Dec 2005, Changing Times

Understanding theLogic of Atheism

Creating a Bridge of Understanding

Hooman Katirai

Table of Contents

• Part 1: The Analogies – We create analogies where humans play the role of creator

• Part 2: The Harvest – We use the analogies to learn about the creator-created relationship.

• Part 3: Proofs of God, we examine two proofs of God – one from Aristotle, the other from William Hatcher.

Purpose

“If thou wishest the divine knowledge … purify thy heart … and apply thyself to rational and authoritative arguments … then the eye will be opened and will recognize the Sun through the Sun itself.”

(Abdu'l-Baha, Baha'i World Faith - Abdu'l-Baha Section, p. 383)

Types of Faith

Faith

Belief in an Idea in the absence

of total proof

Blind Faith

(commitment to abelief regardless

of evidence)

Empiricism

Belief in an ideabecause it’s more

likely than itscomplement

The complement of a statement is similar to what we might call an opposite.

The complement of “it’s raining” is everything that’s

not raining. This would include, sunny, cloudy,

windy, etc ..

Some Definitions

God (or gods) do not existAtheist

The question “does God exist?” cannot be proven (or disproven) and is therefore meaningless.

Agnostic

An Might say …

I’m not sure if God exists but I’m open to new evidence.

Undecided

Atheism is difficult to defend

• To make such a claim one must examine– every part of universe – in case one or more Gods were hiding

there.

• But atheists have examined only a small part of the universe.

• Thus they do not have enough evidence to make the claim “there is no God”

TAKEAWAYS: • Atheism is a belief founded on faith. It is not based on

logic.

Belief: God (or gods) do not exist

Agnostics & Undecideds

• Both don’t know if God does or does not exist

• Agnostics believe the question can’t be answered

• These two groups will be the focus of our discussions!

Common Objections to Religion & God

Show that existence of God ismore likely than non-existence I.e. it is not a fiction. Hatcher’s Proof.

We’ll show ideas like An unknowable creator, Manifestations, etc are

all reasonable.

There can be perfect justiceIf there is a next world

Ideas in religion aretoo outrageous to be true

Religion is a fiction adopted by the weak or unhappy

(to feel comforted and happy)

Religion causes war,and suffering

Acts of followers ≠Teachings of religion

Religion can be perfect whileFollowers are not. Precisely

why God sends new messengers

Too much suffering inworld for there to be a God.

Overcoming Obstacles

We’ll show Science is based on Faith! But a specialKind of faith that can

Also be applied in religion.

I don’t believe in religion,which is based on faith

I believe in Science

Answering Objection 1:

We’ll show science is based on a special kind of faith

called empiricism that canbe used in religion

Objection:

I don’t believe in religion,which is based on faith

I believe in Science

Science is based on Faith!

• How do Physicists – discover equations?

• Simple example:– Newton’s Law (F=ma)

Mass (M)Force (F)

Frictionless Surface

F

ATakeaway: Even fundamental equations in physics are based on Faith!!

F=ma

Science is based on Faith! (cont’d)• F=ma

– equation of a line

• Yet, according to math– Infinite number of

points between any two points on a line

– Can’t measure Force and Acceleration at all points

– Yet we assume linear transition holds

F

A

Takeaway: Science is based on Faith! This faith is differentiated from Blind Faith, and is the act of the scientific rational person.

Answering Objection 2:

How we’ll answer it:

We’ll show that an unknowable creator, manifestations, etc are

all reasonable.

Objection:

Ideas in religion aretoo outrageous to be true

Part 1: The Analogies

We’ll find situationswhere we play

the role of Creator.These situations will be closely

examined in the next part,to learn more about our relationship

with God.

