What Is Occam's Razor and Why Does It Matter

In the early 14th century the English logician William of Ockham promoted an idea simply stated as "Entities are not to be multiplied without necessity."  By this he meant (as he expounded in his writings) that in order to explain something, one should make the smallest possible number of wild assumptions.  Otherwise known as the Law of Parsimony (due to the implied frugality or nearness with speculation and hypotheses, "parsimony" being a word that means something like "cheapskate"), this has since become more widely recognized as Occam's Razor, cutting and scraping away the improbable from the reasonable.

This rule-of-thumb concords with more precise, modern analytical methods including Bayesian theory, in which every additional assumption needed to support a hypothesis reduces the probability of the issue.  For instance, two marginally probable circumstances together are significantly less probable than either one on its own. This is why Conspiracy Theories become less and less reasonable for every element that must be added to get it to hold together.

Even Monks / Like to be seen /
 Looking suave and clean / Burma Shave!

And as with all forms of Abductive Reasoning, the Law of Parsimony is not an infallible arbiter of Truth, but is more like a reverse-truth-detector that beeps more insistently the further from truth one strays. It is useful as a kind of triage for selecting which hypotheses may be more productively tested, whether through falsification or verification.

While Ockham was evidently familiar with literal razors and their ordinary use, as a Franciscan Monk, a Deist, and a Theologian, he ironically made rather poor use of his eponymous Razor in his acceptance of gods and the supernatural.  We might forgive him, however, since at the time there were a number of legitimately open questions relating to physics and biology that resisted explanation.  This state of ignorance (a direct consequence of christianity's relentless suppression of scientific progress since the Roman Empire) could not prima facie rule out the existence of supernatural agencies as an explanation for biology and physics.  I mean, other than the obvious absurdity of the very idea of magic sky-men.

The situation is different today, and the open questions that once admitted supernatural agency as a possible explanation are now quite settled without any appeal to the supernatural and requiring no agency or intelligence whatsoever.  Since then, new questions have been both asked and answered, again without need of any intervention by magic invisible wizards.  The evidence points rather to no such intervention ever having occurred.

Yet on the other hand we might not forgive him this failure to apply his own fundamental rule of rationality.  One may defend William of Ockham by pointing out that he was at least a monotheist, and thus walked his talk by not multiplying entities without necessity - just one invisible wizard accounted for all that could be seen.  But was that really true?  Was it though?  Was he indeed a monotheist? And is one magic man really sufficient to account for the world he observed? 

While christianity insists on the label "monotheistic," it does not walk the talk.  To explain the entirety of observed reality, they have posited not just one but an entire pantheon of magical beings.  To begin with, their wholly "good" god has to have a counterpart, Satan, to account for the existence of "evil" (the existence of which is more assumed than detected as substantive).   This "enemy" actually cooperates with their main god to obediently torture all the souls who are not sufficiently in god's camp.  Then, evidently lacking both the omnipotence and the goodness to forgive, their omnipotent and infinitely good god needs another god to act as an intercessory for us naughty imperfect creations that an infinitely wise and good god allegedly created to be like this.  And even that being insufficient for ordinary daily needs, William of Ockham as a member of his church in good standing officially supported a long list of saints, angels, demons, spirits, and other beings (seraphim, cherubim, etc), all of which are indistinguishable from the kinds of entities that the acknowledged polytheistic pagan religions had in multiplicity. 

This confused incoherent tangle of theology is a direct and demonstrable consequence of the syncretic origins of christianity - cobbled together from random bits of numerous previous religions, from zoroastrianism, caananite religions, egyptian cults, and the long lists of greek, roman, nordic, and vedic gods.  Religion has evolved in a clearly Darwinian struggle for survival.  Religious ideas have over the centuries accumulated through random permutations certain "sticky" adaptations that make them harder to get rid of and thus more likely to produce offshoots of ever-widening variety.  

The divergence and proliferation of religions tells us two important things about it.  1) There is no underlying reality or truth towards which religion is converging, as can be observed in other pursuits such as the natural sciences.  2) Religion possesses no means of adjudicating its assertions.  Whenever any two theologians disagree, they split and two new religions are born.

Occam's Razor properly applied is a useful way of avoiding such fruitless pursuits.  In the first place, modern science does not have any need to appeal to magical agency for explanations for things, rendering any such appeal unnecessary and hence immediately excluded by Occam's Razor, which I remind us states that "Entities are not to be multiplied without necessity."

Secondly, we can see in countless instances that an invocation of even one magical agency is never enough, and leads to a never-ending cascade (or multiplication) of further invocations and assumptions; inventions, and speculations.  Opening the door to even one absurdity invites a flood of absurdities to follow. 

Analogously, just one Epicycle was never enough to explain the motions of planets in a geocentric cosmology: you needed either an infinity of epicycles lacking any explanation or mechanism (the nature of which only invited - demanded even - further speculation), or you could adopt just one heliocentric model that does not insist upon ideologically pure circular orbits to substantially solve the problem. Just one more idea - Relativity - gets you all the rest of the way to explaining everything about celestial mechanics.  This is what is meant by an economy or parsimony of ideas. 

When you are on the wrong track, sometimes a proliferation of necessary assumptions is the warning sign you need to turn back and try something else.  This is the power of Occam's Razor: to shave away unproductive wild speculation of things we do not and cannot know anything about, and focus instead on a few things we can know and test.  

The inventor of a thing is rarely its most accomplished practitioner (ref Adolphe Sax whom nobody remembers for his swingin' tunes and sick jams).  William of Ockham was no exception.  Had he applied his razor to his mind as diligently as he did to his face, he would have not wasted any time worrying about what gods were like.  

Can You Prove a Negative?

People who learn a little about Scientific Method or Logic often proudly declare that You Can't Prove A Negative.  The problem is that they stopped learning science just a wee bit too early.  What they think they know about Scientific Method is really a mis-application of a quickie rule of thumb for how to construct a well-stated hypothesis for the kind of experiment you have in mind.  Prove a Negative is shorthand for confirm a negative hypothesis.

A negative hypothesis is just a testable statement framed as a negative, along the lines of humans can't fly.  How can we ever prove that?  We could certainly disprove it by producing even one verified instance of a human that flies.  But to positively prove that humans can't fly, other than specific instances of specific humans failing to fly on specific days, defies logic.  The best you can do is to show evidence that supports it (humans hitting the ground in undeniably un-flight-like fashion), and then to conditionally accept the hypothesis, or regard it as indistinguishable from true.  For the time being.  Until we someday get better at distinguishing.

The perfect hypothesis in the perfect experiment would either be fully confirmed or fully disconfirmed by the experiment.  But this rarely happens.  Usually the best we can do is to either disconfirm a falsifiable hypothesis, or to confirm a confirmatory hypothesis.

To falsify a falsifiable hypothesis means that the hypothesis is definitely disproved.  It is conclusively rejected, never to rise again.  If we fail to disprove a falsifiable hypothesis, then it might be true, but it might still be false as well.  It just means we were unable to reject it this time on the basis of this evidence from this experiment.  In the light of lots of other experiments all of which likewise failed to falsify the hypothesis, we might be forced to accept the hypothesis as indistinguishable from true around the time we run out of ways of testing the hypothesis.

The Natural Sciences tend to use falsifiable hypotheses because it is the most reliable way of finding out objective facts.  Only something that is virtually indistinguishable from true can withstand a determined, persistent onslaught of experiments seeking to disconfirm it.  It is just too easy to find evidence that confirms (erroneously) what you want to be true, because this is a basic operational bias of the human brain.

Falsifying is also a very efficient way of clearing out the myriad possible explanations that are wrong in order to zero in on the one that is right.  And it is generally easier to falsify or prove wrong a positive statement about what is, rather than a negative statement about what isn't.  All humans can fly is readily disproved; whereas no humans can fly is a lot harder to disprove, and these are not the only two possibilities.

You can see how easy it is to frame a hypothesis as either positive or negative.  Just be careful about false binaries.  If one explanation fails, it isn't automatically the competing one.  If all humans can fly fails, it does not automatically follow that no humans can fly, or that all humans can't fly.  It just means you weren't able to do it that time.  Perhaps humans can sometimes fly, with the right sort of suit and a good running start.  NO capes, though.  No capes!

