Weeding and Sowing: Preface to a Science of Mathematical by Hans Freudenthal

By Hans Freudenthal

A name that seems like poetry, and a subtitle that turns out to contradict the identify! however the subtitle is true, and initially it used to be simply the name. an odd subtitle, isn’t it? Preface to a technology of Mathematical schooling. All sciences – of their prenatal degree – have identified this sort of literature: in simple terms the time period used used to be now not ‘Preface’, yet, for example, ‘Prolegomena’, which * skill an identical although it sounds much less provisional. actually such works have been thicker than the current one, through as much as ten instances. there's even more that may be stated a few technology ahead of it comes into being than after; with the 1st effects comes modesty. this is often the preface to a publication that might by no means be written: now not via me, nor via anyone else. as soon as a technological know-how of mathematical schooling exists, it is going to get the preface it merits. however this preface – or what for honesty’s sake i've got labelled so – needs to fulfil a functionality: the functionality of increasing the delivery of a technology of mathematical schooling, that's heavily impeded by means of the unfounded view that such already exists. by contrast view i must argue: it rests on a unsuitable estimation – either over and less than estimation even as – of what's to be regarded as technological know-how.

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Nevertheless teaching background philosophy is not the same as propa­ gandising, because teaching includes testing its consequences, through ‘examinations’. Although I once underwent an examination in philosophy – a reasonable one – I cannot imagine any more dreary happening than a philosophy examination, and for this reason I am utterly sceptical about the efficiency of this ‘short-cut’. Philosophy examined, ideology examined – is it not a boomerang? And if it does not work, what then? Even more back­ ground philosophy?

I will do so though not straightforwardly. 7. SCIENCE AND FAITH For some time I could not make up my mind whether it should be ‘faith’ that joined ‘science’ in this subheading. People who read subheadings only would think of new efforts at confronting dogmas and creeds with science. By mere accident the scale was turned. It was by reading a treatise on econ­ omics where after 270 pages of scarcely digestible mathematics the author asked, and at the same time answered, the question: what is true of all this?

To the first shepherds and hunters the world was just as large as they could drive their flocks and hunt their game; to the settled farmer it looked still smaller; though to all of them it appeared unlimited all around and only closed from above by the blue sky, which one fine morning – one can never tell – would crash down on the Earth. Seafaring extended the Earth; star­ gazing the skies. The ocean and the celestial sphere became new frontiers. 26 CHAPTER I Then what is called the Copernican revolution happened.

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