Formal System

A site about formal logic, literature, philosophy and simulations. And formal systems!

Brief reflection on debates of religion vs atheism. Intellectual battles or co-operation — April 2, 2012

Brief reflection on debates of religion vs atheism. Intellectual battles or co-operation

There have been quite a lot of debates that till now it should be evident. For every argument for or against the existence of God there is another counter-argument for or against his existence. Whenever an argument for or against the existence of God is left without its counter-argument, it’s not because of the argument presented but because of lack of debating skills by one of the sides. Why is this so?

Because:

1- Atheists’ arguments are based on reason.

2- Arguments coming from religion are based on faith.

There is an interesting relationship between faith and reason. Reason implies that the existence of faith is unnecessary while faith is in many ways a negation of reason in the sense that faith belongs to a higher level viewpoint and reason belongs to a lower level viewpoint. So basically, they both deny each other. I shall put an analogy of this relationship:

Who will win in a fight against a literally indestructible rock versus a lance that destroys anything that it touches?

Answer: the premise of the question is illogical and thus, no logically satisfactory answer can be offered. The existence of the indestructible rock denies the existence of the lance and viceversa. So a universe where both objects exist would not be a logical one. In other words, you either believe in the existence of the lance or in the existence of the rock but you cannot believe in the existence of both if you are a logically consistent person.

In a similar way, the same approach can be taken towards the religion vs atheism thing. The main difference here is that, rather than stating that both stances are inconsistent, all that is left to do is acknowledge the basic difference between faith and reason: they deny each other. You cannot have a consistent debate when both premises negate each other. In an ideal setting where both debaters are equally educated in the art of  debating, for every argument for or against the existence of God there will always be a counter-argument for or against the existence of God.

One of the best things to do in order to have fruitful debates between religion and faith would be, for both atheists and believers, to acknowledge that, unless they accept that faith and reason pretty much deny each other and thus, no further debate should be conducted regarding who is right and who is not. Instead, debates could be re-oriented towards humankind and how both atheists and believers can co-operate (yes, co-operation is the keyword) for the sake of a better future for the humankind. And here’s where debates would start. And this time, they would be fruitful debates rather than I-am-right-you-are-wrong-like intellectual battles.

Unexpected Examination Paradox — January 29, 2012

Unexpected Examination Paradox

A teacher announces in class that an examination will be held on some day during the following week,

and moreover that the examination will be a surprise. The students argue that a surprise exam cannot occur. Because of a simple induction inference:

Friday: if by Thursday evening there is no exam, then it will be Friday. But since it would then be expected, it cannot be the Friday.

Thursday: if by Wednesday evening there is no exam, then it will be Thursday. But since it would then be expected, it cannot be the Thursday nor Friday.

Wednesday: if by Tuesday evening there is no exam, then it will be Wednesday. But since it would then be expected, it cannot be the Wednesday nor Thursday nor Friday.

Tuesday: if by Monday evening there is no exam, then it will be Tuesday. But since it would then be expected, it cannot be the Tuesday nor Wednesday nor Thursday  nor Friday.

Monday: it can only be the Monday but then if it is expected on Monday it cannot, because of the expectancy, happen on Monday.

Condent in this conclusion, they are of course totally surprised when the exam occurs (on Wednesday, say).

What is wrong with the students’ line of reasoning?

Let us try to solve the paradox:

1: the exam is expected any of the five days.

2: since it is expected, it cannot happen.

3: line 2 itself is expected.

4: the teacher hands over the exam on monday.

5: the exam is expected any day (see step 1) => it is not not expected to happen any day ( because it cannot happen)

6: since it is not expected to happen, it can happen and happens.

7: go to line 1 and replace Monday with any other of the 5 days.

The backwards reasoning seems to fully cover any hole and assure the student that the exam cannot happen on the basis of the student’s current knowledge but this knowledge is based on probability.

About free will, evil and love: Dialogue with an amoralist God — January 27, 2012

About free will, evil and love: Dialogue with an amoralist God

Smullyan is quite an off-beat person. Why?

He started as magician and later on went to become a logician. The most incredible part is that he also became a Taoist (for details of the core ideas of this eastern philosophy click here). It is no secret that Taoist views are rooted on profound paradoxes nor it is secret that Western logicians have been battling against paradoxes like doctors a disease. It should seem that both logic and Taoism are conflicting but apparently, this fellow has managed to keep inner peace.

“Is God a Taoist?” is a dialogue between God and a theist where the latter asks the former why did he bestow free will on humans.  What follows is an explanation of quite a laid-back God who describes the problem of evil, his love for humans as well as a surprisingly simple idea to show why humans need free will.

P.S. Taoists do not believe in divine entities so the title of the dialogue itself can be taken as a sort of paradox, making the title a subtle reference to a core paradox surrounding the idea of free will (this core paradox happens to be mentioned in the dialogue).

You can read it here for free.

Eastern Philosophy: Tao Te King — January 25, 2012

Eastern Philosophy: Tao Te King

Chinese kanji for "way". Tao means way.

It starts like this:

“The Tao that can be told

is not the eternal Tao.

