Do the assumptions underlying our best mathematical models of something qualify as observations and experiences of the real object itself? Our best ma...
Once again, you are smuggling in an additional premise--in this case, that something must be a quantity in order to qualify as a number. Unfortunately...
An infinite number is a number bigger than any assignable quantity or countable number ... no contradiction. Your original statement implied that only...
The author of the definition that you quoted would presumably reply: It is an infinite number. Once again, you are smuggling in an additional premise-...
Read the definition that you quoted more carefully. It does not state, "A number greater than any number," which would indeed be contradictory. Instea...
I am afraid that I cannot make heads or tails of your first paragraph because of the confusion it exhibits regarding the meaning of terms--infinite, q...
As usual, this reflects conflation of the real with the actual. If numbers are infinite, and mathematics is actual, then I guess there is such a thing...
Again, where can I find such mathematics so that I may interact with it? We can only interact with that which is actual, which is why both words have ...
Wow, do you really think that mathematics is necessary for building things? That would be news to the ancients, or to any young child even today who b...
An infinitesimal is not a number. What is nonsense is claiming that mathematical objects have actual existence at all. In themselves, numbers (for exa...
Again, where is the problem if that "something" is mathematical--i.e., hypothetical--rather than actual? Are you claiming that reality is limited to t...
"Logic" is an English word derived from ????? that names the science of symbols--signs (including words) that represent their objects only by virtue o...
Why is that necessarily a problem? An infinitesimal indeed has no specific or definite or measurable dimensionality, yet it does have real dimensional...
"Infinitesimal point" is self-contradictory--points are, by definition, dimensionless and indivisible; infinitesimals are, by definition, dimensional ...
For me, "Word" makes sense as a translation because John goes on to say "in the beginning" in verse 2 and then "All things were made by him" in verse ...
Right back at you. As I already stated, a continuum is not composed of infinitesimals. Moreover, there is no ultimate compatibility between a continuu...
Not really, since verses 15 and 30 unambiguously indicate that verse 14 is referring to one particular man whom John the Baptist specifically identifi...
I am not qualified to comment on the translation, but taking ????? as referring to Christ comes from verse 14: "And the ????? was made flesh, and dwel...
No, infinitesimals are not units, and they are not "distinct things." False, infinitesimals are real but indefinite--i.e., potential not actual. How s...
There are two fundamental mistakes here: first, infinitesimals are not units; second, a continuum is not composed of infinitesimals. Forms are only ac...
Reality and existence are not synonyms. Harry Potter and unicorns are not real, because their properties depend upon the thinking of an individual min...
Then why are we still having this conversation? I have never been arguing for actual infinity. If the set of natural numbers is actual, then where can...
Says who? Not any actual mathematician (pun intended). First of all, who said anything about "actual infinity"? Secondly, it begs the question to insi...
No, you are obstinately ignoring the difference between actual impossibility and logical impossibility. I suggest that you study up on that distinctio...
That is actually impossible, but not logically impossible. Similar ... more similar ... maybe ... superficially ... but I asked you to tell me exactly...
Please give me an example of something that you can imagine, yet is logically (not just actually) impossible. Please tell me exactly how you can imagi...
A real circle is truly continuous, and its mere possibility is sufficient for its reality. You mean in actuality, which is only one subset of reality....
I suspect that I have encountered them, but it was a while back and I never got very far. I am aware of a few different approaches that seek to captur...
What we can draw on paper is a representation of a circle, and we can mark as many points on it as we like--up to any finite number. However, a real c...
Right, we call such things fictions. Unicorns are not real because they are as they are only because people think of them that way. There is nothing i...
But that is a contradictory statement--"real" means "as it is regardless of what anyone thinks about it," so anything that is "in our minds only" cann...
Design implies intention and choice from among multiple viable options, but causal determinism rules both of those out. Somehow excluding God from cau...
Mathematical modeling is representation for a particular purpose. I already acknowledged that the real numbers serve as an adequate model of a continu...
No one is arguing for actual infinity, or that infinity is a number, or (for that matter) that infinitesimals are numbers. Again, numbers are intrinsi...
What would qualify as "empirical evidence" that the universe is cyclical, repeating the exact same sequence of events over and over? Why would we expe...
In that case, you must believe that this entire conversation--along with everything else that ever has happened and ever will happen--could not have p...
I agree that the real numbers are adequate for modeling, marking, and measuring discrete quantities, no matter how small. My understanding is that con...
If the universe is an eternally repeating cycle, perhaps with some random variations here and there, then no timeless being is required to create it; ...
I think the question is whether the Planck time is properly described as a discrete "unit of time" or as a limitation on our ability to mark and measu...
Sure, but we are discussing the nature and origin of the entire existing universe, not everyday experience. Moreover, many philosophers (and people in...
You have really been operating with this axiom all along, as the necessary conclusion from your two previous premises, "every effect has a cause" and ...
Alternatively, as Peirce argued, there are no instants (NOWs) in any continuous interval of time, and there are no points in any continuous segment of...
Not sure if this was directed at me, but to clarify--I did not mean to imply that Peirce's objections to Cantor and Dedekind carry much weight among p...
Indeed, Peirce independently invented quantification; and he disagreed with Cantor and Dedekind about the real numbers comprising a continuum, because...
In mathematics, pairing and counting are not activities at all; they are concepts, and there is no requirement that they ever actually be completed, o...
Attempting to be maximally charitable, I understand @"Devans99" to be arguing that there are only three possibilities: Our existing universe is eterna...
You have offered no argument for this claim, you have merely asserted it over and over; and now you have completely undermined your own position by fr...
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