Read this!! http://www.gutenberg.org/files/5740/5740-pdf.pdf

This book will perhaps only be understood by those who have themselves

already thought the thoughts which are expressed in it—or similar

thoughts. It is therefore not a text-book. Its object would be attained

if there were one person who read it with understanding and to whom it

afforded pleasure.

The book deals with the problems of philosophy and shows, as I

believe, that the method of formulating these problems rests on the misunderstanding

of the logic of our language. Its whole meaning could be

summed up somewhat as follows: What can be said at all can be said

clearly; and whereof one cannot speak thereof one must be silent.

The book will, therefore, draw a limit to thinking, or rather—not to

thinking, but to the expression of thoughts; for, in order to draw a limit

to thinking we should have to be able to think both sides of this limit

(we should therefore have to be able to think what cannot be thought).

The limit can, therefore, only be drawn in language and what lies on

the other side of the limit will be simply nonsense.

How far my efforts agree with those of other philosophers I will not

decide. Indeed what I have here written makes no claim to novelty in

points of detail; and therefore I give no sources, because it is indifferent

to me whether what I have thought has already been thought before me

by another.

I will only mention that to the great works of Frege and the writings

of my friend Bertrand Russell I owe in large measure the stimulation of

my thoughts.

If this work has a value it consists in two things. First that in it

thoughts are expressed, and this value will be the greater the better the

thoughts are expressed. The more the nail has been hit on the head.—

Here I am conscious that I have fallen far short of the possible. Simply

because my powers are insufficient to cope with the task.—May others

come and do it better.

## Tuesday, 29 March 2011

## Monday, 28 March 2011

### A favourite excerpt from Schopenhauer's 'Wisdom of Life'

You will surely learn from reading this book, I cannot do it justice: you can download it free at http://www.gutenberg.org/ebooks/10741

The brain may be regarded as a kind of parasite of the organism, a pensioner, as it were, who dwells with the body: and leisure, that is, the time one has for the free enjoyment of one's consciousness or individuality, is the fruit or produce of the rest of existence, which is in general only labor and effort. But what does most people's leisure yield?—boredom and dullness; except, of course, when it is occupied with sensual pleasure or folly. How little such leisure is worth may be seen in the way in which it is spent: and, as Ariosto observes, how miserable are the idle hours of ignorant men!—

The brain may be regarded as a kind of parasite of the organism, a pensioner, as it were, who dwells with the body: and leisure, that is, the time one has for the free enjoyment of one's consciousness or individuality, is the fruit or produce of the rest of existence, which is in general only labor and effort. But what does most people's leisure yield?—boredom and dullness; except, of course, when it is occupied with sensual pleasure or folly. How little such leisure is worth may be seen in the way in which it is spent: and, as Ariosto observes, how miserable are the idle hours of ignorant men!—

*ozio lungo d'uomini ignoranti*. Ordinary people think merely how they shall*spend*their time; a man of any talent tries to*use*it. The reason why people of limited intellect are apt to be bored is that their intellect is absolutely nothing more than the means by which the motive power of the will is put into force: and whenever there is nothing particular to set the will in motion, it rests, and their intellect takes a holiday, because, equally with the will, it requires something external to bring it into play. The result is an awful stagnation of whatever power a man has—in a word, boredom. To counteract this miserable feeling, men run to trivialities which please for the moment they are taken up, hoping thus to engage the will in order to rouse it to action, and so set the intellect in motion; for it is the latter which has to give effect to these motives of the will. Compared with real and natural motives, these are but as paper money to coin; for their value is only arbitrary—card games and the like, which have been invented for this very purpose. And if there is nothing else to be done, a man will twirl his thumbs or beat the devil's tattoo; or a cigar may be a welcome substitute for exercising his brains. Hence, in all countries the chief occupation of society is card-playing,[1] and it is the gauge of its value, and an outward sign that it is bankrupt in thought. Because people have no thoughts to deal in, they deal cards, and try and win one another's money. Idiots! But I do not wish to be unjust; so let me remark that it may certainly be said in defence of card-playing that it is a preparation for the world and for business life, because one learns thereby how to make a clever use of fortuitous but unalterable circumstances (cards, in this case), and to get as much out of them as one can: and to do this a man must learn a little dissimulation, and how to put a good face upon a bad business. But, on the other hand, it is exactly for this reason that card-playing is so demoralizing, since the whole object of it is to employ every kind of trick and machination in order to win what belongs to another. And a habit of this sort, learnt at the card-table, strikes root and pushes its way into practical life; and in the affairs of every day a man gradually comes to regard*meum*and*tuum*in much the same light as cards, and to consider that he may use to the utmost whatever advantages he possesses, so long as he does not come within the arm of the law. Examples of what I mean are of daily occurrence in mercantile life. Since, then, leisure is the flower, or rather the fruit, of existence, as it puts a man into possession of himself, those are happy indeed who possess something real in themselves. But what do you get from most people's leisure?—only a good-for-nothing fellow, who is terribly bored and a burden to himself. Let us, therefore, rejoice, dear brethren, for*we are not children of the bondwoman, but of the free*.## Sunday, 27 March 2011