The name that can be named

is not the eternal Name.

The unnamable is the eternally real.

Naming is the origin.

of particular things.

Free from desire, you realise the mystery

Caught in desire, you see only the manifestations.”

So even though the book talks about the Tao it tells you that the Tao that can be told is not the real Tao. We are supposed to make inferences of what they say to understand what it is meant by Tao. It is like the allegory of the finger pointing at the Moon, the finger is needed to point at the Moon, it is a means, but the finger is not the Moon. You must make an inference and understand what the finger is actually doing so then you can follow the direction of the finger and eventually leave it and keep going with your inference. And then, you see the Moon.

Paradoxes abound in this book as in no other, yet universal truths also abound in this book as in no other. As I already explained, making a direct review of the book goes against what the book tell us in order to understand it. Themes of wisdom, humility and respect are frequent.

The author? As with many books, the authorship of masterpieces is a controversial topic, but you don’t need to know the author to enjoy a bit of millenarian wisdom.

Read it here for free

Identity and Paradox: Who is me? Who was me? Both the same? — January 24, 2012

Identity and Paradox: Who is me? Who was me? Both the same?

After dedicating four posts to literary matters, I think it’s time to introduce one of the most striking concepts in the field of logic: paradoxes. We will review two paradoxes and we will make analogies between them and what we call identity.

Paradox: a logical statement that leads to a contradiction.

One of the founders of classical logic, Aristotle stated in his law of identity:  “An object is the same as itself: A → A(if you have A, then you have A).” In my opinion, there is a major flaw that Aristotle did not spot. We shall discuss it later.

Contradiction implies that A = not A or to use another example, “I am going to the library AND I am not going to the library” A (I am going to the library) and not A (I am not going to the library).

What’s the problem with contradictions? Anything follows from contradictions. Things such as 2=1 come into existence. Logic is to certainty what  paradox to uncertainty.

The two paradoxes to be briefly discussed are:

Sorites Paradox (paradox of the heap)

-Theseus Ship (grandfather’s axe paradox)

Sorites Paradox

Consider a heap of  sand, from which grains are individually removed. Is it still a heap when only one grain remains?  If not, when did it change from a heap to a non-heap?

Proposed solutions to the paradox

Solution 1- Bertrand Russell stated that the problem lies in the vagueness of the term “heap” and therefore, implying that with a more rigid meaning of “heap” the paradox would disappear.

Solution 2- Common consensus

A group may decide that:

  • Statement 1 – One grain of sand on its own is not a heap.
  • Statement 2 – A large collection of grains of sand is a heap.

Again, it is suggested that the use of the statements above plus the use of a more precise meaning for “heap” the paradox dissolves. As we can see the solution 1 is part of the solution 2.

So the solution 2 holds onto two diametrically opposite statements (One grain of sand on its own is not a heap) and (A large collection of grains of sand is a heap). So we have 1 grain (not heap) and at the other end x grains of sand together (x stands for at least a number bigger than 1). It is not difficult to see that both S1 and S2 overlap, this is, there is a zone of uncertainty (regarding when a heap comes into existence and when it comes out of existence) between S1 and S2.

Psychological studies in overlapping concepts

According to psychological studies  in colour transition tests, people tend to hold on to the original colour for as long as possible. So if you get to subjects, each watching a colour transition from opposite start points, they will have a massive overlap where one is stating the colour is ‘green’ and the other ‘yellow’. These studies show that it is all context-dependent and subject to the limitations in our physical perception.

So the problem does not seem to be solved by attempts at imposing accuracy and clarity into what defines a heap.

Theseus Paradox

“The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place. Is the ship the same?

Now let us say that we build a new ship from the old planks, is this new built ship Theseus’ one?

Analysis and comparation of both paradoxes

Both paradoxes are analogous. Both deal with identity. The important difference between both paradoxes is that while Sorites paradox lies in what is seemingly just a vague term, Theseus Ship is quite concrete, so any argument about vagueness (most or all arguments against Sorites paradox are about the vague term “heap”) that was meant to be applied to Sorites paradoxes can be applied to Theseus Ship. And still fail. Why?

Identity and C…

At the beginning of this post I mentioned a major flaw in Aristotle’s law of identity. If you have not guessed what I mean, it was change.The problem with Aristotle’s law of identity is that it is fully effective with abstract concepts and systems but when dealing with systems in our concrete world, it is partially effective.

Why?

Because there are two fundamental factors that separate the abstract world (where Aristotle’s laws of thought are fully effective) and the concrete world (where his laws of thought are only partially effective):

time and change. Without having to define neither we know that by the passing of time change does happen, or rather, we could say that change is the physical manifestation of time.

It is all about change. We change from a baby to child to a teen to a young man to an adult, etc. Aristotle’s law of identity does not support, and actually it seems to implicitly reject, change and therefore, the scope of the notion of identity that it captures is rather limited.

In my opinion, a change-friendly definition of identity (for humans) would be a pattern across time. Or a pattern that changes slowly and gradually, non-stopping, forever.

P.S. When I have some free time I write a post about sameness.

🙂