What is the difference between two?

We talk about "two ducks". We also talk about "2 + 2".

It seems almost self-evident to me that "2" is a conceptual(?), mathematical(?) object in its own right. Any mathematician thinks about "2" and only thinks of "two ducks" in connection with a mathematical problem about "ducks". Mathematical "ducks".

"2" exists in the mathematician's mind, but the idea can be transmitted to another mathematician, so in some sense it is an objective thing. Of course I am assuming here that "2" in your mind bears some relation to the "2" in my mind. I can't be sure of that. But the mathematicians' agreement on proofs peripherally or directly related to "2" lends weight to the idea that there is some objective thing called "2".

It is evident however that "2" is not a physical object, like "those two ducks". You can't point at a "2" (except in the trivial sense of a cipher or numeral). You can point at two ducks. It appears that "2" is of a different class of thing to "two ducks".

Ontology

Anyone who's read a philosophy text or discussed philosophy is likely to have heard the word "ontology". Webster's dictionary (via Dictionary.com) says:

"That department of the science of metaphysics which investigates and explains the nature and essential properties and relations of all beings, as such, or the principles and causes of being".

There is an alternate definition which applies in the field of Artificial Intelligence which is a sort of formal definition of the relationships and concepts in a particular field or "domain", but I'm not going to consider that definition.

We can point to anything and say "That exists!" This is true(1) even if the "thing" we point at is an illusion or chimera. Even if we were strapped down, unconscious, with wires feeding impressions into our brains, those impressions would exist, would they not?

But when we consider a table, a 'real, physical object', isn't that different from, say, a unicorn, or a triangular square, or truth? Hmm, both 'real, physical objects' and 'imaginary objects' exist as mental states of the brain. I don't believe that there are any criteria by which we can reliably mentally distinguish between 'real' and 'imaginary' objects. That doesn't mean that there is no distinction of course.

I had a discussion with someone as to whether or not you could conceive of something without conceiving of its surroundings. My feeling is that a conceptual unicorn cannot be considered without its surroundings - a field, or a forest. The other person did not agree. My feeling is that this is an effect of concentration - if you look at a real object, its surroundings become less prominent to your awareness, but they don't completely disappear, and the same, I believe holds true for mental objects. If you mentally draw back from a mental object it is not (unless you choose to imagine it so) suspended in a void.

It is tempting to consider two levels of 'existence', mental and physical. A physically existent tree can be seen to be existent by more than one person - there appears to be an objective component, while the unicorn can be communicated but each person has their own mental object of a unicorn which is distinct from that of the other person.

But I don't like that idea. The easy way out is to doubt the physical realm - it is all in our heads. But the mere concepts of "our" and "heads" seem to indicate otherwise, both intimating something outside of the mental realm. Solipsism doesn't ultimately appeal, even though it is simple and requires nothing outside of the mind - economically in the extreme!

One solution, and I'm not sure if I like it, is to postulate an 'imaginary' realm containing things like unicorns and four-sided triangles. This would then bear the same relation to the mental world as the real world does - 'real' and 'imaginary' both somehow feed into 'mental' realm.

I'm not sure what I think the answer is. I'm not sure I've even got near the topic of ontology. I need to do some more reading!

(1) "What is truth?" cries Pilate as he washes his hands. Pilate asks the philosophical question of Jesus, but although many have tried, before and after Pilate, none have really answered the question to everyone's satisfaction.

Existential Angst

There is a term "Existential Angst", coined by the philosopher Søren Aabye Kierkegaard, to describe a fear of failing in one's responsibilities to God. This was later broadened to cover a fear of failing to reconcile one's responsibilities with one's abilities and principles. But I don't think that the description really does justice to the term "Angst".

I feel that the term Angst refers to something much more than mere fear. Munch's painting The Scream, which conveys to some extent the essence of angst, shows the sheer depth of the feeling. Mere fear, say of something physical, like the fear of dentists, is a real fear, but is not in the same league as angst. Mere fear does not include the feelings of helplessness, valuelessness and powerlessness, or lack of the prospect of any sort of respite, and the terror that induces in one, that characterise angst as portrayed in the painting. Did I leave out hopelessness?

When people talk about depression they talk about being "down" or "feeling worthless". While these are components of depression, they are relatively minor, I feel, compared to the angst. The feeling, which feels like knowledge, that you are worthless and that there is no hope to allieviate your helplessness is a strong part of depression that the usual definitions do not really bring out. Though they may touch on these matters.

Did I say no hope? The concept of hope finds no place in the sufferer's mind, his surroundings, the universe. Hope does not exist for him.