### Mathematics; Invented or Discovered

Mathematics: Invented or Discovered?

I J G

Mathematics is, by most scholars, divided into two sections; arithmetic and geometry. The former involves the computation and manipulation of numbers and identities under addition, subtraction, multiplication and division while the latter constitutes the study of figures represented in space. Mathematics is an interpretive language of reality which is inherently advantageous over conventional speak when one is seeking to understand and manipulate the physical world. In this paper I seek to investigate and to give a heuristic analysis of the question ' Mathematics : Invented or discovered'.

One way of analysing the ontological nature of mathematics, in our search for answering the titled question, is in the understanding of its relationship with nature. However, there exists a problem in defining its relation to nature due to the sometimes abstract concepts described by mathematical thought i.e the ideas which don't directly 'map' onto nature. When mathematics describes reality we are not exclusively concerned about the model's inability to reflect nature perfectly; most, if not all models, are approximations. This is not the abstraction we are concerned with; the abstraction of consideration is the 'higher thought' which seemingly transcends our phenomenological experience which can on first sight enter the realm of metaphysics. If this 'higher thought' was non-existent, we would then say that mathematics is just a language for describing nature and physical processes therein, and would then infer that mathematics is just a descriptive tool for representing nature that was invented by the mind. How do we account for mathematics' ability to obtain insight, and, in retrospective analysis, accurately describe ideas that are on the border of the phenomenological/metaphysical realm. Herein, I wish to separate ideas that just 'appear' as non experienceable due to our intellects inability to 'think' about such. In addition, I wish to reflect on these unexperienecable events and how logical steps resulting from the firm setting of mathematics based on the experiencable world result in ideas and concepts so far removed from its base.

I J G

Mathematics is, by most scholars, divided into two sections; arithmetic and geometry. The former involves the computation and manipulation of numbers and identities under addition, subtraction, multiplication and division while the latter constitutes the study of figures represented in space. Mathematics is an interpretive language of reality which is inherently advantageous over conventional speak when one is seeking to understand and manipulate the physical world. In this paper I seek to investigate and to give a heuristic analysis of the question ' Mathematics : Invented or discovered'.

One way of analysing the ontological nature of mathematics, in our search for answering the titled question, is in the understanding of its relationship with nature. However, there exists a problem in defining its relation to nature due to the sometimes abstract concepts described by mathematical thought i.e the ideas which don't directly 'map' onto nature. When mathematics describes reality we are not exclusively concerned about the model's inability to reflect nature perfectly; most, if not all models, are approximations. This is not the abstraction we are concerned with; the abstraction of consideration is the 'higher thought' which seemingly transcends our phenomenological experience which can on first sight enter the realm of metaphysics. If this 'higher thought' was non-existent, we would then say that mathematics is just a language for describing nature and physical processes therein, and would then infer that mathematics is just a descriptive tool for representing nature that was invented by the mind. How do we account for mathematics' ability to obtain insight, and, in retrospective analysis, accurately describe ideas that are on the border of the phenomenological/metaphysical realm. Herein, I wish to separate ideas that just 'appear' as non experienceable due to our intellects inability to 'think' about such. In addition, I wish to reflect on these unexperienecable events and how logical steps resulting from the firm setting of mathematics based on the experiencable world result in ideas and concepts so far removed from its base.

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