Axiom

ax•i•om* (noun)
in Mathematics, it is the starting point from which all theorems are logically derived, thus, by definition, an axiom cannot be logically derived from anything else. It is a statement that is accepted to be true without proof.
Origin: Greek (axioma = to deem worthy/to require)

There are two forms of mathematical axioms: Logical axioms and Non-Logical axioms.
A logical axiom are usually statements that are taken to be universally true (e.g. let x and y be real numbers; it then follows that x + y is also a real number). Non-logical axioms are taken to be defining properties (i.e. a statement defines a mathematical relationship, often used in setting the bounds of a theorem. e.g. x + y = y + x is the basic axiom of addition)


*I am not a mathematician, and have only studied math as much as a second-year student can, so my definition of Axiom is by no means binding; it is my loose understand as defined by several different sources I consulted; it is liable to be incomplete and incorrect.

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Today's vonerdword is the mathematical Axiom, used to define many things in mathematics. I have this in mind because the very way mathematics approaches the definition of an axiom is similar in the way in which science as a discipline is approached and how we, as the human species, deals with science, and as an extension, religion (yes, today's topic is going to be a little bit on the heavy side of things...).

This is at the top of my though processes at the moment because, as you may have seen, a friend of ours has recently posted a link (which I will reproduce here) to a site that cites a conversation between a professor (who is an atheist) and a student (who is religious). At first, I was rather apprehensive about reading this because science and religion is a very fragile topic, and is one that is likely to "rub people the wrong way," to use the colloquialism.

I did, nonetheless, have a gander at it and I will walk you through my thought processes and comment on it here, because I feel that it is a subject worth pondering and one that requires attention (many people may read through this and accept everything that is said to be through without evaluating the validity and substance the arguments hold, and thus may never come to their own conclusions). Please let me know what you think in a comment or in your next blog post; your thoughts are valuable to me.

SO: First of all, it would be helpful for you to click on the link above and read through the conversation yourself and form your own opinions before comparing them to mine. I can wait.

Have you read it yet?

Good. Let's begin with a play-by-play commentary, shall we?

Okay, so it begins with a professor calling out one of his religious students. Personally, I think the professor is really quite a douchebag and frankly quite rude... He takes on a "I'm gonna prove you wrong and you're going to sit there and take it because there's nothing you can do" type attitude, which already is something I have really big problems with. Quite honestly, it's not very mature of him to do so. The points he raises to argue the non-existence of a God are not all sturdy, in my opinion, for these reasons:

-"if God is good why does he let people die"
How are we to know why God does or does not do certain things? If this professor was thinking from an objective point of view, and if he was really interested in creating a strong argument, he would have attempted to deconstruct his arguments before using them. I argue this: if an almighty God exists, how can we, as imperfect humans, ever hope to understand the complexities of what God does or does not do?

-"how could God let things such as sickness, immorality, and hatred exist?"
This is an interesting point, because I myself am struggling with this issue. One of my greatest heroes is Sir David Attenborough, and once during an interview, he was asked if he believed in a God, and Sir David Attenborough's response was something to effect of this: "I cannot believe in an almighty God as long as he allows millions starving children in Africa, children who have done no wrong in the world, to die." It is a very
 pressing moral question to which I have yet to find an answer.

-"science says that you have five senses to identify and observe the world around you"
First of all, I HAVE MAJOR PROBLEMS WITH PEOPLE USING THIS ARGUMENT. The professor argues that "because we can't sense God, he doesn't exist." To this statement, I provide this argument: Science says nothing about what it cannot sense; it only deals with what it can measure and the data produced. Just because we haven't discovered an animal or other life in the universe, that doesn't mean it doesn't exist! Science says that because we have not discovered something, we can conclude that WE DO NOT KNOW IF IT EXISTS. WE ARE ONLY CONFIDENT IN THE KNOWLEDGE THAT WE DO NOT KNOW. WE CAN HYPOTHESIZE AND GUESS ABOUT THESE THINGS, BUT NOT KNOW FOR SURE.

Next, we see the student providing counter-examples to argue the existence of God. Frankly, I don't think this student is a science student, because I don't understand how his arguments form a cohesive proof, but I shall comment on the individual points anyways because I have a major bone to pick here.