The Wikipedia entry for clinical depression is typically lacking. In part it says "A person suffering a major depressive episode usually exhibits a very low mood that pervades all aspects of life and an inability to experience pleasure in activities that formerly were enjoyed. Depressed people may be preoccupied with, or ruminate over, thoughts and feelings of worthlessness, inappropriate guilt or regret, helplessness, hopelessness, and self hatred".

All good stuff, but it leaves out the terror and the dread, the existential angst that is part of depression. It leaves out the very part that characterizes a depressive illness and the part that leads people to suicide as the only exit open to them. It leaves out the part where one looks into one's own soul and finds a festering pit, or a miasma.

But mere words do not convey the feeling and state of depression. They never could.

Almost a year.....

....since my last post. Oh dear....

Leonard Cohen

To this land comes Leonard Cohen,
The poet and songster from my youth,
Dark, dark poems and dark, dark songs.

Cohen's Hallelujah is a dirge,
A poem to the God left far behind
By a secular generation.

He did his best, it wasn't much,
He said, but it was enough
To be the voice of you and me.

A generation that changed the world,
From Vietnam to suburban streets,
Ban the bomb and protest songs.

Peace was our aim, it never came.
Cohen's was the voice that called,
It seemed alone.

But no, we listened in our millions
To the gravel voice that spoke,
The well turned word.

The world changed as a result of us,
But not in the way we thought.
And we and Cohen grew older.

The world changed and we did too,
Dropped back in but,
In our hearts we held the heady days.

When a glum and serious poet
Sang dark songs
When we looked for light.

(Copyright 2009 - Cliff Pratt)

Reading about happiness

I've been reading about happiness. Those who know me will realise that I've been reading a philosophy book, and I'm waiting to see where it leads me. There's obvious cliches about happiness, such as it can be sought but not bought, and that it is something that can be aspired to but is often found when we are not looking for it. Also that the way to happiness is to through leading a meaningful, fulfilled life. And that while happiness can't be bought, a little money never hurt!

Religion teaches us that true happiness, or more correctly "bliss", is a state that can be achieved in the next world, but only partially in this world. So we can only partially achieve happiness in this world.

Hm, I could invoke the "rule of two" and inquire why we should stop at two world. Maybe if goodness in this world advances you in the next world, then 'super-goodness' in the next world would elevate you to the next world after that. But I digress.

Anyway, I'll plough on through the book and maybe update this blog with the thoughts that occur to me as I read it. Let's hope it's interesting!

Time traveller?

Someone pointed me at the John Titor site. For those who don't know, John Titor claimed to be a time traveller from from the year 2036. He hung around for a while and then, having announced his departure back to 2036, he disappeared from the Internet. He claims that the events in this time frame are subtly different from the timeframe that he originated from. In other words, his memory of events (coming from 2036) is different from the events that actually happened in this time frame. He attributes this at least in part to his anomalous presence in this era.

Superficially this appears feasible. But we Martians have been investigating time travel since before Earth had a civilisation, and the view that we have come to is substantially different from that espoused by Titor. Our science indicates that there is only one 'time frame'. If an event happens it happens, whether or not a time traveller was present or not. You cannot return to kill your grandfather before you were born, because if you did, then you would not be born to return to kill your grandfather. There is no paradox there, just physics.

Our Martian science indicates that the Universe is strictly deterministic - if an event happens, there is a cause, and time travel has to obey that law. A time traveller is caused (born!) because of events which he/she can't negate. At first glance this seems asymmetrical but it isn't because the existence of a time traveller can't negate an event which happens earlier because that would negate his existence at the time that he goes back. Er... Well, the words don't work too well, but the maths does, believe me!

Martian time travel theory doesn't disallow the existence of time travel. It just put logical limits on it. While Martians have built time machines, it's pointless to travel back just to do something that (from your future point of view) has already happened.

Oh, some people (Martians) have tried to go back and change things, but whatever they do, they always end up causing what they try to prevent! However, there is a school of thought that say that some of them did manage to change things and that, ever after, up to the point that they came back from and beyond, that is they way that it always was.

Most Martians however think, as do most Earthians, that the universe is 100% deterministic, and that what happens is determined and cannot be changed. From the metaphysical point of view that means that the time traveller is observed in 2001 because he disappeared from 2036 and events from then on caused him to disappear in 2036.

Some Martian philosophers think of time as a ribbon and time travel as if two points of the ribbon (2001 and 2036) are brought together so that the time traveller can slip from one era to the other. Martian philosophy is unclear about what dimensions the 'ribbon' could be curved and bent in.