Applied Science (e.g. engineering) tends to use confirmatory or provable hypotheses because it is the more efficient way to invent things.  "Cameras are possible, because look at this working prototype I just made."  Hypothesis confirmed in one experiment.  Or you could frame the hypothesis as cameras are impossible and disconfirm that with the same single experiment.  But most of the time x is impossible is not the preferred way to frame a hypothesis in Applied Science.  The first ninety-nine camera prototypes that didn't work could be taken (erroneously) as evidence supporting this poorly framed hypothesis.  The injunction you can't prove a negative is more a rule against framing hypotheses as negatives - a rule that is also frequently broken when appropriate to do so.

I still haven't answered the question - can you ever prove a negative hypothesis of the type XYZ does not exist?  Is it ever possible to confirm this kind of hypothesis?  Many top scientists will say, on principle, "No."  But what if I gave you an example of Science positively proving the non-existence of something?  And to make it harder, what if the thing already had scientific evidence for it and the beginnings of a consensus on its existence?

Our story starts in France in 1903.  Respected and accomplished physicist Prosper-René Blondlot (1849 - 1930) needed an explanation for some weird shit his experiments were doing, and he also really needed to keep up with the other scientists of the age who were discovering new rays left and right.  X-rays.  Alpha Rays.  Gamma Rays.  Beta Rays.  Is there no end to the vast variety of rays to be discovered in Nature?  Well, actually, that was . . . um . . . that's pretty much all of them.

In any case, Blondlot wishfully assumed an experimental glitch he was seeing must be caused by one of these new Rays everyone was constantly discovering, which he named N-Rays.  He set up a new cockamamie experiment that was guaranteed to not detect any other previously discovered kind of ray, and immediately found what he was looking for. Once he reported this amazing discovery, other scientists started reporting confirmations of his discovery in their own labs.  Soon, N-Rays were being reported emanating from a wide range of materials with the oddly specific exceptions of green wood and rock salt.

N-Ray Mania swept France, and in just the first half of 1904 over 50 scientific papers were published on the subject (compared to just 3 about X-Rays).  Eventually there would be over 300 papers on N-Rays.  Over 120 other scientists confirmed the existence and properties of N-Rays.  A serious dispute arose over who was the first to discover N-Rays emanating from the human body.  The French Academy of Sciences awarded Blondlot a prize of Fr 50,000 (almost $600,000 in today's money).  He had international fame, was a national hero in France, and he had his eye on a Nobel Prize.

Only problem was, N-Rays don't exist.  They never did.

And Science proved it with one simple experiment.  Well, a meta-experiment actually.  A wickedly clever and devious experiment conducted on the way N-Ray Science was being done.

So how do you confirm the hypothesis N-Rays Don't Exist?  Well, if N-Rays are a mere phantasm in the minds of scientists (and there was some reason to suspect this alternative explanation) then crucially disrupting the experiment without the knowledge of the scientist should have no effect on the "positive" results of experiment.

The fact that many eminent German and British scientists were entirely unable to replicate Blondlot's discoveries, and that the detection required the involved natural senses of the researchers, made hallucination one possible explanation for the phenomenon of N-Rays.  This hypothesis is testable in an experiment conducted on N-Ray Science rather than on N-Rays themselves.  If N-Ray Science is not affected by disabling the apparatus in a way unknown to and undetectable by the researcher, then this should only be possible if N-Ray Science is basically hallucinations (or outright fraud) on the part of the researchers.  An objective phenomenon is supremely sensitive to technical faults in the apparatus; a subjective experience requires only a belief in the apparatus.

Unfair, you say?  Unethical?  Well they started it.  Those researchers inserted themselves into the experiment, so I say it is fair game to conduct experiments upon them without their knowledge.  Today most science utilizes electronic or otherwise mechanized detection, measurement, and data collection instrumentation in order to prevent the biases of the faulty human brain from contaminating the data.  In cases where this is not possible, the gold standard is a double-blind study, in which neither the researchers nor the subjects (where relevant) know what they are doing or often what the experiment is even about.  Only the designer of the study knows, and she is explicitly forbidden from participating in the data collection or analysis, and definitely forbidden from winking and gesturing in the researchers' direction.

In this case, American physicist Robert W. Wood traveled to Blondlot's laboratory in Nancy, France in September 1904.  His perceived impartiality as neither British nor German was essential to this project.  Whilst Blondlot happily demonstrated the "detection" of N-Rays, Wood removed a crucial part of the experimental apparatus without Blondlot's knowledge, which according to N-Ray theory should have rendered detection of N-Rays utterly impossible.  But Blondlot continued counting and recording N-Rays on his phosphor screen, oblivious to the sabotage.  Wood meanwhile was unable to observe any N-Rays, either before or after disabling the apparatus.  "Not those big, obvious flashes of light," Blondlot explained, "Look for the much, much fainter ones."  Yeah right - the ones that look just like what you see when you close your eyes.

Since N-Rays were detectable only by certain people and detectable whether the apparatus was operational or not, since N-Rays were never able to be recorded photographically in spite of numerous determined efforts, and since N-Rays had neither theoretical explanation nor theoretical reason to exist, there was only one conclusion to make, and that conclusion did not have to be conditional, tentative, or subject to qualification.  Science had confirmed the hypothesis that N-Rays Do Not Exist.

So it is possible to prove a negative if you can do the following:

1. Demonstrate the absence of any solid evidence for the thing.  Solid evidence means evidence which bears no other explanation and is repeatable.  Absence of evidence is very much evidence of absence, in cases where the hypothesis demands such evidence to be found precisely where it is not.
2. Propose and test alternative explanations for all the evidence that does exist, such as it is.  In our story this test consisted of showing that N-Ray detection was unaffected by disabling the apparatus, a state of affairs not concordant with objective phenomena, but perfectly concordant with subjective ones.
3. Demonstrate that the non-existence of the thing is entirely concordant with all other available data.

Things that definitely do not exist can be proven not to exist if these three hurdles can be cleared.  It is not necessary to be agnostic about every potentiality and every absurd claim on the basis that "you can't prove a negative."  Because quite often, you can.







Sources:
Klotz, I.M.  "The N-Ray Affair," Scientific American, May 1980
Wood, R.W.  "The N-Rays," Nature, Sept 1904, 70 (1822): 530–531

Examining Objectivity

Describing statements or reasoning as Subjective means that their validity depends on (is subject to) who is making them.  While it may well be objectively true that mushrooms are good food based on analysis of their nutrients, composition, and demonstrated absence of toxicity, it is not a true objective statement to assert that I like mushrooms and I think they are good, taste good, and are nice to eat.  Some people can truthfully make that statement, but I cannot.  So the truth of that statement is subject to the condition of who is making the statement.

An objective statement is one that anyone can make without changing its veracity status.  Mushrooms often have a rubbery texture. This is demonstrably true whether I say it or someone else does. It is a statement in objective concordance with reality rather than a personal value judgement.  If I wanted to defend or explain my disinclination to eat mushrooms, I might appeal to objective facts such as this, followed by an ultimately subjective statement such as, "and I don't like rubbery things to be in my mouth. Bleah."

Whatever flavor mushrooms may or may not objectively have, to my subjective tastes this alleged flavor does not offset the most unpleasant feeling of rubbery fungus between my teeth.  But I am getting a little bit off track I see.

Objectivity roughly means the ability to reach the same conclusion as anyone else.  More precisely it means the ability to reason or reach a specific conclusion that is determined by the outside reality of things rather than predetermined by who you are or where you were born.

I assert that it is not possible for a religious person to reason objectively about religion.  That was certainly true for myself once upon a time in a galaxy far, far away.  But why would it be universally true?  It's because "My religion is true" and "I like mushrooms" are both subjective statements that only certain people can make, and not objective conclusions that should or even could apply to everybody.

By definition a religious person believes in or accepts a religious conclusion a priori.  When one asks a religious person to reason about a substantive question of religion one finds that there is already a conclusion in place that the person must reach.  He is not free to even consider certain possibilities, such as that this religion is false or that a specifically believed religious premise or claim is wrong.

