This site is dedicated to the memory of Dr. Alan William Smolowe who gave birth to the creation of this database.
Carnap calls such concepts as point, straight line, etc., which are given by implicit definitions, improper concepts. Their peculiarity rests on the fact that they do not characterize a thing by its properties, but by its relation to other things. Consider for example the concept of the last car of a train. Whether or not a particular car falls under this description does not depend on its properties but on its position relative to other cars. We could therefore speak of relative concepts, but would have to extend the meaning of this term to apply not only to relations but also to the elements of the relations.
To worship the product and ignore its development leads to dilettantism and reaction. Art cannot result from sophisticated, frivolous, or superficial effects.
To sense the invisible and to be able to create it ? that is art.
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry... "Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
Clocks are inherently four-dimensional instruments, since the endpoints of their unit distances are events. Measuring rods, on the other hand, are three-dimensional measuring instruments; their end points are space points and they can be changed into four-dimensional measuring instruments only if events are produced at their end points according to a special rule.
Absolute time would exist in a causal structure for which the concept indeterminate as to time order lends to a unique simultaneity, i.e., for which there is no finite interval of time between the departure and return of a first-signal...
Common to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lines as shortest lines as well as their relations of intersection.
One who wants to keep their yard tidy does not reserve a plot for the weeds.
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Nothing improves the taste of pasta more than a good appetite.
The gardener's dog does not eat lettuce and will not let others eat it.
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The fox advised the others to cut off their tails, because he had left his own in the trap.