-"there is no such thing as cold" and "there is no such thing as darkness"
I am hesitant to agree with this statement. Yes, it has been argued to me many times that cold does not exist because it is the absence of heat, but I argue that if this definition is adjusted, could it not be made into a measurable value? We measure heat because it is defined as how much energy moving particles have compared to a state of no-motion, being absolute zero. But could there then (theoretically) exist a point of maximum energy, the point where matter has absorbed so much energy that it ceases to be matter? Could you then measure "cold" as the amount of energy it needs to reach that point? If Heat is the difference between an amount of energy and no energy, could cold not be the difference between an amount of energy and total energy?

-"You are operating on a duality"
I find this quite interesting, because the student argues that life and death are not a duality, but his argument is flawed, in my opinion. He argues that death is "the absence of life." But I ask: Can something be dead if it was never alive in the first place? Secondly, How do you define living from non-living? This is a major debate in molecular and cellular biology. How does one define life from non-life? What measurable properties are there? My question is this: If I look at a rock, because there is an absence of life, is it dead? But if the rock is dead, does it not imply that it was alive and then died? Just because there is an absence of life, does it mean that something has died? This issue really depends on how these words are defined. If "dead"/"death" = "not living" then yes, the rock is dead, but you have created a duality - one is not the other, and vice versa. If you define "dead" as "something that was alive and is no longer living" then the rock is simply "non-living" but then the definition of "dead" and "alive" is still a duality that exists within a larger set of definitions (i.e. Something can be alive or not alive. If it is alive, it can die. Death is still something that is not alive, we have just added the condition that it had to be alive first).

Next, I totally do not understand the student's argument of "you assume there is a good God and a bad God." But is not God perfect and whole and the only perfectly good being? Is the student saying that God is not whole and perfectly good?
He argues that because the professor sees this duality of "good God bad God" he is viewing God as finite, but does the Christian view not say that God the only whole and good being in existence? How is this different from how the professor views the duality? That then defeats your argument, because he says that to be entirely good or bad is to be finite, which I disagree with. Furthermore, how is this relevant to the issue of measuring God (the thing he brings up in the very next sentence). Just because something is finite or infinite, doesn't mean that we can't measure it. In mathematics, infinite sequences and series are just that: infinite, but many calculations can be made to describe their properties.

Please point out the flaw in my thinking, but how is the argument of duality related to the existence of God? I may be mistaken, but all this student has done is proven that the professor is a douche and has not thought through his argument; is he perhaps suggesting that because the professor cannot grasp the definitions of "cold" "darkness" and "death" that he cannot also grasp the concept of God?

Evolution.
This stupid idiot totally did not just bring up the whole evolution issue.
"Have you ever seen evolution?"
YES. YES WE HAVE. SCIENTISTS HAVE OBSERVED EVOLUTION FOR CENTUREIES! EVEN BEFORE WE CALLED IT EVOLUTION HUMANS STILL MANIPULATED IT! DO YOU SERIOUSLY WANT ME TO PROVIDE YOU WITH A SOMEWHAT FULL ARGUMENT FOR EVOLUTION? YES? OKAY, TIME TO BRIEF YOU ON THE SCIENTIFIC PROCESS KNOWN AS EVOLUTION.

Evolution is a natural process. It is (loosely) defined as the change of a population over generations. It can be defined as the change in allele frequency of genes in a population. If the genotypes and phenotypes of a population changes from one generation to the next, the population is said to be evolving.

The process by which this is achieved is through genetics. At any one time, a mutation in the genetic DNA of an individual may occur. By cellular processes, this mutation, by definition, may cause a change in the protein that gene encodes. This, in turn, may cause this individual to have a different trait than other individuals of the population. This trait may help the individual survive better, or it may cause it to be handicapped. If it is harmful, then the individual is less likely to survive and less likely to pass on its genes. If the trait helps it survive better than the others, it has a better chance of surviving and reproducing. Because these traits are (usually) genetic, they are passed on from one generation to the next. This means that this individual's offspring will likely inherit this trait, and they will thus have a better chance surviving, reproducing, and passing on their genes. This deals with how populations change.

Over time, these changes can build up, and cause a population to change so much that it no longer resembles other populations that it used to resemble. This is how new species are formed.

