Tag Archives: Logic

Self-refuting statements defined and some common examples

A conflict of worldviews
A conflict of worldviews

A common thing that I see is people trying to wall off arguments they don’t like by stating a slogan, like “you shouldn’t push your moral rules on other people” or “that’s true for you, but not for me”. Those slogans are meant to get the person out of having to be reasonable about respecting moral obligations, or having to consider how the world really works when choosing what to do.

Here is a fine article by Aaron, who writes at Apologetics Junkie.

Excerpt:

A self-defeating (or self-refuting) statement is one that fails to meet its own standard. In other words, it is a statement that cannot live up to its own criteria. Imagine if I were to say,

I cannot speak a word in English.

You intuitively see a problem here. I told you in English that I cannot speak a word in English. This statement is self-refuting. It does not meet its own standard or criteria. It self-destructs.

The important thing to remember with self-defeating statements is that they are necessarily false. In other words, there is no possible way for them to be true. This is because they violate a very fundamental law of logic, the law of non-contradiction. This law states that A and non-A cannot both be true at the same time and in the same sense. For example, it is not possible for God to exist and not exist at the same time and in the same sense. This would violate the law of non-contradiction. So if I were to say, “God told me He doesn’t exist” you would see intuitively the obvious self-refuting nature of this statement.

Aaron goes on to explain how to deal with self-refuting statements in the article.

Here are 20 examples of self-refutation, just to encourage you to click through and read it:

1. There is no truth.

2. You can’t know truth.

3. No one has the truth.

4. All truth is relative.

5. It’s true for you but not for me.

6. There are no absolutes.

7. No one can know any truth about religion.

8. You can’t know anything for sure.

9. You should doubt everything.

10. Only science can give us truth.

11. You can only know truth through experience.

12. All truth depends on your perspective.

13. You shouldn’t judge.

14. You shouldn’t force your morality on people.

15. You should live and let live.

16. God doesn’t take sides.

17. You shouldn’t try to convert people.

18. That’s just your view.

19. You should be tolerant of all views.

20. It is arrogant to claim to have the truth.

Have you ever heard any of those? It’s amazing how often I hear statements like that when discussing interesting things like moral issues and politics with young people. The trick to being prepared to answer these is to learn lots of them. Then you recognize them when you hear them.

Add yours in the comments!

Christians should support natural marriage because it protects children from adult selfishness

A family praying and reading the Bible
A family praying and reading the Bible

I have been following Katy Faust’s work on Twitter. She runs the organization “Them Before Us”. She fights laws and policies which allow adults to put their desires above the needs of children. And especially a child’s need for a relationship with his or her mother and father. In a recent article for The Federalist, she takes on a Joshua Harris, who is attacking traditional Christian moral values.

She writes:

In a recent interview, newly ex-mega-church pastor Joshua Harris and author of the 1990s best-seller “I Kissed Dating Goodbye” remarked that the support President Trump has received from the evangelical community has been “incredibly damaging to the gospel and to the church.” I’d wager Harris is projecting something fierce.

In August, Harris announced that he and his wife Shannon were divorcing, that he no longer considers himself a Christian, and that he regrets “standing against marriage equality.” Just in case the point was lost on any of us, he followed up his announcement by posting a picture of himself eating a rainbow donut at the Vancouver Pride parade.

It’s no coincidence that Harris reversed himself on biblical teachings on sex and marriage while abandoning the core tenets of the faith.

The denial of sexual and marital norms by believers is often adjacent to a rejection of the core tenets of the faith. That’s because to arrive at these “inclusive” and “affirming” positions on marriage, Christians must exalt intoxicants such as emotion over uncompromising scripture, tradition, and natural law. Once you shift the authority from sola scriptura to sola feels, it’s only a matter of time before every other orthodox teaching finds itself on the woke chopping block.

I love this SO MUCH.

If I had to pick one conclusion that I have found to be true in 30 years of debating Christian truth claims, it would be that the normal process for becoming an atheist has nothing to do with reason or evidence. People abandon their faith in their teens, long before they have ever done any research into whether Christianity is true. And why? Because they know that their desire to be free of the moral demands of Christianity is true. And they know that their desire to be liked by their non-Christian friends is true.

