Q.E.D.

Q.E.D. is an abbreviation for the Latin quod erat demonstrandum meaning ‘[that] which had to be demonstrated’.

‘Q.E.D.: a Mathematician’s way of saying “I win”.’ – Urban Dictionary

The abbreviation of the phrase is traditionally placed at the end of a mathematical proof or philosophical argument to denote the conclusion of the demonstration. The abbreviation thus signals the completion of the proof.

The phrase is a translation into Latin from the Greek ὅπερ ἔδει δεῖξαι ‘what was required to be proved’. The phrase was used by many early Greek mathematicians, including Euclid and Archimedes.

The phrase has also been used outside mathematics and philosophy for comic effect.

For instance, in Thomas Dolby’s 1988 song Airhead, he imagines a conversation with the titular young woman and says “quod erat demonstrandum, baby”, to which she squeals the eager reply “ohhh, you speak French!”

Also, in chapter six of Douglas Adams’ The Hitchhiker’s Guide to the Galaxy, the abbreviation is included in the following exchange:

The argument goes something like this: “I refuse to prove that I exist,” says God, “for proof denies faith, and without faith I am nothing.”

“But,” says Man, “the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.“

“Oh dear,” says God, “I hadn’t thought of that,” and promptly vanishes in a puff of logic.

Degree Argument For God

This proof, formulated by St. Thomas Aquinas (1225 – 1274), originates from the degrees discovered in things. There is discovered greater and lesser degrees of goodness, truth, nobility, and others – this is no ground-braking statement.

Aquinas argues, there exists something ‘truest’, which, in consequence, is the greatest ‘being’. He then argues, based on the metaphysics of Plato and Aristotle, that these superlatives – the things that are most true, beautiful, et cetera – are the greatest truths and therefore the greatest beings, as is stated in Metaphysics Book II.

Furthermore, that which is the greatest in its way, is, in another way, the cause of all things belonging to it. Therefore, there exists something that is the cause of the existence of all things and every perfection whatever. Aquinas calls this ‘God’.

Over 700 years later, there is little credibility left of Aquinas’ proof.

The most prevalent criticism of this argument considers that we do not have to believe in an object of a greater degree in order to believe in an object of a lesser degree. Richard Dawkins, the most (in)famous Atheist thinker of our time, argues that just because we come across a “smelly object”, does not require that we believe in a “preeminently peerless stinker”.

“Something does not necessarily prove something else, let alone something less or more.”

For instance, a fire does not necessitate another hotter fire, nor a cooler one. The hottest fire does not necessitate any other cooler fire (for it could be the only fire in existence and therefore both the hottest and coolest fire, or all fires in existence could have the same temperature). But above all else, if the hottest fire of all fires would indeed exist, it does not necessarily have to be the cause of all smaller fires.

See other: Arguments Concerning God

Cosmological Argument For God

In the 13th century, at the highpoint of the middle ages, Thomas Aquinas formulated one of the most famous proofs for the existence of God: the Cosmological Argument.

That is to say, it was Aquinas who phrased the argument we know today; the cosmological argument however, had been formulated centuries earlier by the Greeks. The fact that it was theorized by Ancient philosophers, like Aristotle, is especially impressive when you consider that at the time, the Universe was not known to have had any sort of origin – the event we nowadays call The Big Bang. The argument consists of the following axioms:

1. Every finite and contingent being has a cause.
2. Nothing finite and contingent can cause itself.
3. A causal chain cannot be of infinite length.
4. Therefore, a First Cause (or something that is not an effect) must exist.

There are two fundamental problems with this argument:

First of all, the cosmological argument is dependent on either a causal chain being of infinite length, or a finite causal chain with a First Cause or Prime Mover at its base.

In any case, it would seem that the argument commits the logical fallacy of infinite regression. If the universe had a first cause, what caused that first cause? Defenders of the argument declare that it is unfair to argue for the cause of every single thing, but then those defenders in turn argue for the sole exception of a First Cause, which according to them did not have a cause.

However, since the third axiom of the argument refutes the existence of any infinite causal chain, a so-called Prime Mover becomes necessary to make the argument work. The problem with any First Cause in the context of this argument however, is that it is just a logical convenience – it is the easiest way out.

Interestingly though, there is no proof whatsoever that a causal chain of infinite length could not exist; it is merely philosophical rhetoric of pre-renaissance quality. Simply put, this fact invalidates axiom three of the argument and it makes axiom four – the Prime Mover – unnecessary.