There are many, many proofs of this.
Example 1: Darwin's Finches.
Darwin examined the finches that inhabited the Galapagos Islands. He noticed that they were all extremely similar and only had minor changes. He explained this with the following argument: The Galapagos Islands are very isolated at sea (known geographical fact: look at a map). This means that it will be difficult for animals to migrate there. Since the Galapagos are Islands formed by volcanic activity, when the islands were formed, no living creatures were there. The finches that live in the Galapagos must therefore have migrated from the mainland of South America, but since it is so far away, it is not likely to happen often. When the first finches arrived on the island, they were a population of one type of finch. Because there are many islands, the population split up and a sub-population colonized each island. Because each island is slightly different, a different trait will be more helpful on each island (eg. one island has trees that make hard nuts, and another has trees that makes fruit. A beak that is able to crack nuts will make finches more likely to survive because they can utilize the nuts as a source of food, but it will be useless on the island with fruit because there are no nuts). This will lead each of the populations to change in different ways, and over many generations, the different populations evolved into different species.

Experiments were conducted using Darwin's Finches in recent years to test for how quickly these species can adapt. One of the finch species was introduced to an island with another finch species, and the physical property of their beak size (which directly affects their diet and what they can eat) were measured over several generations. Almost immediately (in only one generation), because both finch species were competing for the same sources of food, each species changed to better survive: one species evolved smaller, stronger beaks that could crack seeds, while the other evolved larger, more robust beaks that could crack large nuts. This proved that the traits in a population/species can change over time.

Example 2: Medieval farmers used evolution in breeding sheep and cows.
Modern sheep and cows are very different from what they were several hundred years ago. In the medieval times, farmers noticed that cows which were larger and stronger bred calves that grew up to be larger and stronger than others. Same for sheep. Larger cattle and sheep meant that they would produce more wool and meat, and thus each animal would be more profitable, so they only let the largest, strongest cows and sheep breed. Over many years, this resulted in generally larger and stronger animals. If you compare these animals to their ancestors, they would be very different, and arguably would not be able to mate.

Example 3: Crops.
Many people do not realize that the crops of today (wheat, corn, potatoes, etc) are very very very different from their original forms. They have been bred by humans, just like sheep and cows, to bear larger fruit and more fruit than their wild ancestors. In fact, in some regions of South America, you are still able to find wild corn/maize, and the fruit they produce is very different from the fruit that we harvest and eat. We have influenced evolution to provide us with better food sources, and thus our populations of corn are different species of corn than wild corn, even though they used to be the same.

There are many, many, many more examples of this. Evolution is not an opinion; it is a natural process that is observable, measurable, and very real. Whether or not you choose to accept the proof and evidence is a different matter all together. People often refute the "theory of evolution" as "just a theory" without realizing that the word "theory" is used VERY differently than in common vernacular, just as how "aromaticity" is used in Chemistry very differently than in common vernacular. A scientifical /Theory/ is an a statement or set of statements that describe one aspect of the world for which there is a massive amount of evidence for. The Theory of Evolution is similar to the Theory of Gravity in its... well... gravity.

The next point the student makes which I disagree with is his argument of why the professor "has no brain." Just because we cannot directly measure it, doesn't mean that we can indirectly measure it by posing questions and examining the answers we get, and comparing them to known observations. Second of all, he makes the same mistake as the professor: Just because we can't prove that he has a brain, DOESN'T PROVE THAT IT DOES NOT EXIST. ALL WE CAN SAY IS THAT WE DO NOT KNOW. It is the Schrodinger's Cat problem all over again. And do you remember the answer to Shrodinger's Cat? The answer is: WE DO NOT KNOW THEREFORE IT BOTH EXISTS AND DOES NOT EXIST AT THE SAME TIME UNTIL THE MOMENT WE CAN REACH IN AND SEE FOR OURSELVES.

