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Come Reason's Apologetics Notes blog will highlight various news stories or current events and seek to explore them from a thoughtful Christian perspective. Less formal and shorter than the www.comereason.org Web site articles, we hope to give readers points to reflect on concerning topics of the day.

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Thursday, February 23, 2017

What to Make of the New Seven Earth-Like Planets Discovered



The headlines were spectacular. Time Magazine pronounced "NASA Announces a Single Star Is Home to At Least 7 Earthlike Planets."1 Vox exclaimed "NASA has discovered 7 Earth-like planets orbiting a star just 40 light-years away."2 Even the official press release from NASA offered some tantalizing tidbits, noting that all seven planets of the TRAPPIST-1 system reside in the habitable zone necessary for life and it included artists' rendering of what the view may look like from one of these newly discovered sisters of earth.3

Certainly, the discovery of planets orbiting another star is an exciting one. The fact that the TRAPPIST-1 star is relatively close in astronomical terms (40 light years away) means the system is more easily observed by our telescopes; we can gather more data on the planets themselves. To find seven of them ups the chances that we may find water on them, too. But does this mean we've uncovered a bunch of earth-twins that are just ready to be populated by living organisms? Not by a long shot.

What do you mean "Earth-like"?

Since capturing eyeballs and clicks are the driving force behind both news organizations and sites like Vox, one should be a bit cautious before jumping to conclusions by just a screaming headline. When I saw this story, I was intrigued, but upon reading the details, certain terms don't carry the weight one may assume at first.

For example, both the Vox and the Time article called these planets "Earth-like" in their headlines. That will certainly evoke a picture in the minds of most casual readers, but what does Earth-like really mean? Both articles did unpack the term to mean a planet whose size is within a certain percentage of Earth's and is not too hot or too cold for water to exist somewhere on its surface without it being boiled away or perpetually frozen. Mars is within our solar system's habitable zone, while experts disagree about whether Venus qualifies or not.

But just having the ability for water to exist really isn't enough for life. The TRAPPIST-1 star is a much weaker star than our sun. As Hugh Ross explains, TRAPPIST-1 is very small and very weak, not putting out much heat at all. Thus, the planets are a whole lot closer to their star than the Earth is to the Sun, which locks them into a non-rotational position – one side always light and extremely hot while the other is perpetually dark and continually freezing cold.

According to Ross, only the "twilight areas" of each planet would be able to support liquid water. Ross then states "Only in the twilight zone boundary between perpetual light and perpetual darkness will surface liquid water be possible. This possibility presumes that for each planet the twilight edge will not move. Given how close the planets are to one another, it is inevitable that the twilight edge on each planet will move. Thus, realistically none of TRAPPIST-1's planets are likely to ever possess any surface liquid water."4 Of course, it hasn't even been proven the planets have an atmosphere yet.

Also, since these planets must be very close to their weak sun, their years are very short: it takes only about twenty days for the furthest of the seven planets to complete an orbit and only one and a half days for the closest! Knowing how crucial seasonal changes are to life on Earth, there's absolutely no chance of seasons for any of these planets. What's worse, the planets orbits and close proximity mean their gravitational pull will affect each other. The moon's gravity causes the tides on Earth and it is only one sixth the pull of the earth's gravity.* Imagine how an equally sized planet's gravity orbiting close by would affect the Earth. Ross concludes, "These periodic gravitational influences rule out the possibility of life on these planets."

Selling the Sizzle, not the Steak

The "earth-like" description of these planets in the articles is I believe a little misleading. All the outlets I read hyped the possibility of finding life on these planets while never mentioning the incredible difficulties any life would face on them. The Vox story is a good example:
The more Earth-like exoplanets astronomers find in the galaxy, the more they update their estimates of how many Earth-like planets could be out there. "For every transiting planet found, there should be a multitude of similar planets (20–100 times more) that, seen from Earth, never pass in front of their host star," Nature reporter Ignas Snellen explains in a feature article. And the more exoplanets there are, the more likely it is that life exists on at least one of them.5 (Emphasis added).
I highlighted that last line to make a point. While it is true mathematically that finding more planets can make the odds of finding life lower, it's a bit like claiming your odds for dealing four perfect bridge hands are lower the more shuffled decks you use. It's true but still beyond any reasonable explanation that someone will do so, whether you use a hundred, a thousand or a million decks. By obscuring the difficulties these planet offer for life and only highlighting the two or three possible similarities, these reports are selling the sizzle instead of the steak. There's much we can learn from this new discovery. Learning about extra-terrestrial life forming isn't really one of them.

