No, all we can say is that there is no fundamental difference between measuring movement/distance and counting, which I have acknowledged all along. M...
You are talking about length (i.e., measurement), rather than location. Consider two dimensionless points with zero space in between them. How can the...
This right here is the mistake that you keep making. There are two statements here. An object must have passed through an infinite number of prior coo...
This is simply false. In order to build a machine that counts coordinates, you have to set it up using a particular (arbitrary) coordinate system, and...
If the distance between adjacent locations is zero, then by definition they are the same location, not adjacent locations at all. If the distance betw...
No, if space is discrete, then you need to capture every actual location; i.e., you need there to be an infinite number of actual locations (e.g. the ...
Simple - counting is discrete by definition, because it requires explicitly recognizing every intermediate step, but motion is not. You keep insisting...
Even if we define as many coordinates between A and B as there are rational numbers between 1 and 2, the object must still pass through the space betw...
This is a nonsensical question. The only discrete coordinates that an object must actually pass through are those that we arbitrarily establish. Spati...
You keep confusing potentiality with actuality. Either space is infinitely divisible or it is not. Whether anyone can actually divide space into infin...
And like I said, it is a valid type of reasoning - retroductive reasoning, rather than deductive reasoning. The conclusion is thus merely plausible at...
Even the real numbers do not constitute a true continuum, because they still amount to an aggregate of discrete individuals. However, I agree that thi...
You are confusing actual possibility with logical possibility. Mathematics deals with the latter, not the former. It is indeed actually impossible to ...
It is really no different from philosophy in this regard; it all boils down to one's assumptions. To get us back on topic, Zeno's alleged paradox expl...
Mathematics is entirely a matter of necessary reasoning about hypothetical states of affairs. There is no falsity whatsoever in saying that if someone...
Not at all. We can reason about infinity without actually doing anything an infinite number of times. If someone (God, perhaps) were to add up @"Banno...
Of course it can, students have to do it in math class all the time. You can also do it on a calculator. @"Banno"'s example was an infinite series, so...
The whole purpose of any discrete coordinate system is to facilitate measurement. The smallest rational number that is greater than 1 cannot be identi...
The only reason you brought this into the conversation was as a (mistaken) model of moving from point A to point B, which is the subject of the thread...
No, the task is to move from point A to point B. You are mathematically modeling it as counting every rational number between 1 and 2. I am challengin...
You are already being arbitrary by only counting all of the rational numbers between 1 and 2. What is your excuse for not counting all of the real num...
We can plot infinitely many points, but we do not have to plot any points between the two of interest. In other words, there are infinitely many poten...
You have it exactly backwards - the paradox only arises by insisting that space is made up of infinitely many points, and time is made up of infinitel...
I can count from 1 to 2 in a finite time (see, I just did it); there is no need to count every rational number in between. Likewise, I can move from p...
The problem here is equating continuity with infinite divisibility, as if space and time consisted of infinitely many points and instants, respectivel...
Yes, that is how it should be; but over the last several decades, the Supreme Court has gone in a much more activist direction, in many cases determin...
Nonsense. My son is objectively taller than my daughter. Yellow is objectively lighter in color than indigo. A pillow is objectively softer than a sto...
But that is a different question than the merely qualitative comparison of which one is taller than the other, which requires no measurement - and the...
Quantification is NOT necessary for comparison. If my son and daughter stand next to each other, anyone can observe that my son is taller than my daug...
Although mathematics is commonly associated with quantity, it is more broadly the application of necessary reasoning to hypothetical or ideal states o...
I am sorry that you see it that way, but I do forgive you. Obviously Peirce himself did not think so - not even remotely - since he explicitly affirme...
You left out my first two statements ... ... and I am still not following you here: If God is constrained by "existence as the universal growth of rea...
I am not seeing the connection between this comment and the notion that "mathematical symmetries" somehow limited God's options. For one thing, Peirce...
Assuming omnipotence, as Peirce did, the only thing that could have limited God's options were God's own previous choices, including the creation of t...
The standard interpretation of Peirce's cosmology is that the initial state was a chaotic mix of chance and reaction in which anything was possible bu...
I think that what you call dispositions and powers - i.e., what I call tendencies and habits - are the laws of nature. Mathematical abstractions are w...
But how do you know that the observed behaviors themselves are fundamental, rather than manifestations of something else that is even more fundamental...
You do not think that the remarkably consistent behavior of things calls for an explanation? If not, why not? You do not think that questions like why...
If there are no real tendencies or habits that govern things in such situations, then what constrains them to behave in such ways? If laws of nature a...
Do you deny the truth of the proposition, "If I were to let go of a stone, then it would fall to the ground"? If not, how do you explain it? What else...
The law of gravity is not the same thing as the mathematical model that we often use to represent it. Again, it is a real tendency or habit that gover...
Who said anything about precision? We make successful predictions all the time, since success does not require absolute precision. I am not familiar w...
Suppose that I am holding a stone. If I were to let go of it, then it would fall to the ground. This proposition is true, regardless of whether I ever...
And I am simply suggesting that if it is conditionalized solely on someone's knowledge (or lack thereof), background or otherwise, then we should not ...
To rephrase, what is gravity if not the law of gravity? Are you defining it as the actual behavior, or is it a real tendency or habit that governs tha...
As I have noted before, the perfect circle can be real, just not actual. The irrational nature of pi has nothing to do with it - the circumference of ...
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