It was Eugene Wigner who spoke of the "unreasonable effectiveness of math". Nature has dead and alive elements. Many deed phenomena (which doesn't mean they don't contain at least the seeds of life) behave in fixed patterns, contrary to living phenomena. For example, the principle of least action applies to dead matter but not to life. — Landoma1
, and he goes on to observe that we would run out of interesting theorems were it not for the creation or discovery of new concepts.The principal emphasis is on the invention of concepts
As concepts such a tables, apples, governments, ethics, laws of nature, etc require relationships between their parts, and relations have no ontological existence in the external world (see FH Bradley) but only in the mind (see the Binding Problem and Kant's Apperception and its Unity), such concepts exist only in the mind and not the external world. — RussellA
Amazing that inventions work so well, then. Or maybe they're all in the mind as well? — Wayfarer
But the fact that there is structure to the world does not mean that the world comes to our awareness packaged an ‘inherent’ way that is already mathematical. Nature became mathematizable when we contributed our own peculiar interpretive structures to it.
As you can see, I’m a mathematical constructivist, not a platonist. — Joshs
Amazing that inventions work so well, then. Or maybe they're all in the mind as well? — Wayfarer
If you don't see the point of Wigner's essay, there's not a lot of purpose me trying to explain it again. — Wayfarer
As with all inventions they were invented in the mind, and then made into a physical thing of perhaps wood and steel, a circular rim supported by spokes revolving around an axle. — RussellA
I am persuaded by FH Bradley's Regress Argument that relations don't ontologically exist in the external world, meaning that wheels don't ontologically exist in the external world. — RussellA
It could mean that if we turn over the whole universe item by item we will find at least one thing that is to the west of another thing.
There is a case - at least one case - of something being to the west of something else.
From which if finally follows that relations exist...........we can see that relations have ontological existence. — RussellA
Consider such a proposition as 'Edinburgh is north of London'. Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. When we come to know that Edinburgh is north of London, we come to know something which has to do only with Edinburgh and London: we do not cause the truth of the proposition by coming to know it, on the contrary we merely apprehend a fact which was there before we knew it. The part of the earth's surface where Edinburgh stands would be north of the part where London stands, even if there were no human being to know about north and south, and even if there were no minds at all in the universe. ...We may therefore now assume it to be true that nothing mental is presupposed in the fact that Edinburgh is north of London. But this fact involves the relation 'north of', which is a universal; and it would be impossible for the whole fact to involve nothing mental if the relation 'north of', which is a constituent part of the fact, did involve anything mental. Hence we must admit that the relation, like the terms it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends but does not create.
This conclusion, however, is met by the difficulty that the relation 'north of' does not seem to exist in the same sense in which Edinburgh and London exist. If we ask 'Where and when does this relation exist?' the answer must be 'Nowhere and nowhen'. There is no place or time where we can find the relation 'north of'. It does not exist in Edinburgh any more than in London, for it relates the two and is neutral as between them. Nor can we say that it exists at any particular time. Now everything that can be apprehended by the senses or by introspection exists at some particular time. Hence the relation 'north of' is radically different from such things. It is neither in space nor in time, neither material nor mental; yet it is something. ...
It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental. We can think of a universal, and our thinking then exists in a perfectly ordinary sense, like any other mental act. Suppose, for example, that we are thinking of whiteness. Then in one sense it may be said that whiteness is 'in our mind'. ... In the strict sense, it is not "whiteness" that is in our mind, but "the act of thinking of whiteness". The connected ambiguity in the word 'idea', which we noted at the same time, also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an 'idea'. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an 'idea' in the other sense, i.e. an act of thought; and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts.
We shall find it convenient only to speak of things existing when they are in time, that is to say, when we can point to some time at which they exist (not excluding the possibility of their existing at all times). Thus thoughts and feelings, minds and physical objects exist. But universals do not exist in this sense; we shall say that they subsist or have being, where 'being' is opposed to 'existence' as being timeless. — Bertrand Russell, The World of Universals
That's how you interpret it. — Landoma1
If you lived a hundred years ago you couldn't even imagine such a discovery — Wayfarer
But you don't know that. It's quite feasible that the wheel was invented because some Cro-Magnon discovered that you could roll a big rock on logs. Basic empiricism. — Wayfarer
This conclusion, however, is met by the difficulty that the relation 'north of' does not seem to exist in the same sense in which Edinburgh and London exist. — Bertrand Russell, The World of Universals
That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts. — Bertrand Russell, The World of Universals
One is the distinction between the existence of universals and of sensable objects. — Wayfarer
such qualities or relations or whatever they are, are not dependent on thought, but they can only be perceived by thought — Wayfarer
It is equivalent to saying that if relations exist then relations exist. — RussellA
If relations do not exist, then it is not the case that something is to the west of something else.
Glasgow is to the west of Edinburgh.
Therefore (at least one) relation exists. — Cuthbert
A group of people may agree to share a common language. It may be agreed within the group that white objects are linked with the word "white". In the world being observed by the group, not only do white objects physically exist, but also and the word "white" physically exists as an object. — RussellA
If concepts existed in a mind-independent world then they would be "out there somewhere" and discoverable. However, if that were the case, two people independently observing an object, for example a rock, should be able to write down all concepts discoverable within the object, in which case, when compared, their lists should be the same. Concepts in objects cannot be discovered by observation alone, but require the inventive power of reasoning using the intellect. — RussellA
If universals don't exist in a mind-independent world, yet we can perceive them in our minds, then they must have been created in the mind. As universals have been created by thoughts in the mind, they must be dependent for their existence on thoughts in the mind. — RussellA
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