Humans can create universes• Inside a computer

• Like our universe, these universes have– Creatures– Laws

• lend insight to– Relationship between

creator and created

• Case in point– Game of Life

(Conway ’70)

Game of Life (Conway ’70)

• Universe:– A Simple Grid

• Creatures:– Yellow cells

• Empty Space– Gray cells

The Game of Life’s Universal Laws

1. Birth: dead cell with 3 live neighbors becomes alive

2. Survival: live cell with 2-3 live neighbors stays alive

3. Death: all other cases, cell dies or remains dead (loneliness or over-crowding).

Game of LifeDemo

More sophisticated universes

• Creatures can learn• Example:

– Creature behavior governed by probability matrix

– Probabilities updated with experience

– Free will simulated by picking behavior according to probabilities

• Evolution – Survival of fittest

Genetic Programming• Programmer does not explicitly

write computer program• Instead programmer creates

evolutionary environment to evolve solutions.

• Process:– Create “population” of randomly

generated solutions– Allow solutions to “mate” to yield

offspring solutions– Better solutions have higher

chance of mating (Darwinian Natural selection)

• Outcome of process said to be best solution after many cycles of mating

Link to Additional Slides

On GP

Genetic Programming Demo

Genetic Programming Demo

Takeaway:

We can create universes in which the creatures can evolve over time!

An Automatic Invention Machine?

• More than 20 US patents– re-discovered using GP

• Several new patents – discovered using GP– outperform all existing human-

invented solutions • Genetic Programming has

been called– an “Automatic Invention

Machine”• Who is the inventor?

– The human or the machine?– “Who is the potter, pray, and

who the pot?” –Omar Khayyam

Summary of Part 1

• Humans can create universes– Inside a computer– With creatures that can:

• Mate• Learn• Evolve

• In these universes we play the role of God

`

Part 2: The Harvest

We’ll use the analogies we studied to draw deductions

Suppose you wanted to communicate with your

creatures

Could you:– enter their world?– turn yourself into a

square on the grid?

Solution• Since you cannot

enter their universe– you must control

something in their universe

• i.e. speaking to your creatures requires– an intermediary

i.e. this man cannot be God

Evidence from ChristianityChrist is an intermediary who carries actions of God on earth:

“I do nothing of myself; but as my Father hath taught me, I speak these things.”-John 8:28 (King James Version)

Further evidence of distinction between Christ & God:

“But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.”-Mark 13:32

And Islam• Mohammed is an intermediary that delivers

message of God to man:

“Even as We have sent unto you a messenger [Mohammed] from among you, who reciteth unto you Our revelations and causeth you to grow, and teacheth you the Scripture and wisdom …”-The Qur'an, 2:151

• “Muhammad is but a messenger, messengers (the like of whom) have passed away before him.”

-The Qur'an 3:144

And Judaism• Moses in an intermediary that delivered

God’s message to Humankind:

• “Remember ye the law of Moses My servant, which I [God] commanded unto him in Horeb for all Israel, even statutes and ordinances.”

-Prophets

And the Bahá’i Faith• Confirms idea of human

intermediary– "since there can be no

tie of direct intercourse to bind the one true God with His creation … " God ordains that "in every age … a pure and stainless Soul be made manifest in the kingdoms of earth and heaven"

(Baha'u'llah, The Kitab-i-Aqdas, p. 232)

The Holy Spirit“we can understand that the Holy Spirit is the Intermediary between the Creator and the created.” -Abdu'l-Baha, Paris Talks, p. 59

• Anything in between the Created and Created

• In our example includes– Computer– Software running universe– Keyboard

If you were to speak to your creatures ..

• What Language:– English?– their language?

• Level of communication:– According to our capacity?– Or their capacity?

“All that I have revealed unto thee … hath been in accordance with thy capacity and understanding, not with My state and the melody of My voice.” -Baha'u'llah, The Hidden Words

On Miracles

• Should not constitute a “proof”:– Except to

observers– Even then there

are often alternate explanations

Miracles• Nonetheless, we can see

how– miracles could be easy for

creator

• Example: Game of Life– can create life simply by

flipping a bit from a 0 to a 1 in the grid.

– a power creatures do not have

So, why not have a miracle side-show to quell all doubts?

