tonysr comments on How An Algorithm Feels From Inside

Comment author: Desrtopa 13 February 2013 06:42:12AM 7 points [-]

Existence exists; Only existence exists. We exist with a consciousness: Existence is identity: Identification is consciousness.

This seems like a tremendously unhelpful attempt at definition, and it doesn't really get better from there. It seems as if it's written more to optimize for sounding Deep than for making any concepts understandable to people who don't already grasp them.

The only solution is copious dialog, to confirm that what was intended is that which was understood.

The necessary amounts of dialogue are a great deal less copious if one does a good job being clear in the first place.

Comment author: shminux 13 February 2013 07:17:49AM 0 points [-]

One thing I learned is to never argue with a Randian.

Comment author: elriel 08 April 2015 06:11:29PM 0 points [-]

This seems like a tremendously unhelpful attempt at definition, and it doesn't really get better from there. It >seems as if it's written more to optimize for sounding Deep than for making any concepts understandable to >people who don't already grasp them.

There probably isn't any one single way of defining this in a way that is understandable by everyone. That being said, being able to make the distinction between direct experience and concepts is very useful and epistemology has helped many people with this, so I'd say there is value in it.

Comment author: Endovior 13 February 2013 07:09:26AM 1 point [-]

As a former Objectivist, I understand the point being made.

That said, I no longer agree... I now believe that Ayn Rand made an axiom-level mistake. Existence is not Identity. To assume that Existence is Identity is to assume that all things have concrete properties, which exist and can therefore be discovered. This is demonstrably false; at the fundamental level of reality, there is Uncertainty. Quantum-level effects inherent in existence preclude the possibility of absolute knowledge of all things; there are parts of reality which are actually unknowable.

Moreover, we as humans do not have absolute knowledge of things. Our knowledge is limited, as is the information we're able to gather about reality. We don't have the ability to gather all relevant information to be certain of anything, nor the luxury to postpone decision-making while we gather that information. We need to make decisions sooner then that, and we need to make them in the face of the knowledge that our knowledge will always be imperfect.

Accordingly, I find that a better axiom would be "Existence is Probability". I'm not a good enough philosopher to fully extrapolate the consequences of that... but I do think if Ayn Rand had started with a root-level acknowledgement of fallibility, it would've helped to avoid a lot of the problems she wound up falling into later on.

Also, welcome, new person!

Comment author: RobbBB 27 April 2013 09:01:33PM * 2 points [-]

Existence is frequently defined in terms of identity. 'exists(a)' ≝ '∃x(a=x)'

To assume that Existence is Identity is to assume that all things have concrete properties, which exist and can therefore be discovered. This is demonstrably false; at the fundamental level of reality, there is Uncertainty.

Only if you're an Objective Collapse theorist of some stripe. If you accept anything in the vicinity of Many Worlds or Hidden Variables, then nature is not ultimately so anthropocentric; all of its properties are determinate, though those properties may not be exactly what you expect from everyday life.

Quantum-level effects inherent in existence preclude the possibility of absolute knowledge of all things; there are parts of reality which are actually unknowable.

If "there are" such parts, then they exist. The mistake here is not to associate existence with identity, but to associate existence or identity with discoverability; lots of things are real and out there and objective but are physically impossible for us to interact with. You're succumbing to a bit of Rand's wordplay: She leaps back and forth between the words 'identity' and 'identification', as though these were closely related concepts. That's what allows her to associate existence with consciousness -- through mere wordplay.

Accordingly, I find that a better axiom would be "Existence is Probability".

But that axiom isn't true. I like my axioms to be true. Probability is in the head, unlike existent things like teacups and cacti.

Comment author: Kawoomba 27 April 2013 09:38:07PM 1 point [-]

Existence is frequently defined in terms of identity. 'exists(a)' ≝ '∃x(a=x)'

Isn't that just kicking the can down the road? What does it mean for an x to ∃, "there is an x such that ...", there we go with the "is", with the "be" with the "exist".

Comment author: [deleted] 27 April 2013 10:09:25PM 0 points [-]

I should probably let Rob answer for himself, but he did say that existence is frequently defined in terms of identity, not by identity.

Comment author: RobbBB 28 April 2013 02:53:08AM * 0 points [-]

I'm not saying it's a very useful definition, just noting that it's very standard. If we're going to reject something it should be because we thought about it for a while and it still seemed wrong (and, ideally, we could understand why others think otherwise). We shouldn't just reject it because it sounds weird and a Paradigmatically Wrong Writer is associated with it.