"But surely," you say, "It is not impossible for an intellectually honest religious person to suspend belief and consider a question objectively."  Perhaps, but how would we know if or when that ever happens?  More to the point, how would he know?  The brain is very adept at concealing intent from itself and forcing reasoning processes into a predetermined outcome, leaving the Reasoner to invent whatever reasons it needs.  This is called Motivated Reasoning and it in no way needs to be at a conscious level of awareness or intent.  A religious person can be completely unaware of being controlled by motivated reasoning.  He might not be at all aware of whatever feats of cognitive gymnastics he had to perform in order to get to the necessary pre-determined conclusion, and can even be cognitively blind to egregious fallacies and errors he may be committing.

The simple fact is that when someone needs one conclusion to be reached over any other, or is invested personally, emotionally, socially (and yes - often financially) in one outcome over another, that person will not reason objectively, full stop.  Even if by some chance that person reaches a valid conclusion, the conclusion and more importantly the process cannot be relied upon.  It is unreliable, and therefore wrong even if accidentally valid on occasion.

It is useless therefore to ask a religious person to reason through questions of, for instance, whether their religion's origin story is factual (historically accurate), or whether testable claims made by the religion are supported by the evidence.  Whether gods exist and sometimes modify or directly influence events the physical universe.  As James Randi was fond of saying, "Those who believe without reason cannot be convinced by reason."  They are playing a fundamentally different game. It may look and sound a bit like reasoning, but it isn't reasoning. It's justifying a belief, also known as Apologetics.

To which the religious person may reply with turnaround: "Well your atheism is just another belief!  You are motivated to believe my God doesn't exist because you need that to be true."

Bollocks.  Boll.  Locks.

Non-belief is just another belief in the same way that OFF is a TV network and not collecting stamps is a hobby.  Never playing tennis is a sport.  Being dead is a lifestyle.  Baldness is a hairstyle.  None is a breed of dog one owns as a pet.  And accusing me of having "just another belief" is an admission that mere belief is not an intellectually honest or sound position to hold in the first place.

I neither need a religious premise to be true nor do I need it to be false.  But back in the day when I did need a religion to be true and when I was invested in it, it seemed totally true.  If it were objectively true, it should still seem at least a little bit true now, even though I no longer need anything it has. However once that link breaks and Motivated Reasoning is no longer operating in one direction or the other, objective conclusions are possible to reach.  Reliable conclusions can be reached - not just one-off conclusions, but replicated and documented ones that anyone can get to.

Do I need there to be no gods because if there were, they would want to punish me?  On the contrary.  If I thought that, I would be motivated to believe in gods, not to disbelieve.  "But you really need there to be no Hell, because you love your sins and you are for sure going there!"  No, I certainly am doing no such thing.  If I really thought there was such a thing as hell, once again, I would be strongly motivated to defy logic and evidence and believe differently.

I am not going to try to convince a religious person that I am a good and ethical person worthy of the best of all possible afterlife scenarios.  It is an unacceptable powerplay and oppressive control tactic to make people assert their worthiness to the satisfaction of some goddamned self-righteous religious authority, and it ain't gonna happen.  But if I needed to, I could prove beyond doubt that I am above ethical reproach by all the major gods or goddesses in most popular storybooks.  Except for some of the wackier and capricious rules like weird hairstyles, removed body parts, the wearing of silly hats, or arbitrary cultural constructs like calendar-based numerological and astrological observances.  And if the only crime that can be laid at my feet in some sort of post-mortality reality TV show eviction episode is that I did not believe in some bullshit that went against all logic and evidence, then the producers can kiss my big, bare, pasty white ass.

I would be happy to accept the reality of gods or goddesses provided A) evidence concordant with no other ordinary explanation were produced, and 2) satisfactory explanations for all the evidence against gods were also produced.

In short, either produce a specimen for examination and/or interrogation, or fuck right off with this 'gods' bullshit and let us hear no more about it.

Santa Claus Agnosticism

You know who really shits me?  Smart-arses who smugly proclaim,

"Well actually, you can't technically prove Santa Claus doesn't exist, so being agnostic about Santa Claus is the only tenable position to take."

This is a disingenuous and intellectually lazy position.  Such fence-sitters just can't be bothered to understand the evidence behind the fact that there is no Santa Claus; that it is and always was a fiction.  I submit that the reason for taking such a patently absurd position is out of fear of offending people who believe in Santa Claus.

But it gets worse.  There are people either so petrified of offending anybody or so lazy that they do not even want to touch the subject that they are lead to say things like,

"Nobody should even care whether there is a Santa Claus or not."

Really?   Really?  The discovery that Santa Claus was actually real would not be the most astonishing, world-changing event in history?  The discovery that all of reality, all of history, all of science is now proven to be upside-down, inside out, and just plain wrong? If there's even a chance that Santa Claus was a real being who did what the stories claim he does, do you honestly expect me to believe that you wouldn't want to know this?  Well, I don't believe you.

Santa Claus Agnosticism and Santa Claus Apathy are wholly unnecessary positions to take because it can be demonstrated beyond any reasonable person's doubt that there never was any Santa Claus apart from possibly Nicholas of Myra, a 4th century figure of questionable historicity who scarcely resembles the Santa Claus of popular mythology, and who is now widely acknowledged as being dead.


So how do we know there really is no Santa Claus?

1.  Provenance of source materials.  There is no corroborating documentary evidence for Santa Claus apart from a small number of source documents which cannot be regarded as anything other than fictional works.  They have always been recognized as fiction, and were never intended to be anything but.  Also we can trace the development through history of the myth of Santa Claus, demonstrating that rather than arising from an individual's actual acts, they arose in a syncretic manner through ordinary myth-making processes.  Basically, just people making up stories.

2. Demonstrated physical impossibility.  The acts attributed to Santa Claus are provably not things that this universe's physics support or permit.  For Santa Claus to be real, physics, biology, chemistry, and even economics would have had to turn out quite differently to how they are actually discovered to be.

3.  Absence.  No real Santa Claus has ever been observed, communicated with, met with, photographed, or has ever left any physical or documentary evidence not explainable by entirely mundane non-Santa circumstances.  Neither would any real Santa have a legitimate reason for concealing his existence, the existence of elves, flying reindeer, gifts not actually manufactured and delivered by humans, or those three women he's always talking about (rather disparagingly, at that).  Absence of evidence precisely where that evidence must be found to support a hypothesis is perfectly valid evidence of absence.

If you are one of those who crouch behind a misunderstanding and misrepresentation of the Scientific Method and Karl Popper's Inductivism and squawk about being agnostic while feeling superior about it, then you, my friend, are Dumb and Wrong.  Agnosticism is not a reasonable position to take when there is ample evidence against a proposition and zero evidence for it, regardless of how many people believe in some piece of demonstrable nonsense. No, you are merely afraid of ruffling feathers by offending people's cherished delusions.

So don't pretend that agnosticism is a superior position to take, and that it is anything other than disingenuous intellectual laziness.

Good day.

Understanding Mathematics

What is Mathematics?  Everyone has an answer for this; few answers make any sense.  Even highly regarded philosophers and scientists answer this question incorrectly, probably because nobody has challenged the explanations, and they have better things to do than sit around worrying about it.

Daniel Dennett (philosopher) calls mathematics a scientific system attempting to be internally consistent without any direct empirical basis or meaning.  He is sadly wrong.  Lawrence Krauss (physicist) calls mathematics a kind of philosophy - a tool for thinking about things and working out "what if" sorts of questions.  He is slightly less wrong.  Wikipedia and most pedagogical sources define Mathematics as a Formal Science, declaring that it is "not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules."  This is also completely wrong.  Mathematics is supremely concerned with what statements are objectively, universally true.

Any number of statements about what Mathematics is or is not have been made: Mathematics is a language.  Mathematics is a tool.  Mathematics is a game.  Mathematics is puzzles.  Mathematics is an arbitrary construct.  Mathematics is imperialist male-centric in-group signalling.  Bla bla bla.  All mostly misinformed rubbish. And not only offered by people who never use it or who know nothing about it beyond what they were unable to grasp in high school.  People who use mathematics professionally, and even people who consider themselves professional mathematicians, usually have not really thought about what this thing is, why it works, and what it means.

