A Quote by Philip J. Davis
In the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics.
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The structure underlying the phenomena is not given by material objects like the atoms of Democritus but by the form that determines the material objects. The Ideas are more fundamental than the objects.
Materialism is the recognition of "objects in themselves", or outside the mind; ideas and sensations are copies of images of those objects.
Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
I agree that science is the best way of understanding the natural world, and therefore that we have reason to believe what the best science tells us about the objects in that world and the relations between them. But this does not mean that the natural world is the only thing we can have true beliefs about. The status of material objects as things that are "real" is a matter of their having physical properties, such as weight, solidity, and spatio-temporal location. In order to be real, such things need not have, in addition to these properties, some further kind of metaphysical existence.
Mathematical objects are determined by - and understood by - the network of relationships they enjoy with all the other objects of their species.
The mathematics clearly called for a set of underlying elementary objects-at that time we needed three types of them-elementary objects that could be combined three at a time in different ways to make all the heavy particles we knew. ... I needed a name for them and called them quarks, after the taunting cry of the gulls, "Three quarks for Muster mark," from Finnegan's Wake by the Irish writer James Joyce.
These two, I say, viz. external material things, as the objects of SENSATION, and the operations of our own minds within, as the objects of REFLECTION, are to me the only originals from whence all our ideas take their beginnings.
The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation and foreign commerce. ... The powers reserved to the several States will extend to all the objects which in the ordinary course of affairs, concern the lives and liberties, and properties of the people, and the internal order, improvement and prosperity of the State.
If laws are just properties of objects, how can those laws continue to operate when the object is not really there?
In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.
Mathematicians do not study objects, but relations between objects.
Mathematicians do not study objects, but the relations between objects.
I sometimes am challenged to imagine where the timbre of art should be. Should it be about objects that point to this current moment, or how objects are related to ideas of this current moment?
I think the most important work that is going on has to do with the search for very general and abstract features of what is sometimes called universal grammar: general properties of language that reflect a kind of biological necessity rather than logical necessity; that is, properties of language that are not logically necessary for such a system but which are essential invariant properties of human language and are known without learning. We know these properties but we don't learn them. We simply use our knowledge of these properties as the basis for learning.
My pictures are devoid of objects; like objects, they are themselves objects. This means that they are devoid of content, significance or meaning, like objects or trees, animals, people or days, all of which are there without a reason, without a function and without a purpose. This is the quality that counts. Even so, there are good and bad pictures.
When objects are presented within the context of art (and until recently objects always have been used) they are as eligible for aesthetic consideration as are any objects in the world, and an aesthetic consideration of an object existing in the realm of art means that the object's existence or functioning in an art context is irrelevant to the aesthetic judgment.
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