Free Will vs. Miracles• If God performed miracles on demand

– forced to acknowledge him– lose autonomy to recognize (or reject) creator

• Suppose instantaneous {punishment, correction, guidance} for ‘wrong’ acts.

Puppet vs. Growing being-controlled vs. guided-little or no autonomy vs. free will & choice: -brute vs. noble being-loss of self vs. self-no capacity for altruism vs. capacity for altruism

Takeaway: There seems to be a tradeoff between miracles and free-will

Why A Human Intermediary?

• We discovered we needed – an intermediary to

communicate with our creatures

• But the intermediary could have been – a talking tree, or a rock

that glows in Morse code

• Why a human intermediary?

Why a Human Intermediary? (cont’d)

• A talking tree, or glowing rock constitutes – a miracle– But we’ve established that

miracles reduce free-will to accept or reject God.

• A human intermediary is ideal because it allows God to – communicate the message,

while still providing us with– free will to accept (or deny)

God.

More on Miracles

“… Know that the

Word of God … is sanctified from the known elements … It became manifest without an utterance made, or a voice breathed. It is the command of God …”Compilations, Baha'i Scriptures, p. 191, Emphasis added.

How might our creatures perceive us?

• “The world of our creator so vast that it’s composed of an infinite number of squares.”

• “The creator is the source of all life”

• “The creator is all-powerful.”

• “The creator exists above time. Can see the future; knows the past.”

• “The creator is omniscient (all-knowing).”

TAKEAWAY: God is unknowable! Any conception we have of God is not God.

ParallelsOn Praise:

“To have accepted any act or praise from Thy creatures is but an evidence of the wonders of Thy [God’s] grace and bountiful favors, and a manifestation of Thy generosity and providence.”

-Baha'u'llah

On Unknowability:

“… souls shall be perturbed as they make mention of Me [God]. For minds cannot grasp Me nor hearts contain Me.”

-Baha'u'llah, The Arabic Hidden Words

But isn’t God All-Powerful?

• Can’t God turn himself into a human?

• Equivalent question:– “Couldn’t God turn

himself into a square in Game of Life?”

Power of the Creator (cont’d)

• What do we mean by All-Powerful?

• In Game of life we are All-Powerful because

• We can: – change game’s state to

any state – alter universal laws

• No creature can stand in our way

Meaning of All-Powerful (cont’d)

• Though “All-Powerful” in Game of Life – Can we turn ourselves

into a square?

• 1 bit needed to represent square– Bits required to

represent a human?– Information loss

Power of God (cont’d)

• If humans can’t be represented in 1 bit– Can God?

God as Unknowable“… God …can in no wise incarnate His

infinite, His unknowable, … Reality in the concrete and limited frame of a mortal being.”

-Shoghi Effendi, The World Order of Bahá'u'lláh, p. 112

TAKEAWAY: It’s logically impossible for something to be limited andall-powerful at the same time!

Power of God

Takeaway:• Even God’s power has

limits• All Powerful ≠ Ability to

do anything• Specifically God cannot

be not God

Further Questions

Further Questions:• Is humility an attribute

of God?

Why do we declare our powerlessness in the

obligatory prayers everyday?• Is God engaging in some kind of ego trip

by requiring us to humble ourselves before him every day?

• One possible answer to the question:

• We tend to forget who’s in charge– we think we are in control– hence we need a daily reminder that we

are in fact powerless• Only when we are mindful of The Source

of all power– can we turn unto It, seeking It’s help and

guidance.• In sum it seems that God requires us to

declare our powerlessness– for our own benefit– To make us aware of reality (that we are

powerless) so we can act in an educated manner.

What if .. • power withheld from computer

for even a few seconds?

“.. if for one moment the tide of His mercy and grace were to be withheld from the world, it would completely perish”-Bahá'u'llah, Gleanings from the Writings of Bahá'u'llah, p. 68

Is the universe an abandoned experiment?

