And yet the traditional/classical conception of God is that He is absolutely simple; His attributes are not discrete in the way that you seem to be suggesting. — aleteiest
With all due respect, that seems rather ... vague to me. — aleteiest
This seems like a case where Peirce's attempt to use generic terminology for his categories may have been misleading. They are not called 1ns, 2ns, and 3ns because they always and only come about in that order; on the contrary, my interpretation of his cosmology is that in the hierarchy of being, 3ns is primordial relative to the other two. In any case, 1ns/possibility does not "end" where 2ns/actuality "begins," they are both - along with 3ns/necessity - indispensable and irreducible ingredients of ongoing existence. — aleteiest
I knew that you did not invent it; you are just the one who introduced it to this thread. MU wrongly attributed it directly to Peirce and claimed that the latter relied on it to support the proposition that a continuum is divisible. — aletheist
The point that is cut is not afterall a point. It is a place, an infinitesimally small part of a continuum, and so is itself a continuum capable of infinite division.
The parts A and B can be considered different in their location on a line (because a specifiable ordering relation) but the difference is infinitesimally small. They may be thought of as 'overlapping' so that they occupy different places. The difference is infinitesimal, however, so it is in principle indiscernible. If the difference is indiscernible then we might easily say that A and B are the same.
But how did it make a difference to you that you ate one and not the other? And how even did it make any difference to the world, if the world had any discernible interest in the matter. — apokrisis
So - as has been repeated ad nauseum by both me an altheist now - it is not that there isn't a difference, but there needs to be a difference that makes a difference ... which is the difference that makes a difference in this discussion. — apokrisis
It's easy to see that its identity cannot logically be the same as was it is identified as, because Pluto is the entity which had previously been identified as a planet and is now not identified as a planet. — John
If that were true, then you would not be arguing with me, because it is simply a fact that - going back at least to Aristotle - "continuous" means being infinitely divisible though actually undivided. In any event, this is what I mean by continuous, and your insistence on your idiosyncratic definition is not going to change that. — aletheist
The point is the difference is meaningful, no matter how much you might pretend otherwise-- a thing's identity is not found in what it is to you (i.e. your experience of it, semiotics, your "epistemic cut" ), but rather itself. There is a difference ( "This one dies, not the other" ) no matter if you care about it. Your generality is a myth, a dishonest story you tell yourself to eliminate subjects in the contexts of your "practical" concerns. — TheWillowOfDarkness
If I understand you correctly, we are assuming an object which has the identity "Pluto". Now, let's say that we remove this object from sight, and then we bring an object, which also has the identity "Pluto". We want to know if they are both the same object, so we consider differences. Unless we consider all possible differences, we cannot jump to the conclusion that they are both the same object. — Metaphysician Undercover
Your understanding seems not incorrect. — apokrisis
The difference is infinitesimal, however, so it is in principle indiscernible. If the difference is indiscernible then we might easily say that A and B are the same.
So perhaps contextuality means that "P is whatever is distinguished from not-P." — aletheist
I defined it - going the furthest in reducing awareness of reality to a matter of signs - that is, the theory we create and then the numbers we read off our instruments. — apokrisis
The soccer goalie does just the same in the end. Success or failure is ultimately read off a score board ticking over - the measurement of the theory which is the rules of a game. — apokrisis
You are forgetting the role of measurement. Ideas must be cashed out in terms of impressions. — apokrisis
Science is the metaphysics that has proven itself to work. It is understanding boiled down to the pure language of maths. And so measurements become actually signs themselves, a number registering on an instrument. — apokrisis
He was indeed inspired by Cantor, but he also achieved some of the same results and reached some of the same conclusions at least semi-independently. In the end, he became disenchanted with Cantor's whole approach; as Rich has been emphasizing, you cannot adequately represent true continuity with something that is discrete. — aletheist
We could never possibly take account of every difference, and even if we actually had taken account of every difference we would have no way of knowing we had, because it would always be possible that there could be differences we had missed.
So identity is always something stipulated, not something logically proven or empirically demonstrated. — John
So MU, you quote Peirce in a way that directly contradicts you and directly supports me.
Interesting argumentative strategy. — apokrisis
We recognize that the two are different, but we're just going to overlook that fact, and say that they are the same, because the difference is so small. — Metaphysician Undercover
The issue is well explained in BK. 6 of Aristotle's Physics. — Metaphysician Undercover
Now if the terms 'continuous', 'in contact' [i.e., contiguous], and 'in succession' are understood as defined above - things being 'continuous' if their extremities are one, 'in contact' if their extremities are together, and 'in succession' if there is nothing of their own kind intermediate between them - nothing that is continuous can be composed 'of indivisibles': e.g. a line cannot be composed of points, the line being continuous and the point indivisible ...
Again, if length and time could thus be composed of indivisibles, they could be divided into indivisibles, since each is divisible into the parts of which it is composed. But, as we saw, no continuous thing is divisible into things without parts. Nor can there be anything of any other kind intermediate between the parts or between the moments: for if there could be any such thing it is clear that it must be either indivisible or divisible, and if it is divisible, it must be divisible either into indivisibles or into divisibles that are infinitely divisible, in which case it is continuous.
Moreover, it is plain that everything continuous is divisible into divisibles that are infinitely divisible: for if it were divisible into indivisibles, we should have an indivisible in contact with an indivisible, since the extremities of things that are continuous with one another are one and are in contact. — Aristotle, Physics VI.1, emphases added
After stipulating that anything continuous, including time, is divisible, and necessarily infinitely divisible, he proceeds to determine "the present" as indivisible. Then he describes a "primary when" as indivisible also. — Metaphysician Undercover
For what is 'now' is not a part: a part is a measure of the whole, which must be made up of parts. Time, on the other hand, is not held to be made up of 'nows' ... obviously the 'now' is no part of time nor the section any part of the movement, any more than the points are parts of the line - for it is two lines that are parts of one line. In so far then as the 'now' is a boundary, it is not time, but an attribute of it ... — Aristotle, Physics IV.10-11
What is discrete in the Reals? What aspect of the Reals is being inadequately represented by this discrete thing? — tom
Apokrisis appears to be saying that there is no use in assuming such a principle of identity. — Metaphysician Undercover
This seems to be the way that apokrisis speaks of identity, we give a thing an identity relevant to the purposes at hand. — Metaphysician Undercover
Please just make your point, if you have one. The real numbers constitute an analytic continuum, not a true continuum as defined by Peirce (and others). — aletheist
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