Here’s a speculative theory of persons:
- A person is an individual of a sort that pursues the good as such.
What’s interesting on this theory of persons is that mental life is not directly a part of the definition. For pursuit as such does not require a mind: plants pursue particular goods like nutrition and reproduction (but while they pursue particular goods, they don’t pursue the good as such).
I conjecture that pursuit of the good as such requires a mind and will. If this is right, then that brings my teleological definition closer to intuitive accounts of persons. Interestingly, though, I also conjecture that pursuit of the good does not require a conscious mind—just a mind with intention, intentionality and intensionality (funny how different the meanings of these three similar-sounding words are). Since personhood implies dignity, it follows that dignity does not require consciousness. (An important observation for thinking about people in persistent vegetative states.)
But this is all super conjectural.
What if it turns out that one can pursue the good as such without mind? Should I then modify the definition of a person to replace “pursues” with “intentionally pursues”?
I think it depends on whether the kind of being that pursues the good as such without mind still has the kind of dignity that persons have. If so, then I am happy to leave my definition unchanged. But if dignity requires mind, and mind doesn’t follow from pursuit of the good, then I will insert “intentionally” into my account.
As I said, this is all speculative. But one thing I am fairly confident of: being the sort of individual that pursues the good as such is a necessary condition for being a person.
An interesting consequence is this. One could have a kind of being with advanced agency, problem-solving ability, and abstract thought, without its being a person. Indeed, I think such a being might even have the abstract concept of the good, but if it wasn’t of a sort to pursue the instances of that concept as such, it wouldn’t be a person.
If I am right at least about the necessary condition, I think we make some progress on the fine-tuning argument for theism. One of the objections to the fine-tuning argument for theism is this: “Why should we think that a personal designer would want there to be life?” Well, if a person is the sort of being that pursues the good in general, the good as such, and if life is eminently valuable, it is not astronomically unlikely that a personal designer would want there to be life. And given how ridiculously narrow some of the life-compatible ranges in the fine-tuning argument are, “not astronomically unlikely” is all we need.
15 comments:
Quaternions are just as neat for four-dimensional rotations. The cross-product thing is of no real interest, it seems to me, as it's just an inferior stopgap for the wedge product, which works in all dimensions.
Three dimensional space is provably the only one in which waves propagate without distortion, which strikes me as a much more likely explanation.
Do you think intuitively ugly mathematical results constitute any evidence against explanations like this?
e.g. https://x.com/Winterflan/status/1834308016226939295?t=hpULvnHwjHbQzqf6SrEWtg&s=19
Shadow: Fair enough about quaternions. The thing that puzzles me is the smallness of the number of dimensions, and four is still pretty small. (Yeah, everything is small relative to infinity, but we still have some intuition that 1-12 is VERY small.)
I don't know about wave propagation and distortion. It looks like three is optimal, but one can still get signal transmission in other odd dimensions: https://repository.ias.ac.in/1079/1/347.pdf
That twitter link leads to a page that doesn't exist. Do you have any backups of that?
About everything being small relative to infinity, that's true, but I think one could also say infinity has an interesting equalising effect for finite numbers - any finite number, although it can be smaller than other finite numbers, is only ever infinitely smaller than infinity. And all the other finite numbers are also infinitely smaller than infinity.
In the Newtonian approximation to general relativity with d > 2 space dimensions, the gravitational force falls off like 1/r^(d-1), because the force lines spread out over the area of a sphere. However, the centrifugal force always falls off like 1/r^3, regardless of dimensionality. As a result, orbits are not stable if d > 3; with even the slightest deviation from a circular orbit, planets would crash into stars or escape into space. On the other hand, in d=2 GR, there is no gravitatational force at all; instead point masses produce conical singularities of space.
For a related but quantum reason---forces become comparatively stronger at short distances when d is larger---it is impossible to find renormalizable QFT interactions when the number of spacetime dimensions D > 4 (although there are some exotic theories that work in up to D = 6, they are quite different from the Standard Model).
Matrices of quaternions are useful for describing rotations whenever the number of space dimensions MINUS the number of time dimensions, modulo 8, is: 3, 4, or 5. For 2 or 6 you can use complex-valued matrices. For 0,1, or 7, the corresponding matrices are real-valued. Key words include "Clifford algebras" and "Bott periodicity".
So, for example, the Lorentz group in 3 space dimensions and 1 time dimension, can be described by 2x2 complex matrices with unit determinant.
What exactly are additional time dimensions though? Especially anything above the first? Sorry if this is a bit of a layman's question, but do you know of a way to break it down to understand it better?
Regarding Wesley's query, in the spacetime geometry of special relativity, time differs from the other dimensions in that it contributes with a minus sign to the Pythagorean distance formula. See here for an explanation:
http://www.wall.org/~aron/blog/the-geometry-of-spacetime-i-distance/
I would note that, when I was talking about the nature of rotations in different numbers of m space and n time dimensions, I am purely talking about the mathematics of transformations that preserve a distance formula where m dimensions have + signs while n dimensions have - signs. This can be studied without regard to whether it would really make sense (philosophically or physically) to have multiple time dimensions. In particular, nothing in my comment about Bott periodicity requires introducing concepts such as causality, thermodynamics, etc. It's just a purely geometric claim. (Unlike my other comment about gravitional orbits, which concerns actual physics.)
Not an exact backup but the same idea, the optimal way to pack 17 squares into the least amount of space: https://www.reddit.com/r/math/s/UnVI3ouMVW
Dr Wall:
I once said that a difference between space and time is the sign in the metric, and Nic Teh corrected me by observing that you can't use that to differentiate space from time in two-dimensional relativity where you have one space and one time dimension. (I am guessing that he was thinking that the choice of whether timelike distances get a + or - is purely conventional--it's only the difference between + and - that has physical significance.)
If that's right, then we may need something more for the difference between space and time than the signs in the metric. I am inclined to think that the crucial ingredient is causation, which is (at least typically) timelike but not spacelike.
Yes, the choice of sign for space vs time is purely conventional---in fact there are physicists who use the opposite convention from the one I said!
Regarding the actual difference between space and time, I think it is a subtle question. I agree that time has something to do with causality, but there is a question of exactly how to cash this out in physics models. In QFT you have the property that observables always commute at spacelike separation, but can fail to commute for timelike and spacelike separation. (Although, if we restrict attention to time ordered correlators maybe we couldn't detect this problem, however I think in a typical 1+1 dimensional theory there may be other things that go wrong with unitarity.)
Another difference is that switching the roles of space and time would replace massive particles with tachyons (and vice versa).
In the case where you have only massless particles in 1+1 dimensions, which propagate at the speed of light, the considerations above may not suffice to distinguish the two cases, and it might come down to the question of, in which direction we impose the "initial conditions".
@Aron If time is uniquely causal while space isn't, then even in the massless, 1+1 dimension, lightspeed particles case, there'd still be a difference between time and space - it's just that we can't easily tell without knowing or imposing initial conditions.
In fact, if time is uniquely about causation, then any other potential dimensions of time would also have something to do with causation at least.
@Wesley, the principle of "Microcausality" states that failure to commute can only occur at timelike OR lightlike separation.
But, in some theories involving massless particles only, this in fact happens ONLY at lightlike separation. Not at either timelike or spacelike separation. So, if we restrict attention to this special type of theory, it would seem truer to say that causation is associated with lightlike directions. And then, this particular formalization of causality does not seem to discriminate between space and time.
Max Tegmark has a paper on this ~exact topic laying out why 3+1 dimensional spacetimes are the only ones that are likely to contain observers like us: https://arxiv.org/abs/gr-qc/9702052
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