Manny’s Reviews > Philosophy of Mathematics and Natural Science > Status Update
Manny
is on page 185 of 336
It transpired that for the various chemical elements the atomic masses are far from proportional to the atomic volumes. This shattered the basic conception of one matter, the conception of a homogeneous dough of substance out of which the Creator, with the help of a set of baking moulds, at the beginning of time had carved the little atom cakes, and had then given them absolute rigidity and sent them off into space.
— Nov 27, 2013 01:47PM
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Manny
is on page 270 of 336
Gödel's construction is closely connected to the logical paradoxes that had provoked so much discussion among the ancient philosophers. The Socratics reveled in paradoxes of this kind. Aristotle dedicates to them a whole book, De Sophisticis Elenchis. The medieval scholastic development culminated in Paulus Venetus (d. 1428). Most modern philosophers, e.g. C. Prantl, dismissed them contemptuously.
— Nov 29, 2013 12:34PM
Manny
is on page 220 of 336
Our judgement [of how to reconstruct past events] thus proceeds as if the system with which we are dealing had been created before our time. The word 'creation' suggests a metaphysical or even theological interpretation, but this should not prevent us from recognizing the state of affairs which is most aptly expressed by this word.
— Nov 28, 2013 01:14PM
Manny
is on page 205 of 336
The composition of the material world out of one or a few units, existing in a huge number of completely alike specimens, must surely be looked upon as one of the most fundamental features in the nature of the universe, and one that is most profoundly in need of interpretation.
— Nov 28, 2013 12:46AM
Manny
is on page 175 of 336
For Galileo, Huyghens and Newton, the deductive part plays a much greater role than in modern times. Galileo is no less proud of the "abundance of theorems which flow from a single principle" than of the discovery of this principle itself.
[Written in 1926]
— Nov 27, 2013 12:58PM
[Written in 1926]
Manny
is on page 155 of 336
It must be asked in connection with n-dimensional geometry, what inner reasons there are for the distinction of n=3 realized by actual space. Aristotle gave several answers to this, which still move in the sphere of mythical thought. The solution which Galileo proposes is merely a clearer formulation of the problem. The best chances for success seem to me to lie in theoretical physics construction.
— Nov 27, 2013 04:12AM
Manny
is on page 140 of 336
Hume attempted to uphold with inexorable consistency the viewpoint that the given is the whole of reality. Since it became apparent through him that this viewpoint fails completely in the explanation of those cognitive positions which play a basic role in everyday life and in science, he was indeed the first to reveal the problem of reality in its full difficulty.
— Nov 26, 2013 11:35PM
Manny
is on page 125 of 336
It is an appealing interpretation of A. Speiser's that Dante, as in Einstein's theory, assumes the real space of creation to be closed rather than bounded. The radii emanating from the center of the Earth, the seat of Satan, converge towards an opposite pole, the center of divine force. Compare the Paradiso, beginning with the 28th Canto. Einstein's space, of course, lacks a distinguished pair of opposite poles.
— Nov 26, 2013 01:46PM
Manny
is on page 115 of 336
The supreme act of redemption by the Son of God, crucifixion and resurrection, is no longer the unique pivot of world history but the hurried small-town performance of a road show repeated from star to star - this blasphemy displays perhaps in the most pregnant manner the religiously precarious aspects of a theory which dislodges the Earth from the center of the world. (Bruno had to pay for it at the stake.)
— Nov 26, 2013 12:53AM
Manny
is on page 95 of 336
In the projective color plane, the pure spectral colors lie on a curve whose extremities come very close together and are connected by the color purple. Epistemologically it is not without interest that in addition to ordinary space there exists quite another domain of intuitively given entities, namely the colors, which forms a continuum capable of geometric treatment.
— Nov 25, 2013 12:04AM
Manny
is on page 85 of 336
If in summing up a brief phrase is called for that characterizes the life center of mathematics, one might say: mathematics is the science of the infinite. It was the great achievement of the Greeks to have made the tension between the finite and the infinite fruitful for the analysis of reality.
— Nov 24, 2013 12:11AM