We are created of love:“… I knew My love for thee; therefore I created thee ….” -Baha'u'llah, The Hidden Words

• The loving creator guides us:“… Were it not for the love of God the holy books would not have been revealed. Were it not for the love of God the divine prophets would not have been sent to the world … ”

-Abdu'l-Baha, Foundations of World Unity, p. 90

Can we develop a relationship with an “unknowable God?”

1. Prayer: the creator can communicate with us via inspiration

“A servant is drawn unto Me in prayer until I answer him; and when I have answered him, I become the ear wherewith he heareth....“ -Quran 83:28

"For the core of religious faith is that mystical feeling which unites man with God. This state of spiritual communion can be brought about and maintained by means of meditation and prayer.”

Baha’i Writings: Compilations, Lights of Guidance, p. 506

How do we develop a relationship with an

“unknowable God?” (cont’d)• Reading

– Sacred Scriptures (messages sent by creator)

• Meditation– On spiritual teachings

(to understand messages from creator)

• Striving every day – to bring behavior more into

accordance with high standards

• Selfless service – to humanity – in carrying on of our trade or

profession.

Summary of Part 2• Saw computer universes that have:

– Creatures– laws.

• Creatures could:– Learn– Evolve

• If Computer Generated Universes are comparable to our universe then ….

Summary of Part 2• God is unknowable• You cannot:

– fully comprehend or– directly interact with God.

• All Powerful ≠ Ability to do anything• Holy Spirit

– everything between the Creator and Created• Communication with God

– requires an intermediary• Founders of World Religions

– intermediaries (messengers) between humankind & God– are not God but are directed by God– hard to imagine another way God could communicate with

humankind • without loss of our choice to accept (or reject) God.

`Part 3:

Proofs of God

We’ll examine and critique two proofs of God

Cosmological Proof of God (Aristotle)• Suppose you walked into the Amazon jungle and saw some pyramids

• You would probably immediately attribute these pyramids to an ancient civilization because– You know the pyramids don’t just create themselves– You know pyramids don’t appear out of thin air

• In short, you know the pyramids must be preceded by a cause.• In other words, in the domain of human created objects, every object is evidence of it’s

creator.– A chair is evidence of a chair maker– A painting is evidence of a painter– And so on ….

• Applying this same reasoning to the universe, we ask the question. “Can the existence of the Universe be taken as evidence for a Universe-maker (i.e. God?)”

• There is a leap of Faith in saying “yes” because we are moving from the domain of human created objects to non-human created ones. Moreover we are moving from causes within the universes, to the cause of the universe itself.

• Yet at the same time, the answer “yes” seems much more intuitive than the answer of “no” because we have never seen non-causal systems. In fact, the basis of science is that there is a cause for everything and saying no would commit us to the existence of non-causal systems.

• Returning to our • This proof only shows that there exists some kind of creator for the universe; but it doesn’t

prove there is only one creator; or if another entity created that creator.

Hatcher’s Proof of God• William Hatcher (1935-2005)

– Passed Away in Nov. 2005– Produced the strongest proof of God – You can read more in Hatcher’s Book,

Minimalism (ISBN

• Why hasn’t his proof been invented yet?– Some basic mathematical tools needed to

produce it (Von Neumann Set Theory) hadn’t been invented until the 20th century.

– Avicenna, a Muslim philosopher produced a very similar proof using mathematical concepts that were far ahead of their time, but his proof had some subtle errors.

– Hatcher fixed Avincenna’s proof and reformulated in modern math.

Hatcher’s Proof of God

• There are some minor differences between the proof you will find here, and the one presented in Hatcher’s book.

• In particular, I have done my best to avoid references to set theory while remaining faithful to Hatcher’s proof.

• You can get his original version of the proof which includes references to set theory in his book minimalism.

• Another version of the proof appears online here:– http://www.onecountry.org/e102/e10214xs.htm– But this is a book excerpt that may be difficult to understand

without the background material provided by previous chapters.

Hatcher’s Proof

• Let V represent all of reality.