Katy explains that she loves loves to discuss and debate with non-Christians and LGBT people about the issue she cares about: natural marriage and children’s rights. But she gets annoyed with Christian leaders who misunderstand the gospel.

She writes:

Whether approaching the issue from a natural law perspective where male and female complementarity features prominently, or considering the most widely ratified treaty in human history outlines a child’s right to be known and loved by their mother and father, or through the lens of scripture where God joins together man and woman in life-long union because he is seeking “godly offspring” (Malachi 2), Christian leaders have no excuse for getting marriage wrong.

Zip. Zero. Nada. Their more-tolerant-than-Jesus definition of marriage (Mark 10:6-9) is, to use Harris’ own words, incredibly damaging not only to the church, but to the most vulnerable as well.

The reality is that Christians cannot get gay marriage wrong unless they first get the gospel wrong. Progressive Christians are under the wrong impression that ours is a gospel of affirmation: the idea that God affirms everything we think and say and do and want. This misconceived notion of the gospel believes that for God to genuinely love us, he has to love everything about us.

In this self-esteem-driven, everyone-gets-a-prize culture, a God who sometimes disapproves of our thoughts and behavior (*cough* Psalm 19:14) appears to be quite a bigot. In the “Born This Way” version of the Gaga gospel, Matthew 5:29 would read, “If your right eye causes you to stumble, by all means, redefine the word ‘stumble’ because, well, I wouldn’t want you to lose an eye now, would I?”

An honest reading of scripture reveals that ours is not a gospel of affirmation. Leave aside the 613 laws of the Old Testament in which God is rigidly un-affirming as he imposes devastating consequences on his people when they misuse their words, money, bodies, land, and worship. The New Testament and the gospels are also brimming with commands to put off behaviors that displease God and put on an entirely new nature.

Katy likes to tweet a lot of stories where children who have been impacted by divorce or same-sex marriage or donor-conception or surrogacy speak about how they feel about not having a relationship with their father or mother (or both). But she also knows how to argue against adult selfishness using data.

My advice to Christians is this. If you want to have confidence when defending the Christian teaching on marriage, or defending the rights of children to a Mom and a Dad, then you need to be equipped with research, statistical evidence and stories of those who have been impacted. Being a Christian means advocating for the teachings of Jesus. Jesus cared about children, and he wanted adults to act in a way towards children that would help those children to come to know him and follow him. We should not be affirming adult selfishness when it harms the children who are made to know God.

I think one of the reasons why people like Joshua Harris are abandoning the faith is because abandoning the morality came first. And before the abandoning of morality, there was a refusal to get informed about the harm that sin does. Instead of putting in the time to look at the evidence, they just altered their worldviews in order to feel good and be liked. Well, feeling good and being liked has never been important to the Christian life. But valuing truth, defending Christian convictions with evidence, and protecting the weak from the strong is found everywhere in the New Testament.

Atheist Jerry Coyne explains why morality is impossible for atheists

Sherlock Holmes and John Watson about to do philosophy
Sherlock Holmes and John Watson about to do philosophy

Let’s review what you need in your worldview in order to have a rationally grounded system of morality.

You need 5 things:

1) Objective moral values

There needs to be a way to distinguish what is good from what is bad. For example, the moral standard might specify that being kind to children is good, but torturing them for fun is bad. If the standard is purely subjective, then people could believe anything and each person would be justified in doing right in their own eyes. Even a “social contract” is just based on people’s opinions. So we need a standard that applies regardless of what people’s individual and collective opinions are.

2) Objective moral duties

Moral duties (moral obligations) refer to the actions that are obligatory based on the moral values defined in 1). Suppose we spot you 1) as an atheist. Why are you obligated to do the good thing, rather than the bad thing? To whom is this obligation owed? Why is rational for you to limit your actions based upon this obligation when it is against your self-interest? Why let other people’s expectations decide what is good for you, especially if you can avoid the consequences of their disapproval?

