David and James,
DP
What about "the first cake that I bake in 2020". Is it an actual
entity? It is not (currently) observable. It might not even exist
(because I might not bake a cake in 2020). I would claim that it
is of the same type as "the first cake I baked in 2018" (which did
exist until we ate it).
JHD
But the truth value of "the first cake I baked in 2018 is gluten-free"
is determinate (I happen not to know it, but you presumably do). The
same is not true of 2020.
I defined actuality as anything that ever was, is, or will be
anywhere in the universe. Most of us know more about the past
and present than we do about the future, but our knowledge is
irrelevant to its existence.
In fact, all of us know a great deal about the near future and
most of us do a lot of planning for the longer term. For example,
every time I drive a car, I predict that no cars in the opposite
lane will serve over and collide with mine.
So far, that prediction has been absolutely true, and I hope
that it will always be true in the future. I'm sure that
most of us have the same knowledge and hopes, and that our
hopes will be true for the overwhelming majority of us.
DP
I am not sure that the possible/actual distinction makes sense
for examples like this [baking a cake in 2020]
Just note the examples by James and me. For the gluten-free cake
in 2020, the knowledge is uncertain. But most people who bake
cakes can make a very accurate prediction about the likelihood
that they will bake a gluten-free cake in 2020.
In fact, I'll make a prediction about people I have never met:
For anyone who frequently bakes a cake and has never previously
baked a gluten-free cake, the probability that they will not
bake a gluten-free cake in 2020 is greater than 50%.
DP
(and it certainly isn't the mathematics/physics distinction).
The definition I stated is absolutely precise. To emphasize
the precision, I'll restate it in 4-D coordinates -- but it
remains just as precise when you translate it to 3-D plus time:
1. Pure mathematics is the study of possibilities. Every
possible structure or process can be described by some
theory of pure mathematics, but no structure or process
of pure mathematics exists in actuality.
2. Everything in the universe that is actual is either a
4-dimensional region of space-time or it is wholly
contained within some 4-D region of space-time.
3. Applied mathematics is the practice of selecting structures
specified by one or more theories of pure mathematics and
using them to describe something contained within some 4-D
region of space-time. The descriptions of applied mathematics
are rarely, if ever, absolutely true. But it's often possible
to estimate the expected errors in measurement or prediction.
The distinction between #1 and #2 is precise. All the errors
and vague intermediate cases result from difficulties in #3.
John
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