• A phenomenon, is some portion of reality

• I.e. if the blue ellipse represents V, a phenomenon (illustrated in yellow), is some portion of it.

Hatcher’s Proof Continued

• We differentiate between two types of phenomena.

• Composite phenomena have parts.

• Non-composite phenomena have no parts (i.e. they are not divisible).

Hatcher’s 3 Principles

• P1. All existing phenomena are either self-caused (i.e. AA) or other caused (BA where A≠B) but not both.

• P2. If AB, then AE where E is any part of B.

• P3. AE cannot hold if E is a component of A.

P1

• P1 says there is a reason – for everything

• When we write AB we mean “a contains sufficient reason for B”

P2 is Hatcher’s definition of causality.

• There are numerous definitions of causality

• One is the efficient cause in which it’s the straw that breaks the camel’s back”

– Hatcher does NOT use this definition

• Instead he uses what’s called total causality– Under this notion of causality it’s the 1000 previous

straws, the camel, plus the last straw, plus gravity, plus the ground the camel is standing on – and all the other things that would be required to produce the breaking of the camel’s back – that causes the camel to break it’s back.

– Put another way to cause a phenomenon, you need to supply everything required to create it to satisfy the definition of causality provided in P2.

– That is why when we write AB we say “A contains sufficient reason for B”

P3: The Principle of Limitation

• P3 is a logical principle.

• It says that a composite phenomena cannot be the cause of it’s own components.

• A car for example cannot be the cause of it’s steering wheel.

• We illustrate P3 in the next slide

P3 (Continued)

• Every composite phenomena has – parts and – A relationship or structure

between these parts

• A car’s parts laid out on one’s front lawn is not a car

• To be considered a car, the parts need to be put together in certain way

• This is illustrated in the diagram

Parts ofCar

Relationship of Parts to each other

CAR

P3 (Continued)

• What P3 is saying is that there is a logical succession from the parts and structure to the car.

• I.e. once you have the structure AND parts, you have the car.

• This succession is a logical one not a temporal one. I.e. it is not the consequence of the passage of time.– For example the integer 2

following after 1 – but this does not involve the passage of time.

Parts ofCar

Relationship of Parts to each other

(Structure)

CAR

P3 (Continued)• The car can’t cause the

steering wheel (a part), because the car doesn’t exist until all the parts (including the steering wheel exist) and until such parts are put in the right form.

• Put another way, the parts and structure logically precede the car.

• It is possible that the car and it’s parts come into being simultaneously BUT it’s not possible for the car to cause it’s own component.

Parts ofCar

Relationship of Parts to each other

(Structure)

CAR

Proof of a Universal Cause

• Now that we’ve established the 3 principles, the proof follows.

• With respect to V, we know (from P1) that ONLY ONE of the following two statements is true:

a) That V is self caused (i.e. VV)I.e. that reality contains sufficient reason for it’s own existence

b) That V is other-caused (i.e. there exists some GV)That is some portion of reality, which we call G, is the ultimate cause of everything.

Proof of a Universal Cause• Suppose Statement (a) is true i.e. VV

• By P2, the statement VV implies that VA for every A which is a component of V – but this contradicts P3 which says a composite phenomena cannot be a cause of one of it’s components.

• From the above contradiction we know statement (a) must be false

• But according to P1 if (a) is false, then (b) must be true.

• Thus there exists a G, which is the ultimate cause of everything (i.e. GV)

Proof that G has no components

• We know that GV• According to P2, this means GG (since

G is a part of V).• Either one of the following two

statements must hold:– G1. G has components– G2. G has no components

• G1 cannot hold for the same reasons that VV does not hold (i.e. it would violate P3).

• This means G has no components.

Proof of G’s Uniqueness• Here we will prove that there can only be one universal cause.• We already showed there exists a universal cause, G but lets suppose

there exists another universal cause, which we’ll call G’• Because G’ is a universal cause, we know G’V• By P2, this implies that G’ causes everything including G’ itself; i.e.