3) Moral accountability

Suppose we spot you 1) and 2) as an atheist. What difference does it make to you if you just go ahead and disregard your moral obligations to whomever? Is there any reward or punishment for your choice to do right or do wrong? What’s in it for you?

4) Free will

In order for agents to make free moral choices, they must be able to act or abstain from acting by exercising their free will. If there is no free will, then moral choices are impossible. If there are no moral choices, then no one can be held responsible for anything they do. If there is no moral responsibility, then there can be no praise and blame. But then it becomes impossible to praise any action as good or evil.

5) Ultimate significance

Finally, beyond the concept of reward and punishment in 3), we can also ask the question “what does it matter?”. Suppose you do live a good life and you get a reward: 1000 chocolate sundaes. And when you’ve finished eating them, you die for real and that’s the end. In other words, the reward is satisfying, but not really meaningful, ultimately. It’s hard to see how moral actions can be meaningful, ultimately, unless their consequences last on into the future.

Theism rationally grounds all 5 of these. Atheism cannot ground any of them.

Let’s take a look at #4: free will and see how atheism deals with that.

Atheism and free will?

Here’s prominent atheist Jerry Coyne’s editorial in USA Today to explain why atheists can’t ground free will. (Note: link is dead)

Excerpt:

And that’s what neurobiology is telling us: Our brains are simply meat computers that, like real computers, are programmed by our genes and experiences to convert an array of inputs into a predetermined output. Recent experiments involving brain scans show that when a subject “decides” to push a button on the left or right side of a computer, the choice can be predicted by brain activity at least seven seconds before the subject is consciously aware of having made it. (These studies use crude imaging techniques based on blood flow, and I suspect that future understanding of the brain will allow us to predict many of our decisions far earlier than seven seconds in advance.) “Decisions” made like that aren’t conscious ones. And if our choices are unconscious, with some determined well before the moment we think we’ve made them, then we don’t have free will in any meaningful sense.

If you don’t have free will, then you can’t make moral choices, and you can’t be held morally responsible. No free will means no morality.

Here are some more atheists to explain how atheists view morality.

William Provine says atheists have no free will, no moral accountability and no moral significance:

Let me summarize my views on what modern evolutionary biology tells us loud and clear — and these are basically Darwin’s views. There are no gods, no purposes, and no goal-directed forces of any kind. There is no life after death. When I die, I am absolutely certain that I am going to be dead. That’s the end of me. There is no ultimate foundation for ethics, no ultimate meaning in life, and no free will for humans, either.

Richard Dawkins says atheists have no objective moral standards:

In a universe of blind physical forces and genetic replication, some people are going to get hurt, other people are going to get lucky, and you won’t find any rhyme or reason in it, or any justice. The universe that we observe has precisely the properties we should expect if there is, at bottom, no design, no purpose, no evil and no good, nothing but blind, pitiless indifference… DNA neither knows nor cares. DNA just is. And we dance to its music. (Richard Dawkins, River Out of Eden: A Darwinian View of Life (1995))

When village atheists talk about how they can be moral without God, it’s important to ask them to justify the minimum requirements for rational morality. Atheists may act inconsistently with their worldview, believing in free will, expecting praise and blame for complying with the arbitrary standards of their peer group, etc. But there is nothing more to morality on atheism that imitating the herd – at least when the herd is around to watch them. And when the herd loses its Judeo-Christian foundation – watch out. That’s when the real atheism comes out – the atheism that we’ve seen before in countries that turned their backs on God, and the moral law. When God disappears from a society, anything is permissible.

William Lane Craig debates Alex Rosenberg: Does God Exist? Video, audio and summary

British Spitfire and German Messerschmitt Me 109 locked in a dogfight
British Spitfire and German Messerschmitt Me 109 locked in a dogfight

Here is the video of the debate:

Here is my summary of the Craig-Rosenberg debate, which occurred on February 1st, 2013 at Purdue University.

The debaters

Below is the summary.