Furthermore, it is simply not necessary for the universe to have had a cause, original purpose or prime mover, nor is it necessary that there was at some time in the past ‘nothing’. If fact, it seems unlikely that it did. There is no evidence to suggest that there ever was a state without matter – that something came out of nothing. Of course, it might well be true, but as yet, it is impossible to determine. That, however, does not change the fact that the need for a First Cause, which Aquinas outlines in his argument, is outdated.

See other: Arguments Concerning God

Ontological Argument For God

The ontological argument concerning the existence of god was first formulated by St. Anselm (circa 1033 – 21 April 1109), who was Archbishop of Canterbury from 1093 until his death.

“God exists, provided that it is logically possible for him to exist.”

This argument is quite brazen in its simplicity, requiring not only a belief in a higher entity, but a belief in the necessity of god. Anselm argues, ‘if you believe a higher entity is necessary, then you must believe a god exists’. Unfortunately, the logic is rather dated and quite ridiculous in its simplicity.

“X exists, provided that it is logically possible for X to exist.”

First of all, when we dissect this phrase, Anselm’s logic allows the variable X to be literally anything: Quetzalcoatl, Ra, Thor, Sergei Fedorov, Jeremy Clarkson, Anna Karenina, Homer Simpson, a 1972 Pink Floyd album, that girl you fancy, the mango I had the other day, et cetera. I suppose one could argue X only applies to the god of your choosing (and is therefore not a real variable), but then the inevitable and painful follow-up question is going to be ‘why exactly should X have only one possible meaning? or why should Anselm’s logic not allow X to be a variable?’; this is a dead end, and since there is no reasonable or logical reason to pursue this line of arguing, we are forced to call X a variable. And in doing so, we are left to cut up Anselm’s argument.

Of course, we should not mock Anselm too much. With our 21st century minds, it is quite easy to see and understand that his argument is plainly untrue. To be precise, Anselm’s ontological argument is a bare assertion fallacy, which means it asserts qualities inherent solely to an unproven statement – it asserts without any support for those qualities. It is also a circular argument, revolving from a premise to a conclusion which in turn relies on the very premise from which it was deduced, which relies on the conclusion… ad infinitum.

To put it simply, Anselm’s ontological argument is one of the oldest cases of (what we would nowadays call) primary school logic ‘X is true – because!’ and it is therefore not surprising that the counter for such a line of argument is frankly: ‘saying so, does not make it so’. After all, what kind of universe would we live in if that kind of reasoning were possible?

See other: Arguments Concerning God

Apatheism

Apatheism is defined as apathy towards belief and disbelief in gods. Apatheism (a portmanteau of ‘apathy’ and ‘theism’) is the belief that the very question of whether or not deities exist is not relevant or meaningful in life. Apatheists are not even interested in addressing any claims for or against god(s).

“It is very important not to mistake hemlock for parsley; but not at all so to believe or not in God.” – Denis Diderot

Apatheism sometimes goes a bit further and asserts that even if it were proven conclusively and without a doubt that some sort of god existed, then the person’s general behaviour and life would not change.

‘Theist: Believe in Jesus and reform your sinful life! God will throw you in hell!
Atheist: No, religion is a mental disease!
Apatheist: Hey guys, try apatheism. It’s very nice. You won’t have to care about this issue!’ – Urban Dictionary

According to the philosopher Kant, this indifferentism represents an extreme form of skepticism which argues that there is no rational ground for truly accepting any philosophical position.

On Physics And God

“Physics makes it possible not to believe in God; before science, everything was a miracle.”

– Stephen Weinberg

Spectrum of Theistic Probability

Richard Dawkins posits that “the existence of God is a scientific hypothesis like any other.” He goes on to propose a continuous spectrum of probabilities between two extremes of opposite certainty, which can be represented by seven milestones. These milestones are:

1. Strong theist.
(100 per cent probability God exists.)
“I do not believe, I know.” – Carl Jung

2. De facto theist.
(Very high probability, but short of 100 per cent.)
“I don’t know for certain, but I strongly believe in God and live my life on the assumption that he is there.”

3. Leaning towards theism.
(Higher than 50 per cent, but not very high.)
“I am very uncertain, but I am inclined to believe in God.”

4. Completely impartial.
(Exactly 50 per cent.)
“God’s existence and non-existence are exactly equiprobable.”

5. Leaning towards Agnosticism.
(Lower than 50 per cent, but not very low.)
“I do not know whether God exists but I’m inclined to be sceptical.”

6. De facto atheist.
(Very low probability, but short of zero.)
“I don’t know for certain but I think God is very improbable, and I live my life on the assumption that he is not there.”

7. Strong atheist.
(100 per cent probability there is no God.)
“I know there is no God, with the same conviction as Jung knows there is one.”