G’G’ (i.e. G’ is self-caused) (1)

• But we also know that the other universal cause, G, causes V i.e. GV. But according to P2, this means G causes everything in V including G’; i.e.

GG’ (which means G’ is other caused) (2)

• According to statement (1), G’ is self-caused, but according to statement (2), G’ is also other caused.

• But this violates P1, which says that G’ must be either self caused, or other caused but not both.

• The only way to avoid a contradiction is for G’=G• Thus there is only one universal cause.

Hatcher’s Proof• Put together, we have shown that there exists a

unique (i.e. there’s only one), universal (i.e. the cause of everything), self-caused (i.e. it contains sufficient reason for it’s own existence) cause. This cause is distinct from the universe, but is the cause of everything within it.

• The proof doesn’t require this G to be the immediate cause of everything; but it does say that God is the ultimate cause of everything.

• The proof does not tell you if this G, is the same as the God of Christianity, Islam, or the Baha’i Faith – but the findings of the proof are consistent with the God of those religions.

Critique of Hatcher’s Proof

• Hatcher used first order logic – most well understood and accepted form of logic

• As a result there are only three possible ways to attack his proof all of which are very difficult to defend. These attacks are:

1. To attack logic itself (not the act of a reasonable person)

2. To show that one or more principles do not hold (this approach is also very difficult to defend – see next slide)

Critiquing Hatcher’s ProofIf you accept logic, you can only use attack 2. Attack 2 requires one to negate one

or more of the 3 principles, but in practice this very difficult to defend; lets go over each principle:

– P1 says there is a cause for everything, and that the question “why?” is always meaningful. Negating this principle is difficult because P1 – which says that there is an explanation for everything – is one of the core ideas in Science. ; i.e. that every phenomena is preceded by a cause. Further, those who deny P1, commit themselves to the existence of non-causal systems – something humanity has never observed.

– P2 is just a definition of causality

– P3 is simply a logical idea. It too is difficult to attack.

• As introduced at the beginning of this presentation, Science picks as true, statements that are more probable than their complement.

• It would seem that all 3 of Hatcher’s principles pass this test• Thus this proof shifts the burden of proof to people to show there isn’t a

God.

Dec 2005, Changing Times

Understanding theLogic of Atheism

QUESTIONS

Hooman Katirai

(hooman@alumni.mit.edu in 2006)

`Backup Slides

More details on Genetic Programming

Final Questions

• What could we possibly offer our creator that it doesn’t already have?– Thankfulness

Nature Vs. Genetic Programming

• Survival of Fittest

• Several Males will compete to mate with one female or vice-versa

• Parents mate to produce offspring whose genetic makeup a combination of parents

• Offspring contain some genetic code independent of parents

• Genetic Code = DNA

• A Fitness function tells you how well any given solution solves the problem

• A technique called Tournament selection mimics this phenomenon

• Parents mate to produce fratenal twins, with genetic code from the parents BUT parent’s immediately die after doing so.

• Mutation operator

• Genetic Code = Parse Trees

Parse Trees: The DNA of Solutions

+

/

7

52

+

5

8 4

+7

52

A Simple Example

A More Complicated Example

Parse Trees: The DNA of Solutions

/

+

4

A More Complicated Example

Freq(“Credit Card”)

Freq(“Huge Savings”)

• The parse trees shown in previous slides are somewhat boring– They always reduced to the same answer– More interesting is when we add feature detectors which allow the result to change

according to some input. For example the parse tree above will give you a different answer according to how many times the phrases “credit card” and “huge savings appears in a document.

– Indeed, parse trees using feature detectors have been used to filter junk e-mail with greater than 90% accuracy (See Katirai, “Filtering Junk Email,” 1999).

How two solutions can be mated to produce “children”

solutions*

2

+

5

8 4

+

72

*

2

+

5

8 4

+7

2 /

Gives

Mated with

And

/

To Mate two solutions

We swap two randomly selected sub-trees (shown below in gray)