Dr. Craig’s opening speech:

The topic: What are the arguments that make belief in God reasonable or unreasonable?
First speech: arguments for reasonableness of belief in God
Second speech: respond to arguments against reasonableness of belief in God

Eight arguments:

  1. Contingency argument: God – a transcendent, personal being – is the explanation of why a contingent universe exists.
  2. Cosmological argument: God is the cause of the beginning of the universe, which is attested by physics and cosmology.
  3. Applicability of mathematics to nature: God is the best explanation for the applicability of mathematics to nature.
  4. Fine-tuning argument: God is the best explanation of the fine-tuning of the universe to permit life.
  5. Intentionality of conscious states: God is the best explanation of the intentionality of our mental states.
  6. The moral argument: God is the best explanation for the existence of objective moral values and duties.
  7. The resurrection of Jesus: God is the best explanation for the core of historical facts accepted by most ancient historians across the ideological spectrum.
  8. Religious experience: God is the best explanation of our immediate experience and knowledge of his existence.

Dr. Rosenberg’s opening speech

First argument: The fallacy of ad hominem

  • I don’t know whether to laugh or to cry
  • Dr. Craig has said all of that before in other debates
  • You didn’t need to come out on this cold night
  • Craig’s arguments have all been refuted
  • Dr. Craig just doesn’t listen
  • Dr. Craig is not interested in getting at the truth
  • Dr. Craig is just interested in scoring debate points
  • The adversarial system is the wrong approach to decide truth
  • Dr. Craig is very confident about his take of physics

Second argument: The fallacy of arguing from authority

  • 95% of members of the NAS are atheists
  • Therefore Dr. Craig cannot use science

Third argument: Effects don’t require causes

  • I am going to pretend that Craig said that “every effect requires a cause”
  • Quantum mechanics shows that some effects occur without causes
  • A particle of uranium (which is not nothing, it is something) decays without a cause
  • This uncaused effect is the same as the universe coming into being out of nothing uncaused
  • Therefore the principle of sufficient reason is false

Fourth argument: Silicon-based life and the multiverse

  • If these constants had been different, maybe we would have other kinds of intelligent life, like silicon-based life
  • Carbon-based life is not the only kind of life, maybe you can have other kinds of life, none of which have been observed
  • There could be different kinds of life in other areas of the universe that we can’t see
  • There are things we can’t see that disprove the current physics that we can see
  • Quantum foam is evidence that a multiverse exists
  • The multiverse would solve the problem of fine-tuning

Fifth argument: The Euthyphro dilemma

  • The moral argument is refuted by Euthyphro dilemma
  • Dr. Craig is such a moron that he has never heard of the Euthyphro dilemma ever before
  • This is found in the first and simplest of Plato’s dialogs
  • Why is Dr. Craig so stupid that he has not read this simple dialog ever before?
  • Evolution explains why humans evolve arbitrary customs and conventions that vary by time and place
  • Alternative moral theories: utilitarianism, social contract, etc. that don’t require God

Sixth argument: Mormonism undermines Dr. Craig’s three minimal facts about Jesus

  • Why is Dr. Craig so stupid and ignorant to persist in pushing such an ignorant, stupid argument?
  • Mormonism is a silly religion that is not historically well founded
  • Therefore, Jesus was not buried
  • Islam is a silly religion that is not historically grounded
  • Therefore, the tomb was not found empty
  • Scientology is a silly religion that is not historically grounded
  • Therefore, the eyewitnesses didn’t have post-mortem appearances
  • Eyewitness testimony is unreliable in some cases
  • Therefore, eyewitness testimony was unreliable in this case
  • Apparitions of Mary are bizarre
  • Therefore, the majority of historians are wrong to think that the disciples saw post-mortem appearances

Seventh argument: Deductive problem of evil

  • Evil and suffering are logically incompatible with an all good, all powerful God

Eight argument: God is not just to allow evil and suffering

  • God cannot make the evils of this life right in the afterlife

Dr. Craig’s first rebuttal

Dr. Rosenberg sketched the deductive argument from evil.