I agree with you that there's something circular about this definition, if it's meant to be explanatory. (Is it?) But I'm not sure that circularity is quite that easy to demonstrate. ∃ could be defined in terms of ∀, for instance, or in terms of set membership. Then we get:

'exists(a)' ≝ '¬∀x¬(a=x)'

or

'exists(a)' ≝ 'a∈EXT(=)'

You could object that ∈ is similarly question-begging because it can be spoken as 'is an element of', but here we're dealing we're dealing with a more predicational 'is', one we could easily replace with a verb.

Comment author: Kawoomba 28 April 2013 06:38:22AM * -1 points [-]

If a definition is not meant to be explanatory, its usefulness in understanding that which is to be defined is limited.

Taking the two alternate formulations you offered, I can still hear the telltale "is" beating, from beneath the floor planks where you hid it:

'exists(a)' ≝ '¬∀x¬(a=x)'

The "∀" doesn't refer to all e.g. logically constructible x, does it? Or to all computable x. For the definition to make sense, it needs to refer to all x that exist, otherwise we'd conclude that 'exists(flying unicorns)' is true. Still implicitly refers to that which is to be defined in its definition, rendering it circular.

'exists(a)' ≝ 'a∈EXT(=)'

What is EXT(=)? Some set of all existing things? If so, would that definition do any work for us? Pointing at my chair and asking "does this chair exist", you'd say "well, if it's a member of the set of all existing things, it exists". Why, because all things in the set share the "exist" predicate. But what does it mean for them to have the "exist" predicate in the first place? To be part of the set of all existing things, of course. Round and round ...

Not much different from saying "if it exists, it exists". Well, yes. Now what?

Comment author: shminux 28 April 2013 06:49:47AM -1 points [-]

I've had this circular discussion with RobbBB for a couple of hours. Maybe you will have better luck.

Comment author: RobbBB 28 April 2013 10:18:48AM * 0 points [-]

If a definition is not meant to be explanatory, its usefulness in understanding that which is to be defined is limited.

Exactly.

The "∀" doesn't refer to all e.g. logically constructible x, does it? Or to all computable x. For the definition to make sense, it needs to refer to all x that exist, otherwise we'd conclude that 'exists(flying unicorns)' is true. Still implicitly refers to that which is to be defined in its definition, rendering it circular.

That's one option for explaining the domain of ∀. Another is to simply say that that the domain is the universe, or that it's everything, or that it's unrestricted. All of those can be expressed without speaking in terms of existence.

If you have no idea what those ideas mean, but understand 'exists', then, sure, maybe you'll need to demand that all those ideas be unpacked in terms of existence. But what of it? If you do understand those terms but not 'exists', then interdefining them can be cognitively significant for you. Broadly speaking, the function of a definition is to relate a term that isn't understood to a term that is. If you already understand both terms, then the definition won't be useful to you; but that isn't a criticism of the definition, if other people might not understand both terms as well as you do. It's just a biographical note about your own level of linguistic/conceptual expertise.

What is EXT(=)? Some set of all existing things?

It's the extension of the identity predicate, a set of ordered pairs. Relational predicates of arity n can be treated as sets of n-tuples.

If so, would that definition do any work for us?

Do any work for who? What is it you want, exactly? If you've forgotten, the first thing I said to you was "I'm not saying it's a very useful definition". You don't need to prove it's circular in order to prove it's useless, and if you did prove it's circular ('circular' in what sense? is there any finite non-circular chain of definitions that define every term?) that very likely wouldn't help demonstrate its uselessness. So what exactly are you trying to establish, and why?

Comment author: Kawoomba 28 April 2013 11:12:52AM -2 points [-]

Another is to simply say that that the domain is the universe, or that it's everything, or that it's unrestricted. All of those can be expressed without speaking in terms of existence.

Any domain which is not constrained to iterate/refer only to things which themselves exist would lead to wrong conclusions such as "flying unicorns exist".

What is it you want, exactly?

To show that the definition you referred to, in all its variants, isn't useful. I did not forget that you didn't claim it was useful, just that it was common, but I also noticed you did not explicitly agree that it was not useful. If you do agree on that, there is no need to further dwell on useless rephrasings.

I agree that since the body of human knowledge is limited, any definition must eventually contain circles of some size. However, not all circles are created equal: To be useful, a definition must refer to some different part of your knowledge base, just because without introducing new information, there is nothing which could be useful.

"2 is defined as something with the property of being 2" isn't useful because there is nothing new introduced. "That which exists, exists" isn't useful for the same reason. Because all the definitions you referred to still contain "exist", the additional information ("things in a set") is superfluously added, the "exist" on the right part of the definition still isn't unpacked. Hence, no additional information is introduced, and the definition useless, being equivalent to "2 is defined as 2".