The professor then makes his final error. He should not have responded with "you'll just have to take them on faith" because NO STUDENT SHOULD HAVE TO TAKE ANYTHING TAUGHT IN A SCIENCE COURSE ON FAITH. THE WHOLE POINT OF SCIENCE IS TO RID DOUBT AND THE NEED TO TAKE THINGS IN FAITH FOR THE CONCLUSIONS BY USING FACTS AND LOGICAL ARGUMENTS THAT EXPLAIN THE CONCLUSION. For anything this professor teaches, he should be able to say "If you do no believe me, here are the data and arguments published in scientific literature that discusses this matter in order to come to this conclusion." Then, the student can review the material and see if they come to the same, or different conclusions. Students should be actively questioning the material they are taught in ANY course and should come to their own conclusions; they should not agree with everything that is taught right away because that is ignorant. Understanding the proofs and arguments for every conclusion is vital to understanding the course material, and it is good if you do not agree because you may either be missing.not understanding an important fact or argument, or you could have found a valid flaw in the current conclusions. NEVER should ANYONE take ANYTHING to be true without evaluating the validity of the statement.

Finally, I must say that I agree that Faith is what connects humans to God. The student did not create a very good argument for it; rather he argued that his professor was an illiterate jerk, but in doing so did not prove what I felt he was trying to prove. I felt that he was trying to disprove science, which is something that I cannot accept. I cannot see how Science and Faith cannot go hand in hand. If God created the world, and if Science describes the world, then is science not a product of God? Does not science strive describe the world that God has created and the miracles he performs here? The other thing is that Science deals with the Physical. It deals with how the world works, but it cannot (as of yet) deal with the metaphysical, and it probably never will. These are two separate entities that should be kept separate; Science should not prove nor disprove God, just as God should not disagree with Science.
I feel that in trying to disprove his professor, the student tried to disprove science, when he really should have been trying to separate science from religion. I guess I'm trying to say that I don't agree with the method he chose of arguing his case, but I agree with the case he was trying to argue, if that made any sense.

I think this is my main problem with this article: SCIENCE DOES NOT HAVE AN ISSUE WITH GOD, NOR DOES GOD HAVE AN ISSUE WITH SCIENCE (in my opinion). People need to stop trying to make science do something it isn't designed to do, and people need to realize that God and religion is a matter of faith and morality, which are things that cannot be realistically measured, nor can they be used to measure the world. Science and religion are relatively separate entities and should be kept relatively separate from each other.

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MIDTERMS ARE OVER (for now) CELEBRATION!!!!!

I finished my last midterm of October last night, Biology 200. IT WAS A JOKE. SO EASY. I'm pretty confident I did well. There were some questions that were interesting, but there was nothing to which I had no idea how to solve. I feel that the problems they asked did not require much cognition, and it felt more like a difficult high school exam than a university exam. I believe that university should challenge the way one looks at things, and should encourage and enforce the habit of making connections. Oh well. Easy mark for me.

I also got my Lab Exam marks back! Remember the NVP Bio Lab exam that I was freaked out about because it was hard last week? I GOT AN 86%!!! SO HAPPY!~ I can finally take a breather now =P All I have to do is study material, do a French Oral Presentation on Monday, write an essay for Biology for the following monday, AND THAT'S IT! I CAN FINALLY BREATHE FOR A BIT!

I seem to have survived this wave of midterms better than I did last year... I've got 95% (Fungi), 86% (lab exam), 88% (Math 1), 77% (Math 2), and 83% (OChem) so far. I'm certainly not complaining.

School is still hard but I enjoy it; it's fun learning about all these things. I'm glad I'm here, and I hope I can continue to be here. I hope everything at Trinity is going well! You mentioned that you had a lot of papers due, so I hope you managed to finish them and are happy with the end product. I admire you for being able to pursue a degree in English; I was never that good at arguing in essays at a university level (at least for literature; I pwned at the theoretical analysis we did in Engl 112).

Anyways, I'll leave you alone now. The length of the past few posts have been quite atrocious; I apologize. Next week I'll try to make something lighter in material and shorter in length... I'm glad that we're still keeping in touch this way though; it is very good for me and I hope you are benefiting from it as well.

I CAN'T WAIT TO SEE YOU TOMORROW! =D PLUS ONE! =D
CHAT VERY SOON,
~Tim~

PS - Since you missed Tuesday, perhaps sometime before the month is over you could make it up with a bonus post? Only if you have time! I don't want to over-load you with responsibilities less important than school and your life out at Trinity.