Dr. Rosenberg presupposes naturalism. Naturalism is a false theory of knowledge:

1. It’s too restrictive: There are truths that cannot be proved by natural science.
2. It’s self-refuting: no scientific proof for naturalism exists.

That’s why epistemological naturalism is considered false by most philosophers of science.

But more importantly than that: Epistemological naturalism does not imply metaphysical naturalism. (E.g. – W. Quine)

Dr. Rosenberg has to present arguments in favor of (metaphysical) naturalism, not just assume that (metaphysical) naturalism is true.

Dr. Craig presented eight arguments against metaphysical naturalism taken from Rosenberg’s own book:

1. The argument from the intentionality (aboutness) of mental states implies non-physical minds (dualism), which is incompatible with naturalism
2. The existence of meaning in language is incompatible with naturalism, Rosenberg even says that all the sentences in his own book are meaningless
3. The existence of truth is incompatible with naturalism
4. The argument from moral praise and blame is incompatible with naturalism
5. Libertarian freedom (free will) is incompatible with naturalism
6. Purpose is incompatible with naturalism
7. The enduring concept of self is incompatible with naturalism
8. The experience of first-person subjectivity (“I”) is incompatible with naturalism

Metaphysical naturalism is false: it is irrational and it contradicts our experience of ourselves.

And epistemological naturalism is compatible with theism.

Rebutting Dr. Rosenberg’s responses:

1. Contingency: no response

2. Cosmological: he mis-states the first premise to say every effect… when it is whatever begins to exist…, the origin of the universe was not from a vacuum, virtual particles come from a vacuum not nothing, there are interpretations of QM that are compatible with determinism. Rosenberg has to believe that the entire universe popped into being from non-being.

3. Mathematics: no response

4. Fine-tuning: the multiverse is refuted by empirical observations of the universe. Without fine-tuning, it’s not that we still have silicon to make life out of. It’s that we lose basic minimal things like chemical diversity, matter, stars, planets, etc. No life of any kind, not just no carbon-based life.

5. Intentionality: no response.

6. Moral argument: the answer to the dilemma is that you split the dilemma: God is the standard of good, and the commands flow from his unchanging moral nature. The commands are not arbitrary, and the standard is not external to God. Dr. Rosenberg is a nihilist and he cannot ground good and evil on his nihilistic view.

7. Resurrection: The Gospels are early eyewitness testimony. Mormonism and Islam have nothing to do with the minimal set of historical facts about Jesus agreed to by the majority of ancient historians across the ideological spectrum, general statements against eyewitnesses do not refute the specific eyewitness testimony in this case.

8. Religious experience: No response.

Dr. Rosenberg’s first rebuttal

I wrote a book and you should buy it, because it got me invited to this debate. Let me repeat the title a few times for you. Please buy it.

Dr. Craig is right, there are multiple interpretations of QM, not just the one I presented, including deterministic ones.

All the disturbing implications of naturalism that Dr. Craig stated follow from metaphysical naturalism, and metaphysical naturalism is true. (Note: he equates science with metaphysical naturalism)

Science proves that metaphysical naturalism is true, but I won’t say what specific scientific tests prove my philosophical assumption of metaphysical naturalism.

I’ll pretend that the Big Bang (science) doesn’t disprove naturalism, like Dr. Craig said. Again. (covers ears) La la la, there is no Big Bang.

We didn’t come here to debate epistemological naturalism and metaphysical naturalism.

Let me explain the problem of intentionality since I’m so smart and no one knows what it means.

There are many answers to this problem of intentionality.

My answer is that most scientists are naturalists, therefore naturalism is true, regardless of the argument from intentionality of mental states.

That’s how I would respond to one of the eight problems with naturalism that Dr. Craig raised. I won’t answer the other seven problems.

It is an argument from ignorance to argue that the applicability of mathematics to the universe requires a designer, because there are non-Euclidean geometries. Craig’s argument, which he gets from people like respected physicists like Eugene Wigner, is bizarre. It is bizarre, therefore I refute Eugene Wigner and all the other scholars who make that argument. It is bizarre! Bizarre!

