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Dec 2005, Changing Times Understanding the Logic of Atheism Creating a Bridge of Understanding Hooman Katirai Slide 2 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. Slide 3 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) Slide 4 Types of Faith Faith Belief in an Idea in the absence of total proof Blind Faith (commitment to a belief regardless of evidence) Empiricism Belief in an idea because its more likely than its complement The complement of a statement is similar to what we might call an opposite. The complement of its raining is everything thats not raining. This would include, sunny, cloudy, windy, etc.. Slide 5 Some Definitions God (or gods) do not exist Atheist The question does God exist? cannot be proven (or disproven) and is therefore meaningless. Agnostic An Might say Im not sure if God exists but Im open to new evidence. Undecided Slide 6 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 Slide 7 Agnostics & Undecideds Both dont know if God does or does not exist Agnostics believe the question cant be answered These two groups will be the focus of our discussions! Slide 8 Common Objections to Religion & God Show that existence of God is more likely than non-existence I.e. it is not a fiction. Hatchers Proof. Well show ideas like An unknowable creator, Manifestations, etc are all reasonable. There can be perfect justice If there is a next world Ideas in religion are too 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 while Followers are not. Precisely why God sends new messengers Too much suffering in world for there to be a God. Slide 9 Overcoming Obstacles Well show Science is based on Faith! But a special Kind of faith that can Also be applied in religion. I dont believe in religion, which is based on faith I believe in Science Slide 10 Answering Objection 1: Well show science is based on a special kind of faith called empiricism that can be used in religion Objection: I dont believe in religion, which is based on faith I believe in Science Slide 11 Science is based on Faith! How do Physicists discover equations? Simple example: Newtons Law (F=ma) Mass (M) Force (F) Frictionless Surface F A Takeaway: Even fundamental equations in physics are based on Faith!! F=ma Slide 12 Science is based on Faith! (contd) F=ma equation of a line Yet, according to math Infinite number of points between any two points on a line Cant 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. Slide 13 Answering Objection 2: How well answer it: Well show that an unknowable creator, manifestations, etc are all reasonable. Objection: Ideas in religion are too outrageous to be true Slide 14 Part 1: The Analogies Well find situations where we play the role of Creator. These situations will be closely examined in the next part, to learn more about our relationship with God. Slide 15 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) Slide 16 Game of Life (Conway 70) Universe: A Simple Grid Creatures: Yellow cells Empty Space Gray cells Slide 17 The Game of Lifes 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). Slide 18 Game of Life Demo Slide 19 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 Slide 20 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 Slide 21 Genetic Programming Demo Slide 22 Takeaway: We can create universes in which the creatures can evolve over time! Slide 23 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 Slide 24 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 Slide 25 ` Part 2: The Harvest Well use the analogies we studied to draw deductions Slide 26 Suppose you wanted to communicate with your creatures Could you: enter their world? turn yourself into a square on the grid? Slide 27 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 Slide 28 Evidence from Christianity Christ 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 Slide 29 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 Slide 30 And Judaism Moses in an intermediary that delivered Gods 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 Slide 31 And the Bahi 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) Slide 32 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 Slide 33 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 Slide 34 On Miracles Should not constitute a proof: Except to observers Even then there are often alternate explanations Slide 35 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? Slide 36 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 Slide 37 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? Slide 38 Why a Human Intermediary? (contd) A talking tree, or glowing rock constitutes a miracle But weve 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. Slide 39 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. Slide 40 How might our creatures perceive us? The world of our creator so vast that its 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. Slide 41 Parallels On Praise: To have accepted any act or praise from Thy creatures is but an evidence of the wonders of Thy [Gods] 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 Slide 42 But isnt God All-Powerful? Cant God turn himself into a human? Equivalent question: Couldnt God turn himself into a square in Game of Life? Slide 43 Power of the Creator (contd) What do we mean by All-Powerful? In Game of life we are All-Powerful because We can: change games state to any state alter universal laws No creature can stand in our way Slide 44 Meaning of All-Powerful (contd) 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 Slide 45 Power of God (contd) If humans cant be represented in 1 bit Can God? Slide 46 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 Bah'u'llh, p. 112 TAKEAWAY: Its logically impossible for something to be limited and all-powerful at the same time! Slide 47 Power of God Takeaway: Even Gods power has limits All Powerful Ability to do anything Specifically God cannot be not God Slide 48 Further Questions Further Questions: Is humility an attribute of God? Slide 49 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 whos 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 Its 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. Slide 50 