[link] Is Alu Life?
I recently read (in Dawkins' The Ancestor's Tale) about the Alu sequence, and went on to read about transposons generally. Having as I do a rather broad definition of life, I concluded that Alu (and others like it) are lifeforms in their own right, although parasitic ones. I found the potential ethical implications somewhat staggering, especially given the need to shut up and multiply those implications by the rather large number of transposon instances in a typical multicellular organism.
I have written out my thoughts on the subject, at http://jttlov.no-ip.org/writings/alulife.htm. I don't claim to have a well-worked out position, just a series of ideas and questions I feel to be worthy of discussion.
ETA: I have started editing the article based on the discussion below. For reference with the existing discussion, I have preserved a copy of the original article as well, linked from the current version.
The Apparent Reality of Physics
Follow-up to: Syntacticism
I wrote:
The only objects that are real (in a Platonic sense) are formal systems (or rather, syntaxes). That is to say, my ontology is the set of formal systems. (This is not incompatible with the apparent reality of a physical universe).
In my experience, most people default1 to naïve physical realism: the belief that "matter and energy and stuff exist, and they follow the laws of physics". This view has two problems: how do you know stuff exists, and what makes it follow those laws?
To the first - one might point at a rock, and say "Look at that rock; see how it exists at me." But then we are relying on sensory experience; suppose the simulation hypothesis were true, then that sensory experience would be unchanged, but the rock wouldn't really exist, would it? Suppose instead that we are being simulated twice, on two different computers. Does the rock exist twice as much? Suppose that there are actually two copies of the Universe, physically existing. Is there any way this could in principle be distinguished from the case where only one copy exists? No; a manifest physical reality is observationally equivalent to N manifest physical realities, as well as to a single simulation or indeed N simulations. (This remains true if we set N=0.)
So a true description requires that the idea of instantiation should drop out of the model; we need to think in a way that treats all the above cases as identical, that justifiably puts them all in the same bucket. This we can do if we claim that that-which-exists is precisely the mathematical structure defining the physical laws and the index of our particular initial conditions (in a non-relativistic quantum universe that would be the Schrödinger equation and some particular wavefunction). Doing so then solves not only the first problem of naïve physical realism, but the second also, since trivially solutions to those laws must follow those laws.
But then why should we privilege our particular set of physical laws, when that too is just a source of indexical uncertainty? So we conclude that all possible mathematical structures have Platonic existence; there is no little XML tag attached to the mathematics of our own universe that states "this one exists, is physically manifest, is instantiated", and in this view of things such a tag is obviously superfluous; instantiation has dropped out of our model.
When an agent in universe-defined-by-structure-A simulates, or models, or thinks-about, universe-defined-by-structure-B, they do not 'cause universe B to come into existence'; there is no refcount attached to each structure, to tell the Grand Multiversal Garbage Collection Routine whether that structure is still needed. An agent in A simulating B is not a causal relation from A to B; instead it is a causal relation from B to A! B defines the fact-of-the-matter as to what the result of B's laws is, and the agent in A will (barring cosmic rays flipping bits) get the result defined by B.2
So we are left with a Platonically existing multiverse of mathematical structures and solutions thereto, which can contain conscious agents to whom there will be every appearance of a manifest instantiated physical reality, yet no such physical reality exists. In the terminology of Max Tegmark (The Mathematical Universe) this position is the acceptance of the MUH but the rejection of the ERH (although the Mathematical Universe is an external reality, it's not an external physical reality).
Reducing all of applied mathematics and theoretical physics to a syntactic formal system is left as an exercise for the reader.
1That is, when people who haven't thought about such things before do so for the first time, this is usually the first idea that suggests itself.
2I haven't yet worked out what happens if a closed loop forms, but I think we can pull the same trick that turns formalism into syntacticism; or possibly, consider the whole system as a single mathematical structure which may have several stable states (indexical uncertainty) or no stable states (which I think can be resolved by 'loop unfolding', a process similar to that which turns the complex plane into a Riemann surface - but now I'm getting beyond the size of digression that fits in a footnote; a mathematical theory of causal relations between structures needs at least its own post, and at most its own field, to be worked out properly).