Deductive problem of evil: there is no response to this argument, certainly not Alvin Plantinga’s free will defense. The deductive argument from evil has not been entirely abandoned at all! It’s not like arch-atheist J.L. Mackie himself admits that the deductive problem of evil doesn’t lead to a logical inconsistency between evil and God.

Dr. Craig has to tell me why God allows evil or God doesn’t exist.

It is offensive that Dr. Craig cannot tell me why God allows every evil and suffering that occurs.

He literally said this: “I will become a Christian if Dr. Craig can tell me why God allowed EVERY EVIL THAT OCCURRED IN THE LAST 3.5 BILLION YEARS”

Dr. Craig’s second rebuttal

We are not in a position to know why God allows specific instances of evil and suffering.

God cannot force people to freely do anything – freedom is not compatible with determinism. Freedom is a good, but freedom opens up the possibility of moral evil. You cannot have the good of free will without allowing people to choose to do morally evil things.

God can permit evil and suffering in order to bring more people into a relationship with him.

The atheist has to show that God could allow less evil and achieve more knowledge of God in order to say there is too much evil.

The purpose of life is not happiness, but knowledge of God.

Dr. Craig quotes agnostic Paul Draper (Purdue) and Peter Van Inwagen (Notre Dame) to state that the deductive problem of evil is dead because of free will and morally sufficient reasons for permitting evil.

1. Contingency: no response.

2. Cosmological: QM does not apply, because the universe came from nothing, not a vacuum, and QM only works in a vacuum.

3. Mathematics: He mentions alternatives like non-Euclidean geometry, but we have to explain the structure of THIS universe.

4. Fine-tuning: ???

5. Intentional states: intentional mental states proves that minds exist, which fits with theism better than it fits with atheism.

6. Moral argument: You need God to ground morality, and Dr. Rosenberg believes in morality. He needs God to ground objective moral values and duties.

7. Historical argument: He has to respond to the minimal facts supported by the consensus of ancient historians across the ideological spectrum.

8. The problems of naturalism: He says that you can’t have science without naturalism, but you can have science with EPISTEMOLOGICAL NATURALISM, and theists accept science and methodological naturalism. We don’t accept METAPHYSCIAL NATURALISM because of the eight problems Craig presented, like intentionality, first-person, persistence of self, etc. You can believe in both science and theism, by embracing epistemological naturalism, while rejecting methaphysical naturalism.

Dr. Rosenberg’s second rebuttal

Dr. Craig hasn’t answered many of my points, I won’t say which ones though.

Debates don’t work as a way of deciding what’s true, so we should overturn the entire criminal justice system.

The principle of sufficient reason is false because it is disconfirmed by quantum mechanics. And quantum mechanics (vacuum and virtual particles that exist for a short time) is similar to the origin of the universe (nothing and entire universe and 14 billion years).

We know that alpha particles come into being without cause all the time from a quantum vacuum for a tiny sub-second duration before going out of existence, so we can say that the entire physical universe came into being for 14 billion years from absolute nothing which is not a quantum vacuum.

Peter Van Inwagen is the best metaphysician working today, and he says that my deductive argument from evil is not decisive, it’s not a successful argument. (Why is he undermining his own problem of evil argument????!)

Dr. Craig invoked Plantinga’s free will defense to the deductive POE. Freedom allows us to do evil. God could have given us free will without evil and suffering. I won’t show how, but I’ll just assert it, because debates are such a bad forum for supplying evidence for my speculative assertions.

If you answer the question 3 + 5 as being 8, then you don’t have free will – you are biologically determined if you answer 8, because everyone answers 8, and that means everyone is biologically determined with no free will.

Why can’t God give us free will and then prevent us from making a free choice?

No scholars date the gospels earlier than 60-70 AD, especially not atheists like James Crossley who dates Mark to 40 AD. Therefore Jesus’ burial isn’t historical, like the majority of scholars across the broad spectrum of scholarship agree it is.

The original New Testament documents were written in Aramaic.

All New Testament scholars are orthodox Christians, like atheist Robert Funk for example.