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 -Bah'u'llah, Gleanings from the Writings of Bah'u'llah, p. 68 Slide 51 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 Slide 52 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. Bahai Writings: Compilations, Lights of Guidance, p. 506 Slide 53 How do we develop a relationship with an unknowable God? (contd) 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. Slide 54 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 . Slide 55 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. Slide 56 ` Part 3: Proofs of God Well examine and critique two proofs of God Slide 57 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 dont just create themselves You know pyramids dont 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 its 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 doesnt prove there is only one creator; or if another entity created that creator. Slide 58 Hatchers Proof of God William Hatcher (1935-2005) Passed Away in Nov. 2005 Produced the strongest proof of God You can read more in Hatchers Book, Minimalism (ISBN Why hasnt his proof been invented yet? Some basic mathematical tools needed to produce it (Von Neumann Set Theory) hadnt been invented until the 20 th 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 Avincennas proof and reformulated in modern math. Slide 59 Hatchers Proof of God There are some minor differences between the proof you will find here, and the one presented in Hatchers book. In particular, I have done my best to avoid references to set theory while remaining faithful to Hatchers 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.htmhttp://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. Slide 60 Hatchers 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. Slide 61 Hatchers 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). Slide 62 Hatchers 3 Principles P1. All existing phenomena are either self-caused (i.e. A A) or other caused (B A where A B) but not both. P2. If A B, then A E where E is any part of B. P3. A E cannot hold if E is a component of A. Slide 63 P1 P1 says there is a reason for everything When we write A B we mean a contains sufficient reason for B Slide 64 P2 is Hatchers definition of causality. There are numerous definitions of causality One is the efficient cause in which its the straw that breaks the camels back Hatcher does NOT use this definition Instead he uses whats called total causality Under this notion of causality its 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 camels back that causes the camel to break its 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 A B we say A contains sufficient reason for B Slide 65 P3: The Principle of Limitation P3 is a logical principle. It says that a composite phenomena cannot be the cause of its own components. A car for example cannot be the cause of its steering wheel. We illustrate P3 in the next slide Slide 66 P3 (Continued) Every composite phenomena has parts and A relationship or structure between these parts A cars parts laid out on ones 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 of Car Relationship of Parts to each other CAR Slide 67 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 of Car Relationship of Parts to each other (Structure) CAR Slide 68 P3 (Continued) The car cant cause the steering wheel (a part), because the car doesnt 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 its parts come into being simultaneously BUT its not possible for the car to cause its own component. Parts of Car Relationship of Parts to each other (Structure) CAR Slide 69 Proof of a Universal Cause Now that weve 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. V V) I.e. that reality contains sufficient reason for its own existence b) That V is other-caused (i.e. there exists some G V) That is some portion of reality, which we call G, is the ultimate cause of everything. Slide 70 Proof of a Universal Cause Suppose Statement (a) is true i.e. V V By P2, the statement V V implies that V A 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 its 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. G V) Slide 71 Proof that G has no components We know that G V According to P2, this means G G (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 V V does not hold (i.e. it would violate P3). This means G has no components. Slide 72 Proof of Gs 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 well 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. G V. But according to P2, this means G causes everything in V including G; i.e. G G (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. Slide 73 Hatchers Proof Put together, we have shown that there exists a unique (i.e. theres only one), universal (i.e. the cause of everything), self-caused (i.e. it contains sufficient reason for its own existence) cause. This cause is distinct from the universe, but is the cause of everything within it. The proof doesnt 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 Bahai Faith but the findings of the proof are consistent with the God of those religions. Slide 74 Critique of Hatchers 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) Slide 75 Critiquing Hatchers Proof If 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 Hatchers principles pass this test Thus this proof shifts the burden of proof to people to show there isnt a God. Slide 76 Dec 2005, Changing Times Understanding the Logic of Atheism QUESTIONS Hooman Katirai (hooman@alumni.mit.edu in 2006)hooman@alumni.mit.edu Slide 77 ` Backup Slides More details on Genetic Programming Slide 78 Final Questions What could we possibly offer our creator that it doesnt already have? Thankfulness Slide 79 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 parents immediately die after doing so. Mutation operator Genetic Code = Parse Trees Slide 80 Parse Trees: The DNA of Solutions + / 7 52 + 5 84 + 7 52 A Simple Example A More Complicated Example Slide 81 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). Slide 82 How two solutions can be mated to produce children solutions * 2 + 5 84 + 7 2 * 2 + 5 84 +7 2 / Gives Mated with And / To Mate two solutions We swap two randomly selected sub-trees (shown below in gray)