Syntacticism
I've mentioned in comments a couple of times that I don't consider formal systems to talk about themselves, and that consequently Gödelian problems are irrelevant. So what am I actually on about?
It's generally accepted in mathematical logic that a formal system which embodies Peano Arithmetic (PA) is able to talk about itself, by means of Gödel numberings; statements and proofs within the system can be represented as positive integers, at which point "X is a valid proof in the system" becomes equivalent to an arithmetical statement about #X, the Gödel number representing X. This is then diagonalised to produce the Gödel sentence (roughly, g="There is no proof X such that the last line of X is g", and incompleteness follows. We can also do things like defining □ ("box") as the function from S to "There is a proof X in PA whose last line is S" (intuitively, □S says "S is provable in PA"). This then also lets us define the Löb sentence, and many other interesting things.
But how do we know that □S ⇔ there is a proof of S in PA? Only by applying some meta-theory. And how do we know that statements reached in the meta-theory of the form "thus-and-such is true of PA" are true of PA? Only by applying a meta-meta-theory. There is no a-priori justification for the claim that "A formal system is in principle capable of talking about other formal systems", which claim is used by the proof that PA can talk about itself. (If I remember correctly, to prove that □ does what we think it does, we have to appeal to second-order arithmetic; and how do we know second-order arithmetic applies to PA? Either by invoking third-order arithmetic to analyse second-order arithmetic, or by recourse to an informal system.)
Note also that the above is not a strange loop through the meta-level; we justify our claims about arithmeticn by appeal to arithmeticn+1, which is a separate thing; we never find ourselves back at arithmeticn.
Thus the claim that formal systems can talk about themselves involves ill-founded recursion, what is sometimes called a "skyhook". While it may be a theorem of second-order arithmetic that "the strengthened finite Ramsey theorem is unprovable in PA", one cannot conclude from second-order arithmetic alone that the "PA" in that statement refers to PA. It is however provable in third-order arithmetic that "What second-order arithmetic calls "PA" is PA", but that hasn't gained us much - it only tells us that second- and third-order arithmetic call the same thing "PA", it doesn't tell us whether this "PA" is PA. Induct on the arithmetic hierarchy to reach the obvious conclusion. (Though note that none of this prevents the Paris-Harrington Theorem from being a theorem of n-th order arithmetic ∀n≥2)
What, then, is the motivation for the above? Well, it is a basic principle of my philosophy that the only objects that are real (in a Platonic sense) are formal systems (or rather, syntaxes). That is to say, my ontology is the setclass of formal systems. (This is not incompatible with the apparent reality of a physical universe; if this isn't obvious, I'll explain why in another post.) But if we allow these systems to have semantics, that is, we claim that there is such a thing as a "true statement", we start to have problems with completeness and consistency (namely, that we can't achieve the one and we can't prove the other, assuming PA). Tarski's undefinability theorem protects us from having to deal with systems which talk about truth in themselves (because they are necessarily inconsistent, assuming some basic properties), but if systems can talk about each other, and if systems can talk about provability within themselves (that is, if analogues to the □ function can be constructed), then nasty Gödelian things end up happening (most of which are, to a Platonist mathematician, deeply unsatisfying).
So instead we restrict the ontology to syntactic systems devoid of any semantics; the statement ""Foo" is true" is meaningless. There is a fact-of-the-matter as to whether a given statement can be reached in a given formal system, but that fact-of-the-matter cannot be meaningfully talked about in any formal system. This is a remarkably bare ontology (some consider it excessively so), but is at no risk from contradiction, inconsistency or paradox. For, what is "P∧¬P" but another, syntactic, sentence? Of course, applying a system which proves "P∧¬P" to the 'real world' is likely to be problematic, but the paradox or the inconsistency lies in the application of the system, and does not inhere in the system itself.
EDIT: I am actually aiming to get somewhere with this, it's not just for its own sake (although the ontological and epistemological status of mathematics is worth caring about for its own sake). In particular I want to set up a framework that lets me talk about Eliezer's "infinite set atheism", because I think he's asking a wrong question.
Followed up by: The Apparent Reality of Physics
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d)