Dr. Craig’s concluding speech

In order to sustain the deductive argument from evil, Dr. Rosenberg must show that God could create a world of free creatures with less evil.

Principle of Sufficient Reason: not using the general principle of sufficient reason, but a more modest version of this states that contingent things should have an explanation for their existence. And we know that the universe is a contingent.

The New Testament was not written in Aramaic, they were written in Greek. Dr. Rosenberg is wrong there too.

(Dr. Craig spends the rest of his concluding speech giving his testimony and urging people to investigate the New testament).

Dr. Rosenberg’s concluding speech

Some long-dead French guy named Laplace said that he has no need of that (God) hypothesis. He did not know about any of Dr. Craig’s arguments made in this debate tonight when he said that, though.

There is no need to explain how the universe began or how the universe is finely-tuned if you just assume metaphysical naturalism on faith.

The Easter Bunny, therefore atheism.

Most scientists are atheists, therefore atheism.

You can do a lot of science without God, just don’t look at the origin of the universe, the fine-tuning of the universe, or the other parts of science that Craig mentioned, as well as the origin of life, the Cambrian explosion, the habitability argument, and so on.

You can be a Christian, but good Christians should not use arguments and evidence.

Good Christians should be irrational and ignorant. Bad Christians look for arguments and evidence from science and history.

Good Christians should embrace the absurd. Bad Christians want to search for truth and use logic and evidence.

Are Mormon doctrines supported by philosophy, science and history?

A conflict of worldviews
A conflict of worldviews

This post presents evidence against Mormonism/LDS in three main areas. The first is in the area of science. The second is in the area of philosophy. And the third is in the area of history.

The scientific evidence

First, let’s take a look at what the founder of Mormonism, Joseph Smith, believes about the origin of the universe:

“The elements are eternal. That which had a beggining will surely have an end; take a ring, it is without beggining or end – cut it for a beggining place and at the same time you have an ending place.” (“Scriptural Teachings of the Prophet Joseph Smith”, p. 205)

“Now, the word create came from the word baurau which does not mean to create out of nothing; it means to organize; the same as a man would organize materials and build a ship. Hence, we infer that God had materials to organize the world out of chaos – chaotic matter, which is element, and in which dwells all the glory. Element had an existance from the time he had. The pure principles of element are principles which can never be destroyed; they may be organized and re-organized, but not destroyed. They had no beggining, and can have no end.”
(“Scriptural Teachings of the Prophet Joseph Smith”, p. 395)

A Mormon scholar named Blake Ostler summarizes the Mormon view in a Mormon theological journal:

“In contrast to the self-sufficient and solitary absolute who creates ex nihilo (out of nothing), the Mormon God did not bring into being the ultimate constituents of the cosmos — neither its fundamental matter nor the space/time matrix which defines it. Hence, unlike the Necessary Being of classical theology who alone could not not exist and on which all else is contingent for existence, the personal God of Mormonism confronts uncreated realities which exist of metaphysical necessity. Such realities include inherently self-directing selves (intelligences), primordial elements (mass/energy), the natural laws which structure reality, and moral principles grounded in the intrinsic value of selves and the requirements for growth and happiness.” (Blake Ostler, “The Mormon Concept of God,” Dialogue: A Journal of Mormon Thought 17 (Summer 1984):65-93)

So, Mormons believe in an eternally existing universe, such that matter was never created out of nothing, and will never be destroyed. But this is at odds with modern cosmology.

The Big Bang cosmology is the most widely accepted cosmology of the day. It denies the past eternality of the universe. This peer-reviewed paper in an astrophysics journal explains. (full text here)

Excerpt:

The standard Big Bang model thus describes a universe which is not eternal in the past, but which came into being a finite time ago. Moreover,–and this deserves underscoring–the origin it posits is an absolute origin ex nihilo. For not only all matter and energy, but space and time themselves come into being at the initial cosmological singularity. As Barrow and Tipler emphasize, “At this singularity, space and time came into existence; literally nothing existed before the singularity, so, if the Universe originated at such a singularity, we would truly have a creation ex nihilo.