So what is Mathematics really?  Let's break it down. The syntax and notation of mathematics should be considered separately to the facts, discoveries, or conclusions of mathematics.  The way we communicate and work with mathematical ideas is an invention that has been developed over hundreds of years.  Few people for instance can today understand and work through the mathematical notations of early discoverers like Newton, Euler, Gauss, or Leibniz.  Also, different cultures that discovered mathematical facts and principles independently often have mutually unintelligible ways of expressing those facts.  Mathematical systems of notation therefore share characteristics of a language: arbitrary, relative to the culture that created it, and not universal or unique.

And then there's the ideas themselves.  The content of mathematics (as divorced from the syntax) are discovered truths about quantities (numbers), the relationships between quantities and groups of quantities, and truths about operations on quantities and the transformation and manipulation of identifiable quantitative objects.  These facts, being discoveries and not inventions, are universal.  They are also absolute, and not (as many claim) merely relative to a set of assumed axioms.  I assert that the basis of mathematics is not axiomatic, but empirical beginning with the empirical existence of integer counting numbers and their properties, and extending to the empirical, discoverable, and absolute properties of idealized geometric objects, spaces, operations, and functions.  Once we understand and get over the problem of syntax, it is easier to understand mathematics as the following:

Mathematics is the taxonomy of discovered quantities, quantitative objects, their properties, and of mathematical operations, and the discovered relationships between quantities, operations, and quantitative objects.  Mathematics makes use of arbitrary and non-unique invented systems of syntax and notation in order to document and explore this taxonomy.

Mathematical quantities and quantitative objects exist not because we (or any other agency) call them into existence, but because of nothing more than the possibility of the existence of one, two three, or any other number of distinguishable things, be they asteroids, universes, atoms, oranges, or just abstract units or groups of units.  And that is a very, very low bar for the existence of anything - so low that one may as well accept that mathematics is as self-existing as anything could be, existing and awaiting only discovery by competent observers.

Meanwhile the syntax and notation of mathematics are clearly human inventions.  They are somewhat arbitrary in that respect, are not unique (i.e. by no means the only possible systems of notation), have regional dialects, and clearly evolve over time.  While each system of syntax strives to be internally consistent and unambiguous, they are not always perfect.  Syntax, like language, must be learned from other users of the syntax and through determined effort.  We develop with effort and practice the facility to interpret and manipulate the syntax and notation of mathematics in order to read, manipulate, or write universal mathematical ideas.

Syntax and notation allows us to do three things. 

1. Using syntax one can read and interpret a mathematical statement.  This may be in the form of defining a stand-alone mathematical object (quantity or group of quantities) or in the form of a statement about a relationship between quantities, usually in the form of an equality relationship involving an operation.  Mathematical statements often express information about how aggregate quantities are comprised of or related to other quantities, e.g. by addition or multiplication.  The area of a rectangle is the quantity representing the base of the rectangle multiplied by the quantity representing the height.  The length of an object in centimeters is related to the length of that object in inches through multiplication by 2.54.  These cumbersome statements of fact are abbreviated succinctly using an invented notation: A = B*H;   1 in = 2.54 cm.

2.  Through the use of a suitable syntax we can manipulate mathematical statements to find equivalent statements.  The statement "This tree weighs five tonnes," stripped of the ambiguity and possible smarty-pants alternative meanings of a natural language statement, becomes Wtree = 5 t.  As such it can be manipulated to express what else can be known from this statement alone.  This includes the conclusions that two identical such trees would necessarily weigh 10 tonnes together, a tonne is one equal fifth part of this tree, dividing the tree into two parts of equal mass must yield parts of 2.5 t each, and so on.  Notice that such manipulations and transformations do not add any new knowledge, but at best re-state the existing knowledge in order to be applicable or relevant to specific questions one may ask.  It tells us only what we already know, although sometimes in a way that we did not at first appreciate.

For example, if we know that the speed of a certain body increases by 32 feet per second each second, it is pretty obvious that after 3 seconds of accelerating from rest, the object must be travelling at a speed of 3 x 32 = 96 feet/sec.  This we know by mere extension or re-statement of the premise.  No new information is required.  But far less obvious is the fact that after 3 seconds it must also necessarily be 144 feet away.  This non-obvious fact is not new information; it is actually contained within the premise.  It only becomes obvious when the statement, expressed in mathematical syntax, undergoes valid syntactical transformations and manipulations leading to other entirely equivalent statements which we can then interpret.  This is not generally possible with natural-language statements.

Mathematical manipulations of the syntactical expression of a statement accepted as true, done in such a way that each re-statement is also true, permit us to uncover many other true statements implied or required by the original one.  It may be the case however that not all possible true statements about the premise can be discovered.  The only guarantee is that if each manipulation is valid, the result is a true re-statement of the premise.

3.  We can express mathematical ideas including asking questions about quantities and testing hypotheses about the relationships between mathematical objects.  A mathematical object is sometimes literally an object like a line, a triangle, or a sphere, but more generally it is an identifiable collection of numbers, often which have a simple rule for determining which numbers belong to the object.  Sometimes the numbers have to be in a specific order; sometimes it is something simple like "all numbers less than five."

For example, one may ask in natural language, "Which is the larger of the two - the area of a circle of diameter equal to one Glaaarrghtoot (aka a Glaaarrghsnaffian Inchmeter - 1/100,000 the mean circumference of Planet Glaaarrghsnaffia VII), or the area of a triangle, each side of which is also exactly one Glaaarrghtoot?"  And while philosophers and theologians unconstrained by knowledge endlessly dispute the meaning of words like "circle," "diameter," "triangle," "planet," and "equal," and while engineers Space-Google the mean circumference of G. VII in Spaceyards, we can cut right to the chase using mathematical syntax:

√3 >? 𝜋

In this form the question is readily and unambiguously answered: the circle has the larger area, on any planet or on no planet at all; in any universe or in no universe at all.  However, as you may have noticed, finding the answer was not possible by syntax alone, but is also inextricably linked to the meaning of mathematical objects such as "3" and "𝜋," and by the existence of operations such as the square-root. So we leave syntax aside for now with the understanding that while itself an invention, the things syntax expresses are not inventions but discoveries.

Mathematical discoveries include all numbers; groups of numbers; relationships between numbers; mathematical objects including geometric shapes, functions, and other identifiable groupings of quantities; operations that transform numbers, groups of numbers and objects; and relationships between mathematical objects.

These discoveries begin with the discovery of 1. The unit. A thing. Any single thing. Then along comes another thing, and we immediately discover 2. Two things. The idea of two. Two of something. Also, we make the discovery that one and one is two; or that two ones is two, two divided equally into two is one, and one removed from two is once again one. In our notation,

1 + 1 = 2

1 x 2 = 2

2 / 2 = 1

2 - 1 = 1

By careful observation of two units both together and apart, we have also thus discovered (not invented) the operations of addition, subtraction, multiplication, and division. Then we discover 3, 4, 5, and all the other cardinal numbers, and a myriad of facts about the relationships between them. We discover even numbers, odd numbers, square numbers, prime numbers, factors, divisors, etc in endless variety.

We can also discover without any further assumptions (or axioms) whatsoever the existence of an infinity of numbers between the cardinal (integer) numbers, as well as negative numbers. These non-obvious numbers are called into existence by the very existence of the operations we discovered at the start. Because Division empirically exists (you can divide objects or collections of things and count the results), non-integer numbers must therefore also exist. Five must ultimately be capable of being divided by two, for instance. Because Subtraction is a thing, negative numbers must therefore also be a thing. You can have an actual deficit of frogs - negative frogs - if someone owes you a frog.

Because an endless series of dividing whole numbers have no reason not to exist, irrational numbers (not expressible by any finite number of divisions of whole numbers) likewise are permitted to exist, and it can be shown that they do. Even less obviously, if multiplication is to be a logically self-consistent thing that exists, "imaginary" numbers must also exist - numbers which when multiplied together produce negative numbers, which we already know exist.

Besides quantities, there are endless other kinds of mathematical objects to be discovered: the point, the line, the plane, points on a plane, geometric shapes on the plane as identifiable groups of related points, n-dimensional spaces, and n-dimensional geometric objects. There are functions in endless variety: groups of numbers that are related to each other through a sequence of operations. y = 5x. y = sine(2x). All just awaiting discovery, and the discovery of their numerous obvious and not-so-obvious interrelationships. New techniques and better systems of syntax often need to be invented in order to more easily work with more complicated discovered objects.