References

1. Kluger, Jeffrey. "NASA Announces Trappist-1 Star Is Home to Earthlike Planets." Time. Time, 22 Feb. 2017. Web. 23 Feb. 2017. http://time.com/4677103/nasa-announcement-new-solar-system/.
2. Resnick, Brian. "NASA Has Discovered 7 Earth-like Planets Orbiting a Star Just 40 Light-years Away." Vox. Vox, 22 Feb. 2017. Web. 23 Feb. 2017. http://www.vox.com/2017/2/22/14698030/nasa-seven-exoplanet-discovery-trappist-1.
3. "NASA Telescope Reveals Record-Breaking Exoplanet Discovery." NASA. NASA, 22 Feb. 2017. Web. 23 Feb. 2017. https://www.nasa.gov/press-release/nasa-telescope-reveals-largest-batch-of-earth-size-habitable-zone-planets-around.
4. Ross, Hugh. "Earth's Seven Sisters: Are They Really Similar?" Reasons to Believe. Reasons to Believe, 23 Feb. 2017. Web. 23 Feb. 2017. http://www.reasons.org/blogs/todays-new-reason-to-believe/earths-seven-sisters--are-they-really-similar.
5. Resnick, 2017.
* This sentence has been corrected. It originally read "The moon's gravity causes the tides on Earth and it is only one sixth the mass of the earth."

Tuesday, February 21, 2017

The One Sexual Orientation No One Advocates For



I recently wrote that today's western culture has become so craven we have elevated our sexual appetites above our desire for a civilized society. And I'm not simply talking about suggestive advertisements or sexual references in our entertainment. As I noted there, the "pelvic issues," (homosexuality, transgenderism, abortion) have consumed an inordinate amount of our politics and popular discussion.

The proponents of LGBT rights frame their demands as issues of civil rights.1 In so doing, they make the claim that sexual attraction is considered a viable way of understanding another individual, something that is "inherent and immutable."2 Such language implies sexual desires and preferences are what define you. They constitute an essential part of who you are.

Inherent and Immutable Sexual Desires

If sexual orientation and desire are crucial to understanding who an individual is and if it is true that such desires are inherent and immutable as the HRC's definition states, then all sexual orientations should be accepted and championed equally. But there's one sexual orientation I've not heard any of the pro-LGBT groups bolster and that is the occuposexual.

What is an occuposexual? You won't find it by Googling the word, since I just coined the term myself, but the orientation has a long history and is well-represented online. An occuposexual is someone who is sexually attracted to those already committed to another in a relationship. They are drawn to people who are already relationally occupied.

Before you dismiss this as not a real sexual orientation, you should look at the facts. Occuposexual orientation is real. Dr. Valerie Golden wrote in Psychology Today how recent studies have found "90 percent of single women were interested in a man who they believed was taken, while a mere 59 percent wanted him when told he was single." Certainly, the attraction would differ in degree and not all those women would act on their desires, but Alfred Kinsey's heterosexual/homosexual scale makes the same distinctions.3 This scale was also used to justify the "normalcy" of homosexual desires.

The Desire of Occuposexuals is Like Any Other Sexual Desire

Occuposexuals themselves have written about their desires, using language that sounds just the same as other sexual orientations. In this article entitled "I am Dating a Married Man", a twenty-something woman admits that she is simply attracted to married men. She explains her attraction is because "he's already involved with somebody else. In many cases, the Other Woman wouldn't be turned on by the guy if he wasn't. The fact that he's ‘taken' is proof of his desirability. The fact that another woman's husband wants her is proof of hers."4 Everyone from news outlets to Women's' Health Magazine has articles on the subject.

You may be quick to dismiss such an orientation as regular people who just aren't in control of their predilections. But how can you make that judgment? We know occuposexuality occurs in nature, as the article Infidelity Common Among Birds and Mammals, Experts Say clearly proves. Like the lady in the ‘I am Dating a Married Man" article explains, she knows that what she's doing isn't right, but she can't help herself. She's gone from one married man to another even though she knows it's wrong and it's trouble. In fact, in any type of objection that occuposexuality is somehow different from other sexual orientations fails by using the very same arguments the pro-homosexual community has used for decades in their advocacy.

