Reduction to infinity

(An approach to infinite regress)

The fallacy of logic

The main problem with logic is that it cannot prove itself.

If logic is true, then we have to test it. Let’s suppose that logic is false. But

if logic is false then our first assumption that logic is true is false. So logic is

false. But if logic is false then we cannot use logic for any conclusion. But since

logic is all we have then we must consider logic as true without relying on proof.

Reduction to absurdity:

A: ‘Logic is true.’Let’s suppose A is false.If A is false then B.B: ‘Logic is false.’Which contradicts A.Then A: ‘Logic is true’ is true.

A: ‘Logic is false.’Let’s suppose A is false.If A is false then B.B: ‘Logic is true.’Which contradicts A.Then A: ‘Logic is false’ is true.

This is a fundamental logical loop. In fact it didn’t prove much. The basic thing

we demonstrated is that we use logic.

Reduction to infinity

When we try to demonstrate a truth we use syllogisms until we find a

contradiction:

Reduction to infinity

P0: ‘Logic is true.’If P0 is true then… P0 → P1 (if P1 true…)P1 → P2 (if P2 true…)P2 → P3 (if P3 true…)Pn → Pn+1 …

We can repeat this process until we find a proposition wrong. Then the whole

syllogism collapses. But if our first argument is quite strong (or just axiomatic)

then it could hold true for ever. In this case we assume that we are satisfied with

an adequate number of repetitions that support our primary argument more and

more…

Infinite regress

This is what we call an infinite regress. If P0 is our first proposition then it is true

if P1 is true, and P1 is true if P2 is true, and so on:

Pn+1 = Pn + I

(where ‘I’ stands as the ‘next

step’ in the series.)

If the first proposition P0 stands as ‘truth’ (like the sentence ‘logic is true’), then

we will never end with a contradiction nor with an affirmation.

Proof vs. demonstration

- Russell believed that all propositions of mathematics could be proved.

- Gödel showed that truths of a logical system are not provable within its

own premises.

So Gödel’s theorem has given an end to our ambition that there could be

any logical system complete, as Russell in his ‘Principia’ would have expected.

We cannot demonstrate truths, we just accept them. On the other hand, by

demonstration we cannot prove a truth.

- As Aristotle put it forward:

Some hold that, owing to the necessity of knowing the primary premises, there is no scientific knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premises. The first school, assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not know the posterior through the prior… The other party agrees with them as regards knowing, holding that it is only possible by demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal. Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. Such, then, is our doctrine, and in addition we maintain that besides scientific knowledge there is its originative source which enables us to recognize the definitions.

Aristotle therefore believed that we can simply prove a theory by its axioms. Still

the problem remains: How can we find the originative source of a logical

argument?

Infinite causal chains vs. infinite causal loops

Infinite causal chains

Another name for infinite regression is an infinite causal chain. An infinite causal

chain has no beginning or end. We can use any means of logical deduction but we

can never reach an end or a first cause. Infinite causal chains are logically valid

but, let’s say, incomplete with regard to common experience.

Infinite causal loops

There is a fast way to ‘escape’ from a causal chain. For example, if we ask how

the universe started we can simply reply that the universe has always existed. So a

‘previous state’ loses any meaning. This is an example of an infinite causal loop.

But here we have to face a problem: If a causal loop can explain its existence as

its own cause, then logical reasoning loses any sense. Because logic will have to

ask: ‘What is outside a causal loop?

- Richard Hanley has argued that causal loops are not impossible but their

only possibly objectionable feature they all share is that coincidence is required to

explain them.

Therefore ‘causal’ loops are in fact acausal.

Infinite causal chains Infinite causal loops

Open ClosedCausal and infinite Acausal and spontaneousTruths are demonstrable Truths are axiomaticEffects need a cause to explain them

Effects are their own causes and vice versa

Time is an important property of nature

Time is fundamentally an illusion

God is an eternal question God is an internal questionChance is explained with probabilities

Chance is explained with ‘meaningful’ coincidences

Classical determinism Quantum non-localityBig Bang Model Steady State Universe

The ‘cosmological’ argument

This is exactly the key point of the anthropic principle: A human point of view

about the world is always a point of view of the human mind. In the same way we

can rename this ‘human’ principle as ‘bee’ principle, ‘dolphin’ principle, or more

generally as the ‘cosmological’ principle, meaning the cosmological principle as

‘we’ know it.

The cosmological argument

1) Every finite and contingent being has a cause. 2) A causal loop cannot exist.3) A causal chain cannot be of infinite length.4) Therefore, a First Cause (or something that is not an effect) must exist.

1)What caused the first cause?

As we can easily see the famous ‘cosmological’ argument is just a ‘logical’

argument that cannot even prove if our logic is reciprocal or even legitimate

concerning the ‘cosmos’. The quest of a first cause leads to infinite regress that

‘ends’ with an irrational and ‘miraculous’ breakthrough to a self- existent and

self- explaining causal loop which in turn can expand to an infinite series of

causal loops and so on…

Logic and the ‘real’ world

There still remains an important question: Does nature ‘thinks’ the same way

humans do? Are all human problems also problems of nature? If humans are

‘nature’ then the obvious answer is yes. But this answer is still an answer of logic.

Could nature have a more sophisticated way of ‘thinking’ above human logic?

Still the previous question is a question of logic. And so on…

Infinity of infinities…

A: ‘How did the universe begin?’ A syllogism begins without a beginning or an end (an infinite causal chain). B: ‘The universe has always existed.’ A spontaneous reply that explains the origins of the previous question but defies demonstration (a non- causal loop)C: ‘The origin of the universe is acausal but the universe consists of causal events.’ A thought unifying A and B. D: ‘What is there outside the universe?’ The acausal loop breaks into an infinite number of infinite causal chains. Birth of a new syllogism that assumes the existence of a ‘multiverse.’E: ‘What existed before the multiverse?’ Each infinite chain ‘bends’ to find its origins. Many multiverses of spontaneous origin.F: “What lies outside the set of all sets of multiverses?” The process goes on for ever…

Is there really a way through?

As we saw our logic works with an infinite regress procedure. We can stop it but

if we want to have a definite answer then we have to start again. We could admit

that logic is insufficient to understand the world but if we abandon logic then we

lose any ability of common sense. Is there a function within the limits of ‘mind’

that if found could lead us to a new way of thinking? Perhaps this question is just

another question of logic. But since so far our logic and our common sense have

proved worthy of understanding or at least having access to ‘incredible’ things

outside their realm, there is a question left: ‘Why do we understand?’ We may not

be able to reply but I guess we can keep our mind open to the possibility of

miracles.