But you may say all these "empirical" discoveries are merely of abstract ideals, not objects of physical existence. What is the connection then to the physical universe? Why do so many natural phenomena lend themselves so well to mathematical descriptions? What is the nature of the strange link between the real world and the purely abstract world of mathematics?

We need to walk back some of the question-begging smuggled in with these questions. Firstly, it is in no way "purely abstract" to observe that discrete items in the physical universe correspond to the cardinal numbers one discovers in mathematics. This is, indeed, how the cardinal numbers were originally discovered. One rock. Two rocks. Another makes three. One bear. Two bears. Holy shit - run for your lives! In no way is this purely abstract or hypothetical. One gallon - two gallons - not to mention the practically unlimited divisibility of gallons of liquids into smaller non-integer quantities. Mathematics is simply not the abstraction that so many have claimed it was.

Natural phenomena and the mathematics that describe them are likewise not the separate entities that the above questions presuppose, either. We discover natural phenomena at about the same time we discover the mathematics that describes them precisely because they are often one and the same. The inverse square law of physical phenomena such as gravity, radiation, luminescence, electric fields etc are not eerily mathematical due to some kind of conspiracy or fine tuning, or some deep mystery of surprising profundity, nor is the mathematics "just a model of reality." Rather, all these physical laws are nothing more than re-statements of the rather mundane mathematical truth discovery that the surface of any sphere increases as the square of its radius. Exponential radioactive decay and the law of half-lives is not atoms being artificially forced to obey an invented mathematical abstraction by some mysterious conspiracy; instead it is merely an instance of probability (another mathematical discovery) happening to large numbers of objects, not abstractly, but in real life.

It is not at all mysterious, nor should it be, that mathematics works so well in the natural and applied sciences, any more than it should be confusing that one rock and another rock makes . . . two rocks. It is a basic truth about things in the universe that they represent and are represented by numbers. Numbers have relationships that we can discover, and those relationships are again reflected in the real objects in the universe that embody these numbers, as a direct consequence of embodying those numbers. What's interesting is that while numbers are readily embodied by physical objects, they can also be embodied by abstractions. Numbers don't even need a universe in order to exist.


The historical development of mathematics is a confused story of simultaneously discovering mathematical objects while struggling to invent ways of talking about them. These are often ad hoc shortenings of natural language descriptions that evolved into some kind of operative syntax. This can easily account for why it is not obvious to more people - even mathematicians - that mathematics is really two very different things bound together: a taxonomy of discovered universal truths about quantities, and an invented arbitrary system of syntax needed to talk about them.

Addressing Some Questions About Determinism

A while back I wrote three posts in a row about why Determinism in the physical sense is not actually a real thing in the real universe and is not a consequence of physical law.  The initial conditions of the universe do not fully determine all future states of the universe, and in particular do not determine all future actions of organic multi-cellular agents.  Such actions may be and often are determined in a sense, or perhaps more accurately predisposed, but not by the universe's initial conditions.  The actions of a dog may be constrained by instinct, conditioning, interactions with other dogs, reactions to random (stochastic) events such as lightning or earthquakes, or done just because the dog felt like it.  The universe's initial conditions certainly had nothing to do with it.  Nor was the appearance of dogs on a tiny planet orbiting a tiny star in one of billions of ordinary galaxies predetermined. The exact sequence of events that lead to that particular dog existing was in no way inevitable, although one may claim inevitability that some form of life evolved somewhere at some time, given enough of it.

My refutation of physical Determinism requires a certain proficiency in Physics to understand.  That may be inevitable as well, but I would like to add some Explainy Words to the body of work that may help fellow physicists as well as, like, musicians and such, to grasp the idea of our Non-Deterministic Universe.  How can a Universe entirely operating on natural physical laws be non-deterministic?

This must be framed by an understanding of what people mean when they say Determinism. The physical meaning of physical Determinism is that all future states are "locked in" by the combination of the physical laws which 100% control the evolution of the universe from one state to the next, and the initial conditions from which the universe starts off.  Many will focus only on the fact that the evolution of states is 100% determined by the physical laws (which we call physics) and set aside the important role of the initial conditions or the starting point, or even the precise nature of the physics that controls the operation of the universe.  While the fact of the universe evolving or functioning entirely according to physics is not called into question except by Deists,Theists, or other proponents of  willful ignorance, this sense of Determinism does not do what its claimants suppose: it does not fix as inevitable all future states of the universe or all future events.  I show that future states are not necessarily fully determined by previous states even when the evolution of states is entirely governed by physics.  I also show that initial states can and often are sufficiently ambiguous to allow future states to be not inevitable even when arrived at by entirely natural physical processes.

At the most basic level that we are yet to understand, the universe possess a Quantum Mechanical physics.  Quantum Mechanics is an explicitly non-deterministic kind of physics.  Hell, even ordinary cause-and-effect struggles to assert itself in the Quantum regime.  That is the universe at the lowest, most basic level we know so far.  The nature of Quantum Physics is that future states while determined by physics are not fully determined by initial conditions, and any given evolution of states is not foreordained by initial conditions even though the laws of Quantum Physics are always fully complied with.  But this is not even remotely the end of the story.

When a system of Quantum particles increases sufficiently in number, Classical or Newtonian Physics emerges as a result.  Let me repeat that:  Classical Physics emerges from Quantum Mechanics when you add enough interacting parts.  A Classical body emerges from putting together a sufficiently large (maybe 10,000) quantum objects in a semi-bound state, such as a baseball or a tiny pebble. Classical bodies obey classical physics including all of Newton's Laws, Hooke's Law, Electromagnetism, and Gravity.  All of this emerges from or arises from Quantum Mechanics, a fully non-deterministic physics.

Classical Physics applied to a small number of Classical Bodies in a simple system over a Reasonable time period exhibits some properties of Determinism.  Determinism is an emergent and temporary property of Classical Physics, which is emergent from non-deterministic Quantum Physics.  What is a simple system and a reasonable time period?  By simple I mean that the number of interactions is about the same order of magnitude as the number of bodies.  In other words we do not see every body interacting with every other body and hence an exponentially larger number of interactions than bodies.  Reasonable time is the time it takes for there to be about the same order of magnitude of interactions as there are bodies.  Beyond that, this newly emerged Determinism starts to break down because of its intrinsic sensitivity to initial conditions and the number of interactions which tend to magnify ambiguity as the number of interactions increases.

When the system is not so simple and/or the time becomes unreasonably long, a new physics begins to emerge: Chaos.  Chaotic physics emerges or arises from Classical Physics and Classical bodies when the sensitivity to initial conditions becomes so great that only infinitely determined initial conditions could constrain all future states of the system.  Without infinitely determined initial states, Chaotic Physics becomes Non-Deterministic: the Non-Determinism has emerged from the increasing complexity of the deterministic Classical system.  Notice we do not have infinity precision of initial conditions at any time anywhere.  Remember, Classical bodies and Classical Physics emerged from Quantum Physics, which is non-deterministic and ambiguous with respect to the exact state of every particle.  It is not the case that the states exist but are unknown; it is more the case that an infinitely unambiguous initial state did not exist in reality.

But we're not done yet.  As Classical bodies get smaller and greater in number, yet another new Physics emerges: Thermodynamics or Statistical Physics.  This physics is again inherently stochastic and non-deterministic.  Specific internal states of Thermodynamic Systems are not determined by initial conditions for the reasons I explained in the post on that topic.  Due to thermodynamic irreversibility (aka entropy increase) information about previous states is irretrievably lost and those exact states no longer play any role in determining future states or the evolution of the system.  Again, from conditionally deterministic Classical Physics emerges a new non-deterministic physics, and the universe is back to being Non-Deterministic again.

To summarize, the Determinism that people are familiar with is only an emergent property of a limited range of physical phenomenon which itself emerges from more fundamental and fundamentally non-deterministic physics.  This limited Determinism dissolves back into non-determinism as soon as the scope of physical phenomena is further expanded.  Only certain Goldilocks conditions can give rise to a temporary illusion of physical Determinism in our universe.

Is it Mental Illness, or is it Make Believe?