Dawkins argues that while there appear to be plenty of theist individuals that would categorise themselves as ‘1’ due to the strictness of religious doctrine against doubt, most atheists do not consider themselves ‘7’ because atheism arises from a lack of evidence and evidence can always change a thinking person’s mind. Dawkins has identified himself as an atheist between a ‘6’ and a ‘6.9’.

Turtles All The Way Down

A jocular expression of the infinite regress problem in cosmology posed by the unmoved mover paradox – a philosophical concept described by Aristotle as a primary cause or mover of all the motion in the universe. As is implicit in the name, the unmoved mover is not moved by any prior action. Aristotle argues, in Book 8 of the Physics Book 12 of the Metaphysics: “there must be an immortal, unchanging being, ultimately responsible for all wholeness and orderliness in the sensible world.”

“Turtles all the way down” is a phrase that was popularized by Stephen Hawking in 1988. The turtle metaphor in the anecdote represents a popular notion of a so-called primitive cosmological myth, the flat earth supported on the back of a World Turtle. A person who believes the Earth rests on a giant turtle can thereby also deny the existence of the universe.

A Florida Box Turtle or Terrapene Carolina Bauri

A comparable metaphor describing the circular cause and consequence for the same problem is the chicken and egg problem – which came first? Another metaphor addressing the problem of this infinite regression (as the turtles would imply), albeit not in a cosmological context, is Quis custodiet ipsos custodes? – a phrase coined by the Roman poet Juvenus which is often translated as “Who watches the watchmen?” The same problem in epistemology is known as the Münchhausen Trilemma.

The Trilemma was named after Baron Münchhausen, who allegedly pulled himself (and the horse he was sitting on) out of a swamp by his own hair. This Trilemma is a philosophical term coined to stress the purported impossibility to prove any truth even in the fields of logic and mathematics. If we ask of any knowledge: “How do I know that it’s true?”, we may provide proof; yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen Trilemma is that we have only three options when providing proof in this situation:

• The circular argument, in which theory and proof support each other (i.e. we repeat ourselves at some point) “Only an untrustworthy person would run for office. The fact that politicians are untrustworthy is proof of this.”
• The regressive argument, in which each proof requires a further proof ad infinitum (i.e. we just keep giving proofs, presumably forever) “A is proven by B, which is proven C, which proven by D etcetera ad infinitum.”
• The axiomatic argument, which rests on accepted precepts (i.e. we reach some bedrock assumption or certainty) “A. Baron Münchhausen exists, B. Baron Münchhausen has got hairs on his head etcetera.”

The first two methods of reasoning are fundamentally weak, and because the Greek sceptics advocated deep questioning of all accepted values and refused to accept (unconditional axiomatic) proofs of the third sort. The trilemma, then, is the decision among these three equally unsatisfying options.

Back to turtles. The most widely known version of the Turtles All The Way Down story appears in Stephen Hawking’s 1988 book A Brief History of Time, which starts:

A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the centre of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.” The scientist gave a superior smile before replying, “What is the tortoise standing on?” “You’re very clever, young man, very clever,” said the old lady. “But it’s turtles all the way down!”

Hawking’s suggested connection to Russell may be due to Russell’s 1927 lecture Why I Am Not a Christian. In it, while discounting the First Cause argument intended to be a proof of God’s existence, Russell comments (with an argument not relevant to modern Hindu beliefs):

If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. It is exactly of the same nature as the Hindu’s view, that the world rested upon an elephant and the elephant rested upon a tortoise; and when they said, “How about the tortoise?” the Indian said, “Suppose we change the subject.”

There is an allusion to the story in David Hume’s Dialogues Concerning Natural Religion (published in 1779):

How can we satisfy ourselves without going on in infinitum? And, after all, what satisfaction is there in that infinite progression? Let us remember the story of the Indian philosopher and his elephant. It was never more applicable than to the present subject. If the material world rests upon a similar ideal world, this ideal world must rest upon some other; and so on, without end. It were better, therefore, never to look beyond the present material world.

Philosophical allusion to the story goes back at least as far as John Locke. In his 1690 tract An Essay Concerning Human Understanding, Locke compares one who would say that properties inhere in “substance” to the Indian who said the world was on an elephant which was on a tortoise “but being again pressed to know what gave support to the broad-backed tortoise, replied — something, he knew not what.”

The fact is the world does not rest on elephants, turtles or any other animal for that matter. However, the reasoning and philosophical attempts to prove a possibility of there being a giant tortoise on which the earth can rest are fascinating. Just as fascinating as the cultures out of which these beliefs have emerged.

To quote comedian Rich Hall: “This is why America has a space program.”

See other: Admin’s Choice Posts