So Why Is No One Championing the Occuposexual?

You may notice something unique, though, about their occuposexual. While groups like GLAAD and HRC are quick to demand rights for their constituencies, who they classify as "sexual minorities," no one is championing the occuposexual's rights to come out of the closet, to express their sexuality as they feel it, or really to even exist. Why not? The answer is easy. No one wants their significant other snatched from them by an occuposexual. They believe even though this is a sexual desire, one that's real, it is ultimately a desire and the occuposexual doesn't have to act upon it. They believe the person who holds that desire is responsible for his or her actions, even if that means seeking out help to properly deal with those inherent desires. Plus, occuposexuality will never be a big winner in the public's opinion.

But all of this makes my point. It's easy to justify desires when others cannot see the serious impact they have on a society. It's easy to assert the idea that sexual orientation is a fundamental function of who you are and not a secondary function. I say the human being is not whatever his or her sexual attractions may be. Human beings are too valuable to be reduced to their sexual desires. That's true for the occuposexual as well as any other form of sexual orientation. By elevating sexual identity to something inherent and immutable, one must make room for the occuposexual to find his or her fulfillment in sexual expression, too. Are you willing to give up your mate or are you just a bigoted occupophobe?

References

1. Becker, John. "LGBT Rights Are Civil Rights." The Huffington Post. TheHuffingtonPost.com, 23 Mar. 2012. Web. 21 Feb. 2017. http://www.huffingtonpost.com/john-becker/lgbt-rights-are-civil-rights_b_1368381.html.
2. "Sexual Orientation and Gender Identity Definitions." Human Rights Campaign. Human Rights Campaign, n.d. Web. 21 Feb. 2017. http://www.hrc.org/resources/sexual-orientation-and-gender-identity-terminology-and-definitions.
3. "The Kinsey Scale." The Kinsey Institute. The Trustees of Indiana University, 2017. Web. 21 Feb. 2017.
4. DOLCE84. " I Am Dating a Married Man Story & Experience." The Experience Project. The Experience Project, 5 Sept. 2007. Web. 21 Feb. 2017. http://www.experienceproject.com/stories/Am-Dating-A-Married-Man/54661.

Wednesday, February 15, 2017

The Problem of Living in a Crotch-Driven Culture



One can tell a lot about the value of a society by what occupies its attention and effort. The Greeks were thinkers, who spent a significant amount of time developing philosophy and logic. They saw value in the mind, believing that clear thinking was the key to understanding the wider world.

In the 21st century, it's obvious that our culture emphasizes the crotch over the mind. What are the "hot topics" glut our headlines and dominate our conversations? It's sex. Sex is inescapable today. Our media choices are drenched with it and our politics are obsessed with it. That's why the "pelvic issues" are getting so much attention. Homosexuality, transsexuality, abortion, birth control are the focii of recent political protests, where adults will actually dress up as genitals—dress up as genitals!—in order to demand… what exactly? More availability for consequence-free sexual experiences?

Decivilizing Civilization

What does it mean to be civilized? It isn't our infrastructure or our technology that civilizes us. It isn't creating new ways to manufacture things or making it easier to do the mundane tasks life requires. For when we talk of someone being civil, we are commenting on the character of the individual in question. If someone is insulting or brutish, that person is uncivil. They would rather lash out with their feelings than recognize the humanity of the other individual. The three R's of reason, regard, and reverence are what make us human and distinguish us from animals.

Thus, civilization is predicated on the fact that human beings are not slaves to their natural impulses. Just because one feels an urge to copulate doesn't mean one should immediately attempt to do so any more than just because one passes by some delectable morsel one should immediately attempt to eat it. It may not be yours. It may not be the right time, perhaps a business meeting where the food is laid out for the meeting's conclusion or a wedding where the bride and groom should be served first. To give license to on one's base desires is to show contempt for others and to be uncivil.

Identity from a Crotch-Driven Culture

However, in our crotch-driven culture, we now seek to celebrate the base desires. In fact, people use their base desires as their primary form of identity. A person will say he or she identifies as homosexual heterosexual, bisexual, transsexual, or whatever the most recently vogue sexual predilection may be. My question is why in the world would anyone want to have their bedroom activities be highlighted as their primary attribute? How is that a good thing for elevating the understanding of ourselves as human beings?