Unlike some atheists, I do not think that religious delusions are an actual mental illness. This frequently-encountered claim comes from a reading of the DSM-IV (or is it up to V now?) which defines a delusional mental illness in exactly the language that describes religious fervor, but then makes an unjustified ad-hoc special exclusion for "religious" delusions. And they define "religion" as ... well, they don't.  You just know it when you see it.

from Wikipedia, "List of Cognitive Biases"

But to claim that ordinary misinformed delusions including religion are a mental disorder carries a tacit assumption that the human brain is somehow a perfect cognition machine and could only be wrong when defective.  This assumes the brain was created perfect, or has evolved to perfection. When exposed, this assumption is obviously dumb.  The human brain (and body) is so obviously anything but perfect in the healthy natural state.

Cognitive biases and built-in fallacies in the natural way a healthy human brain functions are more than enough to account for religious experience. We have the Bias of Agency which makes the brain assume something it doesn't understand is evidence of some agent acting in the environment. We have Confirmation Bias which makes confirmatory evidence apparent and suppresses disconfirmatory evidence. We have Motivated Reasoning in which something we need to be true in order to avoid unpleasant emotions or social isolation can quite readily be made to seem fully true by the brain. These are all things that a healthy, normal brain does.

Overcoming these natural thinking defects requires an overlay of artificial thinking tools that Nature has not provided us with, but which humans have invented, passed on, and perfected over the last 10,000 years in particular, and which we now use to be better thinkers. We can, when trained, identify, avoid, correct, and overcome fallacious reasoning, cognitive biases, emotional biases, and social motivations that favour a dodgy conclusion over a correct one.

But it is quite unpopular in the PC Age to suggest that some mental disorders are the sufferer's own fault - that they may be the result of an incorrect utilization of the brain by the brain's owner. My experience is precisely that - practically all of my own neuroses (anguish, self-destructive tendencies  and suffering) and some of my psychoses (clinical pathologies e.g. depression) are the result of me using my brain in dumb ways, and correct themselves when I can be bothered to use my brain in smart ways.

However there has been clinical evidence found that serious mental disorders are more prevalent among the fervently religious. Unknown is whether this is causal (religion messes up people's brains and lives), contra-causal (pre-existing mental illness attracts people to religion), both, or just a coincidence. It would be helpful if religions in their position of privilege and platform would actually teach people effective ways to manage common disorders such as depression, anxiety, addictive/compulsive behaviours, etc. But they offer mere placebos instead, and I think they don't even want to know anything about how the brain really works lest their fragile mythology about humans come into question.

In order to fix problems of mind, like fixing problems in a car, it is absolutely prerequisite to understand how the thing operates. We must accept the brain as a physical machine and not as a magical conduit to/from a perfect infallible agency. Think for even a moment about the concept of "sin." If the Free Agent Ghost Hypothesis were correct, there would not be such a thing as sin, because the ghost would have the agency to decide not to sin. But we see daily examples of devoutly religious people sinning repeatedly, and they don't know why. "Oh the devil is tempting them!" Well then do we have free agency or don't we? No - observed human behaviour does not support the ghost hypothesis. Only the brain as a conditioned environmental modeling survival machine fits the data.

When I learned how to operate the brain, I discovered free agency for the first time and "sin" in my life as a devoutly religious man simply vanished. Shortly thereafter, without sin I found I no longer experienced guilt. Without guilt, religion was somehow just not as important as it used to be. When I didn't need religion to be true anymore, both socially and personally, the motivated reasoning fell, and within weeks the apparent logical cohesion of my religious beliefs had vanished into thin air, exposing the many negative and harmful aspects of it as well as all the logical inconsistencies and factual inaccuracies of it. Without religion, being a happy, good, and decent person is easier than ever and life has far more meaning and wonder. But religions teach that people like me are sinful and are lying about not believing in order to not face my sins. Religion does itself no favour by employing such demonstrably, provably dishonest troll tactics.

Does it matter to me that everybody who was ever a part of my life and who is still religious assumes I must be engaged in some vile sinful acts as the only possible explanation for why I am no longer religious?  I could experience that feeling if I wanted to, but I choose not to use my brain in that way.  Got better things to do with my neurons.

The Best Arguments for Gods

Are these the best arguments for the existence of gods?  If so, then the case for gods and goddesses is looking pretty bleak, to be honest.  These are the best arguments, such as they are, that I encounter from time to time from those who are determined to rescue my soul, and I have to say I am rather underwhelmed by their quality and persuasiveness.  I am fairly disappointed at how evidently ambivalent people are about the welfare of my soul, if these arguments are any reflection.

Keep in mind that an Argument is not Evidence.  It is merely the line that connects evidence to a conclusion. The biggest problem with most arguments in support of the existence of gods and goddesses is that even if the arguments were not fallacious or disjointed they still do not actually link back to or produce any good evidence.  But we will be lenient today and allow the advocates of gods to give me their best shots.  Let 'er rip!

"The Bible says so."  Many people when asked why they think gods exist will immediately turn to scriptural authority.  Why I am unmoved by this argument stems from the fact that by this logic we should also believe in Spiderman.  And why stop there: we should all be worshiping Gandalf, Frodo, and Bellatrix LeStrange too, if we admit this line of reasoning.

Flippancy aside, we are compelled to examine biblical authority more closely to determine if there is any reason whatsoever to take it seriously.  The evidence we have for biblical origins and authorship, both from contemporaneous independent historical records, from textual analysis of source documents and related historical documents, and from artifacts and physical archaeology is that many of the individual "books" of the bible are straight-up forgeries which are not at all what they pretend to be.  A few books are genuine and sincere stand-alone religious texts, but such things are not unique in the world and certainly not unique to the abrahamic gods.  More than enough of the bible is outright fraud to compel us in all honesty to reject the content as a whole as having a supernatural origin.  There is every reason to regard the bible as fraudulent, and no reason to take it seriously or at face value. It should be read and studied as the historical fabrication that it is.

Genesis and Exodus for example are not at all contemporaneous to the supposed events they portray, but instead date to about 450 BC.  Archaeology and contemporaneous historical documents and artifacts positively prove that the events described therein never occurred and the main characters were very definitely not historical figures.  Noah, Abraham, Moses, Joshua etc. were all just stories someone made up, often by plagiarizing much older fictional tales from different contexts entirely.

The New Testament is even worse: while there likely was a real Paul who helped unite a cluster of mystery sects in about 50 AD, about half of the Pauline Epistles found in today's bible are widely acknowledged as later forgeries, likely composed in order to strengthen one particular sect's claim to hegemony.  The Gospels date from at least 70 AD, and are contradicted by contemporaneous accounts, borrow from and rewrite each other, and belong to a genre of acknowledged fictionalized pretend histories of purely mythical figures.  They are not recorded oral histories but carefully crafted allegories fashioned by anonymous writers familiar with Greek literary devices, tropes, and constructs, but strangely unfamiliar with the language, peoples, religions, and customs of Palestine. By examining the bible, I am persuaded that Jesus Christ was an entirely mythical construct based on the older Angel Joshua of Judaism, and never an actual living historical person.  So, in other words, no.  The bible is provably factually wrong in countless instances, is very clearly and obviously a man-made  and ever-evolving fiction, and does not authoritatively prove that there ever were any gods at all, any more than comic books prove there is a Spiderman.

"People don't know how to be Moral until God decrees what is and is not Moral."  They call this the argument from Objective Morality, but it is neither objective nor moral.  What the believers in gods have is an arbitrary morality that is fundamentally immoral, as I explain here and again here.  The idea that morality and ethical behaviour in humans and human societies is entirely attributable to the existence of gods is a bad argument for gods precisely because it is false.  Godless humans and human societies somehow find their way to ethical standards of behaviour that often exceed those of religious societies.  Hell, even packs of chimpanzees and dogs have a basic moral sense that guides their behaviour.  You can't tell me they got that by reading the bible.

So let's look at that bible one more time.  The various gods described in the bible beginning with a minor actor in the Caananite pantheon of gods and goddesses are savage, sadistic, primitive assholes whom no one today would describe as "moral."   The jealous, overly-sensitive volcano god Yahweh seems to have a real inferiority complex and keeps trying to convince everyone through his bloodthirsty rage that he's the greatest of all the many, many gods.  And we're supposed to learn morality from that?   Later gods (or possibly the same god slightly grown-up) seem to care a little too deeply about provincial politics and is more than happy to spend the death and suffering of his people for short-term political or territorial gains.  Look, no thinking person takes the bible seriously, and if you actually read the thing you wouldn't be spouting off about how "moral" the utterly barbaric bible is.

