aletheist

I guess you missed my second sentence. I am not sure why we are having this debate at all; it is an uncontroversial principle of modern deductive logi...

Can you (or anyone else) establish or change the properties of space-time just by thinking differently about them? Or is space-time something that we ...

"All A is B" does not entail the existence of any A, but "Some A is B" does; so it is not deductively valid to derive the latter from the former. Note...

Right, and it is not logically valid to derive an existential proposition directly from a universal proposition with the same terms. "All A is B" does...

Correct.

Your statement was, "But can't we imply "some B are C" from "all B are C"?" So the premise was "All B are C," which is equivalent to "For all x, if x ...

No, space-time is real--it is as it is regardless of what any individual mind or finite group of minds thinks about it. On the contrary, space-time is...

You mean a physical line, which is not the same thing. If you were to "zoom in" on space-time itself--not any physical object within space-time--you w...

No, that is invalid. It becomes more obvious if we reformulate the two propositions as follows. For all x, if x is B, then x is C. There exists an x, ...

I stand by my previous answers. Perhaps you should clarify exactly what you mean by "the theory that predicts the existence of Neptune"; or better yet...

When is the answer ever not 42?

I currently have no good reason to doubt that Neptune exists; that is, I believe that the proposition "Neptune exists" is true, where "Neptune" design...

Again, we adopt the belief that Neptune exists, because the hypothesis that Neptune exists not only explained our initial anomalous observations, but ...

"Retrodict" is not a word. We hypothesize the existence of Neptune/Vulcan. "Induce" usually means "cause." We conduct experiments and/or make addition...

"Construct" implies building something up from discrete constituents, which cannot be done in the case of a true continuum. I have never claimed that ...

The existence of Neptune/Vulcan was a valid retroduction--a plausible explanatory hypothesis for the observed (and surprising) anomalies in Uranus's/M...

What is the observed surprising fact that would be a matter of course if Vulcan exists?

Exactly what I said before--not composed of discrete parts. If we were to "zoom in" on a continuous line, we would never "see" anything other than a c...

We describe time as continuous--it is not composed of discrete instants or very short durations. Likewise, we describe a line as continuous--it is not...

Yes, the hypothesis that Neptune exists (A) would make the surprising anomalies in the orbit of Uranus (C) a matter of course; therefore, we have reas...

Then we simply disagree--I believe that space-time is a real continuum; i.e., it is as it is regardless of how anyone thinks about it.

How is that relevantly different from marking two points in time in order to measure duration? Yes--at least from a phenomenological standpoint, think...

As stated in the other thread, the observed (and surprising) fact C is a conclusion that deductively follows from A. In Peirce's own words, also from ...

A well-prepared mind. Again, Peirce called it a conjecture long before Popper did.

Again, how is each dimension of space any different in that regard? You need to mark at least two points in order to measure linear distance. A static...

No, time is not an independent "thing" that changes, it is the (fourth) dimension of space-time that corresponds to spatial change. As I keep pointing...

There is no such thing as an object at rest. Continuous motion through space-time is a more fundamental reality than discrete positions in space or mo...

Charles Sanders Peirce spelled out the scientific method (as outlined here) the year after Popper was born.

Or "now"--like any other durationless instant--is simply an arbitrary human construct that marks continuous space-time, rather than a real constituent...

Force is defined as the product of mass and acceleration, which is the second derivative of space with respect to time, so it is not an additional dim...

Only if one insists that deduction is the only valid form of logic. Charles Sanders Peirce recognized that retroduction (or abduction) and induction a...

The real is that which is as it is regardless of what any individual mind or finite group of minds thinks about it. The actual (or existent) is that w...

A few quotes from Charles Sanders Peirce seem relevant here. "Just as we say that a body is in motion, and not that motion is in a body, we ought to s...

The paradox arises from treating space and time as composed of discrete elements of any kind, rather than recognizing space-time as a true continuum, ...

I stated quite plainly that I was talking about apparent contradictions across a much larger text, especially one that has been carefully scrutinized ...

As I said before ...

I have explained (several times now) what I mean by the principle of charity in this context--treating consistency as the default interpretation and a...

Perhaps you have multiple personalities with different subjective preferences. More seriously, that is an obvious contradiction within the same senten...

On the contrary, you are repeatedly asserting your own dogmatic beliefs about the Bible. Why start the thread at all, if your mind was already made up...

I explained why two of the alleged contradictions are not actual contradictions. As you said yourself ... I am obviously not going to take the time to...

As Abraham Lincoln famously said, "Do not believe everything that you read on the Internet." More seriously, as noted, "contradiction" has a very spec...

If only. and already explain how this is false. The axiom that you are really following is, "When you add a finite quantity to another finite quantity...

Thanks--all of that is consistent with my understanding, as well. :up:

The problem is that relativity does not follow the axiom: "no matter how fast something is traveling, mass, length, and time are constant." That is su...

Because most people only ever deal with and think about finite quantities, which is the domain in which that axiom applies.

Ah, we finally get to the heart of the matter--it is not that the definition of infinity is contradictory, as the thread title asserts, but that you d...

Indeed, infinity is different from any finite quantity. So what? That does not make it illogical or contradictory, just different.

Why? The fact of the matter is that it does not, so we can either throw up our hands (like you do) or find and develop meaningful alternatives (like m...

That is fair. Can you elaborate on how QM supports the continuity of space-time? What is your interpretation of the Planck length and Planck time?

How many numbers are there? How many square numbers are there? Unless you can answer those two questions, you cannot assert that one is greater than t...