a married bachelor, because the term "bachelor" requires that you not be married. You cannot be both married and not married at the same time (I'm sure there are ways around this...don't bring them up ahaha). The point is, he realized that you can't have property A and also not have property A at the same time. This was titled "Aristotle's Principle of Non-contradiction" and he gets all kinds of credit for something that should be obvious. This does actually provide an important premise in disproofs of certain gods, however. For example, God is often referred to as "transcendent" and "omnipresent," however it can be shown that these two properties are mutually exclusive. That is, a being cannot satisfy both conditions, and therefore a god that is both transcendent and omnipresent cannot exist.

P1: If God exists, then he is transcendent (i.e., outside space and time).
P2: If God exists, then he is omnipresent.
P3: To be transcendent, a being cannot exist anywhere in space.
P4: To be omnipresent, a being must exist everywhere in space.

C1: Hence, it is impossible for a transcendent being to be omnipresent (from P3 and P4).
C2: Therefore, it is impossible for a transcendent omnipresent God to exist (from P1, P2, and C1).

This is a mostly trivial example, not very earth-shattering, but it is a good example to illustrate the Principle of Non-contradiction. A being cannot be simultaneously everywhere in space and nowhere in space and time/outside of space and time. Whether you are a theist or an atheist, this holds true. Whether you are a theist or an atheist, next time you hear someone say their god is both omnipresent and transcendental, call them on it!

qwantz.com

Proving a Universal Negative: Is It Possible?

"And in that day, seven women shall take hold of one man, sayingy: [...] let us be called by thy name to take away our reproach."
-2 Nephi 14:1 (Book of Mormon)

A universal negative is a statement of the form "There exists no object or entity 'X' which satisfies condition 'Y'." It seems like a fairly simple statement to make, but as it turns out statements of this form are extremely difficult, in some cases impossible, to prove (for those of you who have read my first two blog posts, this is why gnosticism comes with the burden of proof).

Take the following example, where object 'X' is a unicorn and condition 'Y' is existence in the universe. There is no possible way to search through the universe an prove the nonexistence of unicorns, but do you believe they exists? No, you most likely do not. This is where we get into "reasonable doubt." You have never seen a unicorn, and there have never been any reliable historical sightings recorded of a unicorn sighting, and since you have never been presented with evidence of its existence, you do not accept its existence to be a true claim. It is unlikely, however, that you ever have said, "Unicorns don't exist and I can prove it!" Rather, it is more likely for you to have said, "No, I do not believe in unicorns, but if you show me one, obviously I will be convinced!"

I can't claim to be able to disprove the existence of certain things, like unicorns, but other things can be proven to not exist. According to Aristotle's law of Non-Contradiction, a statement about an object cannot be both true and untrue at the same time. For example, I can 100% positively say that there is no such thing as an invisible pink unicorn. The definition of invisible is that it cannot be seen, and pink is a color which, by definition, requires visibility. It is not possible for such an entity to exist, as its own identity contradicts itself. Another example could be a spherical cube. Cubes have eight vertices by definition, and spheres have none. No matter how long you mess around with Play-Doh and no matter how far you look in the universe, I can positively say that this entity does not and cannot exist, because its properties are such that, were it to exist, its own attributes would contradict themselves, thereby proving this object could not possibly exist.

pixdaus.com

Inductive Versus Deductive Logic and Cum/Post Hoc Ergo Propter Hoc

"Joseph said unto his father: O my father! Lo! I saw in a dream eleven planets"

-Surah 12:4

Despite the frequency with which these terms are used, a lot of people don't really understand what is what. In fact, Sherlock Holmes has the ever-well known reputation for being a master of deductive reasoning, when it was in fact inductive reasoning that he used to solve various mysteries. Similar words, but drastically different meanings.

Deductive Logic and Reasoning:


Deductive logic is when you create a series of premises which then, without doubt, lead to a conclusion. This conclusion, if the premises are true, is inherently true. This is the form of logic used in formal mathematics; axioms make up the most basic premises, and are accepted as true. When a mathematician follows a series of steps, each building off of the previous, new formulas and proofs are created. Once something is proved in math, since it is shown to be true (as it is based off of entirely true premises), it is then accepted to be true universally. . A classic example of deductive logic is as follows:

P1: Socrates is a man.
P2: All men are mortal.
C1: Socrates is mortal.

If the two premises are true, then the conclusion is undeniably true, as it logically follows from the premises. Socrates is a man, and if all men are mortal, then by definition Socrates is mortal. No assumptions are made to connect the premises to the conclusion (although, as we will see, P2 was actually based upon inductive reasoning itself).

As a side note, the mathematical form of proof by induction is, in fact, deductive logic.

Inductive Logic and Reasoning:


Inductive logic is when you draw generalized conclusions from a collection of specific observations. What does this mean? Take, for example, the case of duct tape. For many underprivileged people, the only duct tape available to them is silver. It might seem reasonable to them to assume that, since they have only ever seen silver duct tape, duct tape is only made silver. Most of us, however, know this is not the case (this is a form of the Black Swan fallacy, which I will discuss in a later post). This presents the key issue with inductive logic; you are forced to make assumptions that could very likely turn out to be untrue. Another example, in syllogism form, is the basis for one of our premises above (note also that this and argument from ignorance, which I will also be making a post about):

P1: All things that die are mortal.
P2: Every man in recorded history has died.
C1: Therefore, all men are mortal

This clearly seems like a justified conclusion, and yes, induction is important and often true, though at the same time it often leads to false conclusions, as in the below example (note the argument from analogy):

P1: Every man is an animal.
P2: Every horse is an animal.
C1: Every man is a horse.

Because of the very nature of inductive logic, it cannot provide any proof, in any situation. The most inductive logic can do is provide evidence in support of something.

Correlation Does Not Imply Causation:


This is a fallacy which many people are subject to at one point or another. Whether this be with respect to lucky underwear, prayer to various gods, or shoe sizes affecting handwriting, they all are guilty of committing either the fallacy of cum hoc ergo propter hoc (at the same time as this therefore because of this) or post hoc ergo propter hoc, which translated literally means "after this therefore because of this." It bases itself on the assumption that because two things consistently occur together or because one thing often follows another, the first is the cause of the second.

As an example, there was once a teacher of students from grades 1-8 who graded a lot of writing work. What he noticed was that there seemed to be a correlation between the shoe size of the student and the neatness of his handwriting. He compiled a list of students' shoe sizes and gave them ratings based on the neatness of their handwriting, and found that the larger the shoe size, the neater the handwriting. He then concluded that big feet cause neat handwriting. He fallaciously assumed that one was the cause of the other, when most likely it was simply because, as a person gets older, their feet grow and their handwriting generally improves. This could be attributed to the cause of both, and so a correlation will inevitably exist. This is an example of inductive reasoning gone wrong. 


Another example could be the following, cited from With Good Reason by S. Morris Engel:

"More and more young people are attending high schools and colleges today than ever before. Yet there is more juvenile delinquency and more alienation among the young. This makes it clear that these young people are being corrupted by their education."

This is a post hoc explanation for the rising crime rates. A correlation is seen between college students and delinquency, and therefore one is deemed the cause of the other, without taking the rising population into account. When two thing appear to have a relationship, be careful to assume that one is not causing the other, as this often leads to false conclusions.

xkcd.com