Where does that leave a Martian philosopher with regards to Titor? Titor claims that things are different because of his presence. This does not accord with Martian philosophy. However Titor may be claiming this because he is trying cover up for the inadequacies of his knowledge of the past. No time traveller is going to know everything about his/her past.

He may be hiding unpalatable events from the future, to protect himself from disbelievers in the present. However he does mention things like a civil war in the US that happens in 2005, which has apparently not happened. He could have remembered incorrectly but one would have thought that he would have remembered such significant events. Unless we don't remember such events as civil war, or the events are reported as less significant events that are later identified as 'civil war'.

But overall, we Martians, and I think I speak for a significant number on Earth, would assess Titor as either a clever construction or a deluded individual. A deluded individual would not have 'disappeared' so abruptly, I feel, so on balance, I'd think that Titor was a clever construction, abandoned by his creator when things became boring.

A real time traveller? No, I don't think so.

Object Oriented Plato

Plato came up with the idea that every commonplace object has an 'archetype' or idealized 'form' which all objects of the type have in common as a sort of 'ancestor'. Thus a table has a corresponding 'form' which encapsulates the idealized attributes of the object that makes it a table.

There are arguments against the theory of forms, but I'm not concerned with them here. I'm concerned with the similarities between the idea of 'forms' and the idea of 'objects' as used in programming.

'Object orientated' programmers use objects to represent collections of data and the things that can be done to that data. For instance you may have collection of data about a person who you know, which you categorize as a 'contact'. The collection might contain 'attributes' or 'fields', such as name, address, phone number and so on. There are also the things that can be done to the collection such as adding a phone number, correcting an address, or removing the whole collection, which are commonly called 'methods' by programmers. There are distinct programmatical advantages in treating the collection as a whole.

There is a special action associated with the collection which is the creating of the collection (eg adding a new contact). This special method is called the 'constructor'. When you use the constructor you create a new 'instance' of the collection. Each instance has the same methods (actions on the collection) and the same fields or attributes (names, addresses, whatever) but the fields and attributes will contain different data. Mr X's instance will contain Mr X's details, while Mr Y's instance will contain Mr Y's details. In general the things that you can do to the instance, the methods, are the same.

The two instances are both examples of 'contacts' and there is a generic contact from which both instances spring. In programming terms this is the 'class' or 'type' to which the 'instances' belong.

So where are we in regards to Plato? Well, the 'instances' correspond to real world objects, the 'methods' to things that you can do to them and the 'fields' and 'attributes' to their properties. A physical table has the property of being made of pine, it has methods of 'polish', 'lay' or 'set', 'eat off', 'clear' and so on. The archetypal table also has such properties, but they are in the main not defined. The archetypal table is like a template that is filled in to 'construct' a real table. In other words the 'class' is the 'form' of the table and 'instances' of tables are the real tables.

So far so good, but the ideas of Object Orientated programming (OOP) can be used to extent Plato's ideas, because of the idea of 'inheritance'.

Consider the class of tables. You can have dining tables, bedside tables, card tables and so on. An OOP programmer would consider 'dining tables', 'card tables' and all other types of tables to be classes or types derived from the class of 'table'. They are sub-classes, and not instances of tables however. Specific dining tables are instances of 'dining tables', but, an important point, they are also instances, by derivation, of the table type or class. There is a hierarchy of classes (or forms in Plato's terminology). OOP programmers consider all objects to be instances derived ultimately from the archetypal object called, confusingly, 'Object'.

The Object object has essentially no fields or proprties and one method, the constructor method. It is up to the derived types or classes to add the appropriate methods and fields or properties, which give, say, the table class its table-like characteristics. An instance may 'inherit' characteristics from more than one class. For example a packing case used as a table would derive methods and fields and properties from both the packing case class (which might derive from a 'container' class) and the table class. This explains why it is so difficult to categorise things! They may and probably do relate to more than one type of thing.

Going back to Plato, I have kept his idea of 'Forms' in the sense of a class or template, and introduced the idea of instances which are distinct from the class or form. Instances exist in the 'real' world, while classes or forms are conceptual. I've also used the idea of 'inheritance' of forms or classes from other, more general, forms to explain things like 'packing case tables'. All classes derive hierarchically from one ultimate form, the Object which, zen-like, only exists to be inherited or instantiated.

One final point - Plato's objects derived from an ideal 'form'. In doing this they lost something and became mere shadows. In considering objects to be instantiations of
a generic form or class, the instantiated objects become more than forms - they gain values for attributes and physical existence. Forms then become templates which represent potentiality.