Religious societies are more likely to abuse the human rights of its citizens, especially of women, ethnic minorities, religious minorities, political minorities, and  sexual minorities (e.g. transgender people, homosexuals, etc).  How do they justify the objectively immoral inflicting of suffering and abuse on the powerless?  Religion and the ridiculous arbitrary behavioural code they have confused with and substituted for actual morality.

The comeback argument usually sounds something like "If people didn't think there would be an ultimate justice, they wouldn't be afraid of doing whatever they wanted all the time - steal, kill, rape, and be atheist."  Really?  What "people" is that you're talking about?  Normal people don't need to be threatened with hell in order to want to do the right thing and create through their own acts the sort of world they'd like to live in.  If the fear of eternal torture in hell and a watchful, vengeful god is all that is keeping you from doing horrible things to your fellow humans, then what you are is a psychopath and I hope you never stop believing in hell.

"The Universe had to start somehow, and it could only be Gods."  Couldn't it though?  That is a bold assertion to make without evidence.  Why could not the universe posses entirely natural causes, origins, and workings?  Everything we know about this universe so far, after just a few centuries of serious investigation, is that it is entirely naturalistic and requires no universal intelligent agency or supernatural finnanglings in order to function as it does.  We also understand (or should - see my earlier series of posts beginning with this one) that the universe is not fully deterministic.  This fact ruins the deistic fancy that some god or goddess magically poofed the universe into existence for some obtuse purpose and then stood back and allowed it to carry on naturally in the fulfillment of a divine master-plan.  That plan would only work if the universe and nature were indeed fully deterministic.  But it is not, and your gods and goddesses would be compelled to constantly tweak and nudge the universe in its random wanderings back onto the divinely specified trajectory. We explicitly see this exact thing not happening, as well as the positive absence of a mechanism by which this could happen from outside the universe.  The only agency observed to marginally influence the course of Nature is that of Man, and that of a few other animals on this planet.

If you see a symmetric web hanging with dew in the morning, only determined willful ignorance could license you to assume it was the act of some supernatural agency.  Even a rustic innocent understands that it was the work of a spider, an animal fully competent to carry out such modifications to the environment. Sometimes designs have a designer, and sometimes designs emerge without one.

But the most damning flaw of this bad argument for gods, that everything that exists could only exist if it had an intelligent agent as its prime instigator, is this very argument itself.  If we were to foolishly be persuaded by this baseless assertion, accept it as valid and apply it evenly, then we would be in the awkward position of having to respond to the objection that if Gods exist, someone or something must have created them.

"Logic and Reason can only exist as a result of the Gods inventing them."  Oh for fuck's sake, not this puddle of donkey cack.  Really?  Have you never even seen a logic or a reason, much less used one?  OK - I may have to break it down to toddler level for the fundamentalists out there who are fond of this nonsense garbage argument and who (by straining hard enough) somehow find it persuasive.  But first it seems necessary to seize the narrative and talk about one of my favorite subjects - Mathematics.  Math means Quantitative Reasoning and encompasses the fields of Logic and Geometry.  Math is essentially the taxonomy of the properties of quantities and functions (identifiable groups of quantities, e.g. the points on an idealized circle or sphere).  The claim is that these properties and their relationships could somehow only exist if an invisible wizard casts a magic spell or something.  Could they really not exist simply on their own?

But to be fair, let us allow the question and conjecture an entirely godless universe - I know, rather inconceivable, but bear with me.  Suppose this utterly god-free universe contained an asteroid.  And then suppose there was a second asteroid, one that was not merely the first one all over again.  Now if we, who are not present (because this is a godless universe, remember) and thus cannot see this, but instead merely speculate that these asteroids exist, proceed to count the number of separate asteroids in the universe, do we not arrive at the result, being one asteroid plus another asteroid?  Do we not empirically see what we shall designate as Two asteroids?    Even in a godless universe one plus one makes two, an empirical fact which requires no proof, nor derivation from a priori axioms, nor magic, nor divine imprimatur.  Now let us imagine as a thought-experiment that the two asteroids crash into one another and each breaks into two pieces.  Is it not an empirical fact that if this
were to happen, then the asteroids now number two times two, and also two plus two, namely four?  What this demonstrates is that it is entirely possible for math to exist of its own accord, waiting only to be discovered by an animal at least as competent at counting as a Labrador Retriever.

Math (and by extension Logic and Reason) is not an invention, but a discovery.  While mathematical notations and methodologies are certainly invented, the properties and relationships of quantities and functions themselves can only be discovered.  While whiny post-modernists hipsters in their bourgeois parlors playing middle-class word games reassure themselves that math is just a subjective eurocentric cis-male construct, in the real world math exists whether we know about it or not, or are capable of using it or not.   A circle's circumference of unit diameter was 3.14159... long before pi was known to humans, and long before an oblate spheroid planet following a precessing elliptical orbit around an unremarkable sun formed on which people would eventually understand any of this.  The surface of a sphere has ever increased as the square of the radius, and the volume as the cube, even before the first stars and galaxies formed and light shone in concordance with these facts, and would have done so whether gods existed or not. 

Attributing the existence of logic and reason solely to either the existence of magical invisible sky people or to human culture is equally willfully ignorant of the true nature of any of those things.  In small words: this argument is bad, silly, and dumb. It does not work.

"The orderly universe is finely tuned to support human life and this proves that some Gods probably did it."  Ah the Fine Tuning argument.  This one backfires on the godologists rather spectacularly, which is why I quite enjoy getting this one.  Consider first the orderliness of nature - the sun rising, the tides and seasons coming and going in regular succession as though rehearsed by a master-orchestrator, the exact conditions by which we experience life, and so on.  This is sometimes floated as a separate, standalone argument.  Setting aside the fact that at large timescales the universe is nowhere near as orderly and predictable as this argument requires, this was once a compelling reason to suspect there may be gods about.  It was certainly one possible explanation for things, once upon a time.  Which gods, though ...?  That was always an open question.  But the fact that things were a little too orderly and predictable, like clockwork, should have been a clue that perhaps this was not an agency at work, but the result of some mechanistic system, like a clockwork.

However that all changed the moment we learned how gravity works and that all of this orbiting stuff is exactly what can and would occur whether gods existed or not; whether they intervened or not.  Astronomy including the true nature of the earth, sun, planets, stars, and other bodies detectable in the heavens are all understood well enough now that the presumption of some supernatural agency keeping it all going is no longer justified on this basis, and is indeed laughably unfounded.  This universe works exactly the way a completely god-free universe would work, and not at all the way a god-controlled universe should work, according to all the things godologists certify about their gods.

OK so the universe is doing nothing other than following physical laws.  But how do we know some gods didn't decree those very laws? How is it not fine-tuned just for us?  Nope - sorry, you're indulging in a "begging the question" fallacy, so let's step back from some of those built-in assumptions.  This universe is not necessarily fine tuned just for us - it may be an accident that we are here discussing this universe at all.  It may seem perfect for us, but is there any other way we could possibly be having this discussion?  I know how difficult it can be to understand the logic this objection, having once been strongly motivated to see it as good evidence for gods.  But bear with me:  If we accept that Life in our present form requires some very fortuitous initial conditions and some lucky breaks along the way, then by even having this discussion we presume that those conditions are factual.  It may not actually be the case that we or something like us could only be here under these exact conditions, but we'll allow this for the present.  So, what are the odds?  One in ... five?  How many planets and solar systems are out there that are just right for life?  How many universes are there or have there been?  We do not actually know, and so we cannot assert that this one is too improbable to have happened by chance.  So we are left with this: it either happened by chance, or by some natural cause which somehow favors these conditions, or by the design of some powerful supernatural agency.    The mere fact that we are here wondering which one it is neither presupposes nor precludes any one of these three possibilities, because these are the only conditions under which we could be wondering this in the first place.

