"Hypothesis is a tool which can cause trouble if not used properly. We must be ready to abandon out hypothesis as soon as it is shown to be inconsistent with the facts. (William I B Beveridge, "The Art of Scientific Investigation", 1950)
"Consistency and completeness can also be characterized in terms of models: a theory T is consistent if and only if it has at least one model; it is complete if and only if every sentence of T which is satified in one model is also satisfied in any other model of T. Two theories T1 and T2 are said to be compatible if they have a common consistent extension; this is equivalent to saying that the union of T1 and T2 is consistent." (Alfred Tarski et al, "Undecidable Theories" , 1953)
"Physics is at present a mass of partial theories which no man has yet been able to render truly and clearly consistent." (Norbert Wiener,"I am a mathematician, the later life of a prodigy", 1953)
"[…] the scientific picture of the real world around me is very deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity. Science sometimes pretends to answer questions in these domains, but the answers are very often so silly that we are not inclined to take them seriously. (Erwin Schrödinger, "Nature and the Greeks", 1954)
"Within the confines of my abstraction, for instance, it is clear that the problem of truth and validity cannot be solved completely, if what we mean by the truth of an image is its correspondence with some reality in the world outside it. The difficulty with any correspondence theory of truth is that images can only be compared with images. They can never be compared with any outside reality. The difficulty with the coherence theory of truth, on the other hand, is that the coherence or consistency of the image is simply not what we mean by its truth." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)
"As an operation, multiplication by i x i has the same effect as multiplication by -1; multiplication by i has the same effect as a rotation by a right angle, and these interpretations […] are consistent. […] Although the interpretation by means of rotations proves nothing, it may suggest that there is no occasion for anyone to muddle himself into a state of mystic wonderment over nothing about the grossly misnamed ‘imaginaries’." (Eric T Bell, "Gauss, the Prince of Mathematicians", 1956)
"Within the confines of my abstraction, for instance, it is clear that the problem of truth and validity cannot be solved completely, if what we mean by the truth of an image is its correspondence with some reality in the world outside it. The difficulty with any correspondence theory of truth is that images can only be compared with images. They can never be compared with any outside reality. The difficulty with the coherence theory of truth, on the other hand, is that the coherence or consistency of the image is simply not what we mean by its truth. (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)
[…] observation and theory are woven together, and it is futile to attempt their complete separation. Observation always involve theory. Pure theory may be found in mathematics, but seldom in science. Mathematics, it has been said, deals with possible worlds - logically consistent systems. Science attempts to discover the actual world we inhabit. So in cosmology, theory presents an infinite array of possible universes, and observation is eliminating them, class by class, until now the different types among which our particular universe must be included have become increasingly comprehensible. (Edwin P Hubble, "The Realm of the Nebulae", 1958)
No comments:
Post a Comment