Planescape Planescape IS D&D Says Jeremy Crawford

Planescape is Jeremy Crawford's favourite D&D setting. "It is D&D", he says, as he talks about how in the 2024 core rulebook updates Planescape will be more up front and center as "the setting of settings".

​

 

[ersatzphil]

No, “we” have very reliable, consistently verifiable descriptions of how these things work (which is what a “theory” is in a scientific context). And we have a very good understanding of infinity, which is a mathematical concept. It is absolutely possible for a set to be infinite and to still not include everything that exists or could conceivably exist.

100%.

The ‘set of all real numbers’ is larger than the ‘set of all even real numbers’. Both are equally infinite.

Calling the default setting of D&D the multiverse is, if I understand correctly, meant to be inclusive of your homebrew world; not so much so we can now claim cainites and garou are now D&D things.

 

[Charlaquin]

The ‘set of all real numbers’ is larger than the ‘set of all even real numbers’. Both are equally infinite.

I’m not 100% sure about this statement. I’m not a mathematician, but aren’t all even numbers integers by definition? All even integers would be “countably infinite,” as would all integers, so both sets would be equally large. Whereas all real numbers is not countable, making it a larger set than the set of integers (or the set of even integers). All three are infinite, but the real numbers are a higher “class” of infinity, so to speak, than the other two. “All even real numbers,” if I’m not mistaken, would be the same set as “all even integers,” because there are no even real numbers that aren’t also integers.

 

[ersatzphil]

I’m not 100% sure about this statement. I’m not a mathematician, but aren’t all even numbers integers by definition? All even integers would be “countably infinite,” as would all integers, so both sets would be equally large. Whereas all real numbers is not countable, making it a larger set than the set of integers (or the set of even integers). All three are infinite, but the real numbers are a higher “class” of infinity, so to speak, than the other two. “All even real numbers,” if I’m not mistaken, would be the same set as “all even integers,” because there are no even real numbers that aren’t also integers.

I'm going to explicitly preface this with the statement: "If we go much farther down this train of thought, I'm going to have to resort to digging out my copy of Halmos and doing some remedial reading", but: wouldn't sets of integers always be larger than sets of real numbers, as integers include negative numbers and sets of real numbers don't?

edit: I mistakenly referred to something as a 'group' instead of a 'set'. Not a can of worms I want to open.

 

[Veltharis ap Rylix]

I'm going to explicitly preface this with the statement: "If we go much farther down this train of thought, I'm going to have to resort to digging out my copy of Halmos and doing some remedial reading", but: wouldn't sets of integers always be larger than sets of real numbers, as integers include negative numbers and groups of real numbers don't?

Integers are whole numbers - both positive and negative, but no fractions/decimals.

Real Numbers contain all Integers (positive and negative) and also include fractions/decimals.

So the set of Real Numbers is larger.

 

[Charlaquin]

I'm going to explicitly preface this with the statement: "If we go much farther down this train of thought, I'm going to have to resort to digging out my copy of Halmos and doing some remedial reading", but: wouldn't sets of integers always be larger than sets of real numbers, as integers include negative numbers and sets of real numbers don't?

Err… Again, I’m not a mathematician, but I’m pretty sure negative numbers are real numbers. My understanding is that all whole, rational, and irrational numbers are real numbers. Imaginary numbers are the only type of number not included in the set of real numbers.

Also, the set of all positive numbers and the set of all integers (which does include negative numbers) are both countably infinite, so they are the same size.

 

[tsadkiel]

Negative numbers are real numbers, unless they are imaginary. I tell my ACT students that for test purposes, real numbers including everything that doesn't have an i in it.

 

[Charlaquin]

Integers are whole numbers - both positive and negative, but no fractions/decimals.

Real Numbers contain all Integers (positive and negative) and also include fractions/decimals.

So the set of Real Numbers is larger.

All of these statements are true, but the set of all rational numbers (the integers and fractions/decimals) is also countably infinite, so it’s the same size as the set of all integers (which is the same size as the set of all positive integers, etc).

The reason the set of all real numbers is larger is because it includes irrational numbers (like Pi and friends), which makes it not countable.

 

[ersatzphil]

The reason the set of all real numbers is larger is because it includes irrational numbers (like Pi and friends), which makes it not countable.

This is definitely “time to reread Halmos” territory for me

edit: I will just add that this sort of debate is exactly why I loved the 2e era Planescape line as much as I do.

 

[Incenjucar]

Clearly there can be no reconciling the Singularitarians and Pluralites, so we shall stake our claim in different wards and let the Lady decide which faction will be graced by her shadow.

 

[doctorbadwolf]

I’m sorry, but you are just wrong about this. This isn’t a hypothetical scenario, real physicists do really talk about multiple universes right now, and they don’t use the word the way you are trying to use it here. We can’t currently verify or falsify the existence of other universes, but there are valid models that describe them, and those models treat them as separate universes from the one we inhabit.

If this were a scientific debate, I’d be interested in this line of argument. It is not, however.

Scientific usage doesn’t just trump all other usage by default.

A Multiverse and an omniverse are simply types of universal models used in fiction and in philosophical thought experiments. These are simply linguistic objects, not even scientifically testable theories even were that context relevant.

Not to mention I’ve literally observed arguments like this one between physicists, because the terminology of non-verifiable hypotheticals tends to not be set in stone.