All of this doesn't mean I am taking some kind of "don't ask, don't tell" approach. What I'm saying is that previous generations saw sexual drives and desires as things people did, not who people were. The concept of homosexuality as it is used today is actually very new. It shifts the focus from the act to the attraction itself. But doing so tells us nothing of the rightness or wrongness of homosexual acts. There are base desires that people have where it may be sometimes wrong to act upon them (such as above) and other desires where it is always wrong to act upon them. Placing the emphasis upon the fact that one has the desire gives us no information as to whether one should act upon them or not. But we know that to be civilized would mean that one must be able to control oneself in spite of those desires.

To identify as homosexual or heterosexual or whatever strikes me as elevating the base instincts one has to a status they shouldn't occupy. Yet, that seems to be exactly what Pride parades, genital costumes, and such are seeking to promote. Why would you want me to think of the primary driver of your life as satiating an urge that most people accomplish in half an hour once or twice a week? It is decivilizing. (And if your first reaction to that prior sentence is to mock the frequency or duration, then you're proving my point—that's the reaction of pre-pubescent boys, not thoughtful adults.)

I don't identify as heterosexual; I'm simply attracted to people of the opposite sex. I identify as a rational, civilized human being who will reserve the details of my most intimate moments for personal rather than public consumption. I seek to view other people in the same way. Those campaigning for the pelvic issues aren't advancing civilization, they're regressing from it.

Image courtesy Gnhn. Licensed via the Creative Commons 3.0 Attribution Share-Alike CC BY-SA 3.0 license.

Friday, February 10, 2017

Does Religion "Fly You Into Buildings"?


Physicist and anti-theist Victor Stenger famously claimed "Science flies you to the moon. Religion flies you into buildings." This kind of throwaway line is standard fare for the new atheist types and is often repeated via memes shared on social media sites. Stenger isn't the only one who thinks religion is a way to manipulate others into doing immoral acts. Sam Harris claimed "One of the most pernicious effects of religion is that it tends to divorce morality from the reality of human and animal suffering. Religion allows people to imagine that their concerns are moral when they are not."1

I'm not sure how Harris concluded that religion divorces morality from suffering. If he were a true student of world religions he would recognize that the question of human suffering is the primary focus of most faiths. Hindus seek to be come closer to the divine, eliminating the suffering associated with the cycle of reincarnation. Buddhists teach balance to avoid pain and suffering. Islam holds suffering as Christianity focuses on eliminating suffering by eliminating sin and its consequences. While I don't agree with the underlying assumptions of other faiths, it is disingenuous to say that religion divorces morality from suffering. The problem of human suffering is front and center in religious faith.

What about Jihadists?

 So how do we explain the ISIS or Al Qaeda suicide bombers then? Isn't it obvious that such horrendous acts are religiously motivated? I would say it's true only in part. Islam is a faith that offers Muhammad as its exemplar—the model Muslim to which all others should aspire. Muhammad was a warrior who slaughtered innocents and the famous "sword verses" of the Qur'an commands the faithful to "slay the idolaters wherever you find them, and take them, and confine them, and lie in wait for them at every place of ambush." (Sura 9:5) and "When you encounter the unbeliever, strike off their heads until you have made a great slaughter among them" (Sura 47:4). Also, the Qur'an promises a reward to the warrior who dies in his fight for Islam: "So let them fight in the way of God who sell the present life for the world to come; and whosoever fights in the way of God and is slain, or conquers, We shall bring him a mighty wage" (Sura 4:74).

Because Islam offers both the commands of the Qur'an and the example of Muhammad, it allows for jihadists to kill themselves while killing the enemy in the name of martyrdom. But that doesn't mean suicide terrorism is the first resort of Muslims. In fact, it turns out that suicide terrorism isn't a historically popular strategy for followers of Islam. Robert Pape in his book Dying to Win: The Strategic Logic of Suicide Terrorism notes that there were no suicide attacks by Muslims or any other groups from 1945 to 1980. From 1980 through 2003, Pape catalogued 315 suicide terrorism campaigns around the world with 462 individual suicide terrorists.2 Pape notes that "every suicide campaign from 1980 to 2003 has had as a major objective –or as its central objective—coercing a foreign government that has military forces in what they see as their homeland to take those forces out." 3Pape concludes, "The bottom line, then, is that suicide terrorism is mainly a response to foreign occupation."4 So, politics and power are the real motivation for terrorist campaigns. It thrives in Islam because the belief system doesn't contradict its use.