[…]On such a model the universe originates ex nihilo in the sense that at the initial singularity it is true that There is no earlier space-time point or it is false that Something existed prior to the singularity.

Christian cosmology requires such a creation out of nothing, but this is clearly incompatible with what Mormons believe about the universe. The claims about the universe made by the two religions are in disagreement, and we can test empirically to see who is right, using science.

Philosophical problems

Always Have a Reason contrasts two concepts of God in Mormonism: Monarchotheism and Polytheism. It turns out that Mormonism is actually a polytheistic religion, like Hinduism. In Mormonism, humans can become God and then be God of their own planet. So there are many Gods in Mormonism, not just one.

Excerpt:

[T]he notion that there are innumerable contingent “primal intelligences” is central to this Mormon concept of god (P+M, 201; Beckwith and Parrish, 101). That there is more than one god is attested in the Pearl of Great Price, particularly Abraham 4-5. This Mormon concept has the gods positioned to move “primal intelligences along the path to godhood” (Beckwith and Parrish, 114). Among these gods are other gods which were once humans, including God the Father. Brigham Young wrote, “our Father in Heaven was begotten on a previous heavenly world by His Father, and again, He was begotten by a still more ancient Father, and so on…” (Brigham Young, The Seer, 132, quoted in Beckwith and Parrish, 106).

[…]The logic of the Mormon polytheistic concept of God entails that there is an infinite number of gods. To see this, it must be noted that each god him/herself was helped on the path to godhood by another god. There is, therefore, an infinite regress of gods, each aided on his/her path to godhood by a previous god. There is no termination in this series. Now because this entails an actually infinite collection of gods, the Mormon polytheistic concept of deity must deal with all the paradoxes which come with actually existing infinities…

The idea of counting up to an actual infinite number of things by addition (it doesn’t matter what kind of thing it is) is problematic. See here.

More:

Finally, it seems polytheistic Mormonism has a difficulty at its heart–namely the infinite regress of deity.

[…]Each god relies upon a former god, which itself relies upon a former god, forever. Certainly, this is an incoherence at the core of this concept of deity, for it provides no explanation for the existence of the gods, nor does it explain the existence of the universe.

Now let’s see the historical evidence against Mormonism.

The historical evidence

J. Warner Wallace explains how the “Book of Abraham”, a part of the Mormon Scriptures, faces historical difficulties.

The Book of Abraham papyri are not as old as claimed:

Mormon prophets and teachers have always maintained that the papyri that was purchased by Joseph Smith was the actual papyri that was created and written by Abraham. In fact, early believers were told that the papyri were the writings of Abraham.

[…]There is little doubt that the earliest of leaders and witnesses believed and maintained that these papyri were, in fact the very scrolls upon which Abraham and Joseph wrote. These papyri were considered to be the original scrolls until they were later recovered in 1966. After discovering the original papyri, scientists, linguists, archeologists and investigators (both Mormon and non-Mormon) examined them and came to agree that the papyri are far too young to have been written by Abraham. They are approximately 1500 to 2000 years too late, dating from anywhere between 500 B.C. (John A. Wilson, Dialogue: A Journal of Mormon Thought, Summer 1968, p. 70.) and 60 A.D. If they papyri had never been discovered, this truth would never have come to light. Today, however, we know the truth, and the truth contradicts the statements of the earliest Mormon leaders and witnesses.

The Book of Abraham papyri do not claim what Joseph Smith said:

In addition to this, the existing papyri simply don’t say anything that would place them in the era related to 2000BC in ancient Egypt. The content of the papyri would at least help verify the dating of the document, even if the content had been transcribed or copied from an earlier document. But the papyri simply tell us about an ancient burial ritual and prayers that are consistent with Egyptian culture in 500BC. Nothing in the papyri hints specifically or exclusively to a time in history in which Abraham would have lived.

So there is a clear difference hear between the Bible and Mormonism, when it comes to historical verification.

Further study

If you want a nice long PDF to print out and read at lunch (which is what I did with it) you can grab this PDF by Michael Licona, entitled “Behold, I Stand at the Door and Knock“.