If this universe is exquisitely fine tuned to favor anything, it favors (as we physicists now know) the production of as many Black Holes as possible.  But, however, there may be natural, physical reasons for this which we may learn eventually, so we are not justified in assuming the existence of some Black Hole God who crafted this universe purely based on His Holeyness' preferences.  So don't go throwing out all your action figures of a guy being murdered to death on a big "t" and replacing them with photos of Stephen Hawking, which is what the Fine Tuning argument would require if you were to absolutely insist upon its validity.

"Human beings and human societies are self-evidently the result of divine creation."  Again, at one time in the past this might have been a compelling reason to suspect the existence of some invisible magic man with a plan.  Even if one accepts divine creation as the best explanation, there is still an awfully long way to go before any one particular god or religion can be awarded the credit for it. But even in the pre-scientific age there were reasons to doubt this claim.  A lot of outlandish and ad hoc explanations had to be invented over time in order to account for facts about humans and their societies that did not fit the "gods did it" hypothesis.

Of course today there are well-tested and compelling hypotheses that account for everything we see in humanity without invoking the supernatural.  I will not present or argue here the oceans of evidence that support the fact and theory of human evolution, the indisputable facts from molecular biology that place homo sapiens sapiens squarely in the animal kingdom right in among the chimpanzees, the fact that nothing about humans is qualitatively outside the range of animal behaviour or competence, but only quantitative extensions of animal behaviour. The God Squad claims that gods are the only explanation for the existence of us.  To address that claim, all that is needed is one viable alternative theory that withstands every determined attempt at falsification.  I do not have to positively prove that the alternative explanation is true; I only have to point out that it exists and is not contradicted by any evidence we have in order to dismiss the claim that only gods could have done it.  It is demonstrably false that only some gods could have done it.  While perhaps gods might have done it, this is definitely not the only explanation, nor even the best explanation.

There is clear and unequivocal evidence - vast quantities of myopically coherent evidence - that humans and all other living things were not created in their present forms, but have evolved.  Therefore any explanation about the origins of life must account for the proven fact of past and present evolution of life to be considered at all.  Could gods have utilized evolution to manufacture us?  If they did, we must assume they are comfortable - sanguine even - with the evolutionary imperfections, useless vestigial structures, and mental and physical weaknesses and vulnerabilities of our species, as well as patient with the millions of years of pre-human primates and at least a hundred thousand years of modern but pre-monotheistic human beings.  It is not at all self-evident that some gods did this for any coherent purpose, and the gods hypothesis is very far from the best explanation while lacking any explanatory or predictive power.  In terms of testability, the creationist hypothesis fails again and again - fails to find evidence of intentional design, and fails to account for very un-design-like phenomena in biology.

A once-compelling subset of this argument is the argument of the human Self and conscious self-awareness.  For a long time it could not be understood how the thing we all experience could possibly emerge naturally from a wet and springy 1300-g blob of 90 billion neurons. However this bastion of magic has fallen in the path of Science.  Consciousness is no longer an unassailable mystery but is even now being unraveled and explored as an entirely natural phenomenon.  I often did and still sometimes do boggle at the fact of finding myself existing as a conscious being.  How did this happen?  Why am I me?  However there are now some very plausible, testable, and continually improving hypotheses about how the brain as a machine produces conscious experience and the illusion of a Self that do not involve, invoke, or rely on theology or the supernatural in any way.

"There was this one guy who was sick, and then he wasn't sick anymore, and so ... Ta Da! Gods!"  The argument from miracles is difficult to deal with because the claims are slippery.  The evidence of the actual events diffuse conveniently into obscurity, or the tale spins out to ever more fanciful variants.  Unexplained occurrences or healings are simply that: unexplained.  To make a Deistic much less a Theistic claim on this basis requires that you first produce incontrovertible evidence that the event actually took place, and then show precisely how all alternative ordinary explanations fail.  Then you have to show evidence of the proffered explanation - that some particular god and no other did it.  In most cases this is merely assumed.

But most of the miracle stories out there have serious authenticity problems.  It is possible to show in some cases that the event could never have occurred, and that key facts are contradicted by independent evidence.  In other cases it is simply impossible to verify any of the details.  And in the small number of verified, documented occurrences, there are easily other less marvelous, sadly banal, and vastly more probable explanations.

There will always be the unexplained in this world, however.  Just keep in mind that unexplained is merely unexplained - it no more justifies belief in gods than it justifies belief in Harry Potter.

"Life does not have any meaning without gods; so therefore the obvious fact that life must have meaning proves that gods exist."  Hey! great begging-the-question fallacy.  Well done.  But I have to ask, why must life have meaning?  How do you know that is an incontrovertible fact?  Or do you merely need it to be so?  Let's look at this another way.  You need life to have meaning.  You make up gods and you invent fancy stories that you tell yourself that puts human life in a cosmic context that makes it seem bigger and more important and lasting.  You make up a story in which this short existence is an epic critically important quest or test with infinitely bigly consequences.  And it feels really good.  But guess what - you did that.  You gave your life meaning.  You did it even though gods don't really exist and the stories aren't actually true, but there you are.  You have a meaningful life.  So why couldn't the story be something else closer to actual reality?  Your religion's very existence proves that it is possible for us to give our own lives meaning by ourselves.  That power is ours and does not require gods to be real.

"No! No good - if it isn't actually true then it's meaningless.  God gives my life meaning only because he actually exists for real!"  Ah - but gods do not exist and this fact does not stop people from feeling that their lives are meaningful.  However I take your meaning, and acknowledge that this route to meaning would not work if people knew it was fake.  What then do you do when you find out that it is?  Give up on life because that was the only possible meaning it could have had?  No.  It is possible to give your life a meaning that is more based on fact and reality.  But no one can do that for you.  Step One is to learn more facts.  A lot more facts. 

"I personally felt a feeling, saw a thing, &/or heard a voice, and gods are the only possible way this could ever happen."  OK - this is probably the only argument I take seriously because this was my own ultimate fallback once upon a time.  So, I get it.  "I know what I know, I saw what I saw, I felt what I felt."  As a believer my only concern about the argument from testimony was that other people who believed the wrong stuff about the wrong gods kept getting the wrong answers using this exact same methodology.  If God was sending these telepathic messages to my brain, then why were other people getting similar but factually incorrect or even directly contradictory messages?  Why was God gas-lighting me so hard in this really mean way?

There are field dressings and apologetics for this problem, but I found no real satisfactory answer until I learned that the brain basically works by hallucinating everything all the time.  Mostly the hallucinations should closely reflect what is going on in the real world around you, but this isn't strictly necessary.  It is not just possible, but quite common for a brain to produce hallucinations of sight, sound, voices, or feelings as required and at a moment's notice.  And the nature of hallucination as the normal mode of braining is that you cannot readily tell when the hallucination is tracking reality or when it has gone off the rails. You have to be constantly vigilant and always testing your experience to verify that it is tracking reality; and even then the brain can fool you for lengthy periods of time.

Personal "spiritual" experiences are not evidence of actual gods, but are evidence of belief in gods.  You can condition a human to believe in practically any absurd thing, and the person will have internal experiences that confirm the belief to him.  Some people talk to or even see ghosts, which are entirely an imaginary thing.  Some people see aliens, bigfoot, mermaids, fairies, or an endless array of phantasms limited only by imagination but strongly influenced by the memes to which the person had previous exposure.  If your proof of a particular god is by telepathy only, then you essentially have no proof.  And your hallucinations are inadmissible evidence that I too should infer anything from your claims. I've had hallucinations, too.  I know all about them. And people who were raised with entirely different beliefs have entirely different hallucinations.

The godophiles invent a lot of excuses for why the gods only communicate cryptically, through numerology or astrology, through obtuse word games, in ways that are completely identical to hallucinations, or through specific people with whom he/she/they/it insist on dealing exclusively.  But why must that be the case?  If there were real gods about, they would certainly be capable of revealing themselves in indisputable ways, and have no real need to be so evasive.  It turns out the only way we know anything at all about these gods is through humans making the claims without proof, evidence, or valid argument.


I reject the existence of gods and goddesses, and denounce their expounders as dishonest frauds.  There is no good reason to assume that such things are real or are anything other than bedtime stories for children.  If I am wrong, show me evidence that is concordant with no other explanation.  Better yet, produce specimens of your gods for examination.