What about the Destructive Power of Science?

The biggest problem with Stenger's quip is it is so self-selective. It gives a rosy picture of science by the example of one of our greate3st achievements and then contrasts it with one of our greatest horrors. But it isn't "science" that flies us to the moon. It's human beings who do that. Science allows human beings to understand thrust and gravity. It is a tool to help us accomplish whatever goals we have. Humans used science to develop the planes that Stenger seems to be so worried about, but he doesn't mention that. We use science to construct better weapons, too, producing some of them most incredible destructive powers on earth. Without science, we would never have had a Hiroshima or Nagasaki.  And without religion, we would never have a Mother Theresa or a Father Damien.

The Golden Rule and the concept of the Good Samaritan find their origin in Christianity.  Dr. Alvin J. Schmidt explains that it was the teachings of Jesus that "elevated brutish standards of morality, halted infanticide, enhanced human life, emancipated women, abolished slavery, inspired charities and relief organizations, created hospitals, established orphanages, and founded schools."5

Harris and Stenger's comments not only show their bias, but they are demonstrably wrong. They have simply created straw men in order to easily knock them down. Perhaps if they showed a little more Christian charity toward those with whom they disagree, they wouldn't be so nasty and could see things a bit more clearly.

References

1. Harris, Sam. Letter to a Christian Nation. New York: Vintage, 2006. Print.
2. Pape, Robert Anthony. Dying to Win: The Strategic Logic of Suicide Terrorism. New York: Random House, 2005. Print. 14-16.
3. Pape, 2005. 42.
4. Pape, 2005. 23.
5. Schmidt, Alvin J. How Christianity Changed the World. Grand Rapids: Zondervan, 2008. 8.

Wednesday, February 08, 2017

Atheists: Thor is not a Rational Substitute for God



Yesterday, I responded to a common atheist claim that one cannot prove a universal negative. But can one really prove that something does not exist, especially when that thing is mystical or other-worldly? For example, one atheist responded to the idea that a personal God was the best explanation for the beginning of the universe with "I think Thor is the best explanation. My claim isn't falsifiable." He seems to think that by invoking the name of a Norse god instead of the Christian God he has made an equally valid claim, but he hasn't. Of course the claim that Thor is responsible for the creation of the universe is falsifiable. Let's see how.

The Properties and Attributes of Thor

How do you identify a person? If you send your spouse to pick up your old friend at the airport, whom they've never met, you will describe that person to them. You may say, "My friend's name is Dan. He's 5'9", dark hair, mustache, and will be wearing a black coat carrying a green suitcase. These attributes help identify Dan. Certainly, they aren't exhaustive, but by providing a description to your spouse, you are helping your spouse eliminate a great number of other individuals coming out of the airport. The right person to place in your car must have at least these attributes.

When our atheist invokes the name Thor instead of God, what does he mean? Is he pointing to the same being under a different name? No, because the Thor and Yahweh, the God of the Bible, have different attributes. For one thing, Thor is not eternal. He is the son of Odin and Jord, other Norse gods.1 Norse gods can and do die and Thor is capable of dying. Thor also must experience the passage of time.  As Tolkien states, "In Norse, at any rate, the gods are within Time, doomed with their allies to death. Their battle is with the monsters and the outer darkness. They gather heroes for the last defence."2  Notably, Thor isn't all powerful. In "The Lay of Thrym" from the Poetic Edda, Thor loses his hammer to the lord of the giants who has hidden it from him and Thor is forced to pretend to be a bride in order to retrieve it.3 In the poem, Thor is presented as an exaggerated human, who eats and drinks, but is a material entity.

The God of the Bible holds none of those limitations. He is eternal and everlasting, sitting outside of time. He is all powerful. He cannot be killed and he cannot be forced to do something or have a foe who overpowers him. Yahweh is definitely not Thor.

Why Thor cannot create the universe

While it's clear that Yahweh and Thor are different beings, it is also because of Thor's limitations that we can falsify the claim that Thor is responsible for creating the universe. When we seek to answer the question of the universe's beginning, we are trying to explain the origin of all material existence, of space itself, and of time. Why there is space-time and matter are what needs explaining. However, Thor cannot be the explanation for all matter space and time since Thor himself is material, is subject to time, and has a beginning. He sits within a spacial dimension, as the loss of his hammer (hidden "eight leagues deep in the earth") indicates. Therefore, Thor cannot be the explanation of the universe for Thor, if he exists, is part of the universe that needs explaining! The atheist's claim is clearly falsifiable using the basic rules of logic. Any attempt to change Thor's attributes b the atheist would mean that we are no longer talking about Thor, just as any attempt by my spouse to look for a clean-shaven man who is 5'11" would mean she's no longer searching for my friend.

It is reasonable to ask the questions "Why is there something rather than nothing?" It is reasonable to ask "How did all this get here?" It is not reasonable to think invoking Thor is an equally viable explanation to the Christian God. To answer such questions with "Thor" is clearly to not answer them at all and those who wish to be taken seriously should think a little harder before doing so.

References

1. "Thor." Encyclopedia Mythica. 2017. Encyclopedia Mythica Online. 08 Feb. 2017 http://www.pantheon.org/articles/t/thor.html.
2. Tolkien, J. R. R. Beowulf: The Monsters and the Critics. Folcroft, PA: Folcroft Library Editions, 1936. Print. 26.
3. "The Lay of Thrym." translated by D. L. Ashliman. Professor D. L. Ashliman. University of Pittsburgh, 2009. Web. 08 Feb. 2017. http://www.pitt.edu/~dash/thrym.html.

Tuesday, February 07, 2017

How to Prove the Nonexistence of Something



Atheists commonly claim that they bear no burden of proof since one cannot prove a negative. A couple of years ago, I debated Richard Carrier on the question "Does God Exist?" Given this was a question and not a proposition, each party bears an equal burden of proof in asserting his claim; I must provide evidence for why I believe God exists and Carrier must provide evidence for why he believes God does not. Yet, a lot of atheists felt that I should shoulder the burden is such a debate. "How do you prove the non-existence of something? That's ridiculous" exclaimed one commenter. In fact, proving universal negatives is important, and something we do all the time in other contexts.

The idea that a universal negative is unprovable is what Steven D. Hales calls "a principle of folk logic," not rigorous thinking. Hale writes:
Among professional logicians, guess how many think that you can't prove a negative? That's right: zero. Yes, Virginia, you can prove a negative, and it's easy, too. For one thing, a real, actual law of logic is a negative, namely the law of non-contradiction. This law states that that a proposition cannot be both true and not true. Nothing is both true and false. Furthermore, you can prove this law. It can be formally derived from the empty set using provably valid rules of inference. (I'll spare you the boring details). One of the laws of logic is a provable negative. Wait… this means we've just proven that it is not the case that one of the laws of logic is that you can't prove a negative. So we've proven yet another negative! In fact, ‘you can't prove a negative' is a negative—so if you could prove it true, it wouldn't be true! Uh-oh.1
Hale goes on to explain that any proposition that is stated as a positive (i.e. "God exists") can also be restated as a negative ("it is not true that God doesn't exist.")

Understanding What We Mean by Prove

I agree with Hale that a lot of misunderstanding isn't in what counts for or against evidence, but a misunderstanding of what the word prove actually means. It seems that a lot of atheists mean prove in an incontrovertible sense, meaning something that is 100% certain. But assuming one must provide complete certainty before believing a proposition is itself illogical. Imagine you have a nasty infection but refuse to receive penicillin because no one can prove with 100% certainty it will be effective for you. Is such a stance rational? Of course not.

Hale offers the example that when we eat our lunch, we assume it will be nourishing and not deadly. We use our inductive reasoning to make that conclusion and we are justified in calling it knowledge, even if there are outlier examples of people being poisoned.

Because Christians argue inductively for God, this is the kind of proof they offer. One can similarly argue inductively for the non-existence of God, just as one can for the non-existence of invisible pink unicorns, like I've done here. So, asking for proof of God's non-existence is not ridiculous. It is actually very rational.


References

1. Hales, Steven D. "Thinking Tools: You Can Prove a Negative." Think 4.10 (2005): 109. Web. 7 Feb. 2017.  https://departments.bloomu.edu/philosophy/pages/content/hales/articlepdf/proveanegative.pdf

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