"Pain is when something which is in the set of 'being able to experience pain' experiences pain" just reduces to "pain is when pain", which must be useless since it contains no additional concepts.

If the additional "identity" aspects etcetera helped any in explaining the concept of "exist", then the definition would not need to refer again to just the same "exist" which the "identity" supposedly helped explain.

Comment author: RobbBB 28 April 2013 11:41:45AM * 0 points [-]

Any domain which is not constrained to iterate/refer only to things which themselves exist would lead to wrong conclusions such as "flying unicorns exist".

If I'm not misunderstanding you, you're advocating a view like Graham Priest does here, that our quantifiers should range over anything we can meaningfully talk about (if not wider?) until we restrict them further. I'm inclined to agree. We both dissent from the orthodox definition I posted above, then. You'll need to dig up a Quinean if you want to hear counter-arguments.

I also noticed you did not explicitly agree that it was not useful.

Well, I'm sure it's been useful to someone at some point. It lets logicians get away without appealing to an 'exists' predicate. Logicians are generally much more attached to 'is identical to' than to 'exists'. Again, you'll have to explain exactly what kind of use you want out of the ideal Definition of Existence so I can evaluate whether the above ones I tossed about are useful with respect to that goal. What are some examples of new insights or practical goals you were hoping or expecting to achieve by defining 'exists'?

To be useful, a definition must refer to some different part of your knowledge base

Could you say more about what you mean by 'different parts of your knowledge base'? Is there a heuristic for deciding when things are parts of the same knowledge base?

"2 is defined as something with the property of being 2" isn't useful because there is nothing new introduced.

Is "2 is defined as SS∅" useful? Or "2 is defined as {{},{{}}}"? Or "2 is defined as 1+1"? Are there any useful definitions of 2?

Because all the definitions you referred to still contain "exist"

What do you mean by "contain"? They didn't make reference to existence twice. You noted we could reverse the definitions or build a chain, but that's true of any definitions. (If they weren't dreadfully boring, we'd probably not call them definitions.)

Do you mean that they presupposed an understanding of existence, i.e., if you didn't first understand existence then you couldn't understand my definitions? Or do you mean that concepts are combinatorial, and the concepts I appealed to all have as components the concept 'existence'?

"Pain is when something which is in the set of 'being able to experience pain' experiences pain" just reduces to "pain is when pain", which must be useless since it contains no additional concepts.

Your definitions are circular in the strong sense that they're of the form '... a ... = ... a ...'. But interesting and useful identities and equalities can re-use the term on both sides. Generally they then reduce to predications. For instance, "pain occurs when something experiences pain" is a pretty hideous attempt at a definition, but it doesn't reduce to "pain is when pain" (which isn't even a sentence); it reduces to "pain is an experience". That's potentially useful, but it would've been more useful if we hadn't dressed it up as though it were an analysis.

All of this seems a bit beside the point, though. None of the definitions I cited re-used the same term, whereas all the examples you made up to criticize them do re-use the same term on both sides of the definition. If your goal is to draw an analogy that problematizes certain practices in mathematical logic, you should include at least some problem cases that look like the formulas I first posted.

continue this thread »

Comment author: nshepperd 28 April 2013 03:32:30PM * 2 points [-]

I suspect the above definitions look meaningful to those who have studied philosophy and mathematical logic because they have internalised the mathematical machinery behind '∃'. But a proper definition wouldn't simply refer you to another symbol. Rather, you would describe the mathematics involved directly.

For example, you can define an operator that takes a possible world and a predicate, and tells you if there's anything matching that predicate in the world, in the obvious way. In Newtonian possible worlds, the first argument would presumably be a set of particles and their positions, or something along those lines.

This would be the logical existence operator, '∃'. But, it's not so useful since we don't normally talk about existence in rigorously defined possible worlds, we just say something exists or it doesn't — in the real world. So we invent plain "exists", which doesn't take a second argument, but tells you whether there's anything that matches "in reality". Which doesn't really mean anything apart from:

$P(\text{exists}(Q)) = \sum_{w \in \text{models}} (1 \text{ if } \exists_w Q \text{ else } 0) P(w)$

or in a more suggestive format

$P(\text{exists}(Q)) = \sum_{w \in \text{models}} P(\text{exists}(Q) ~|~ w) P(w)$

Where P(w) is your probability distribution over possible worlds, which is itself in turn connected to your past observations, etc.

Anyway, the point is that the above is how "existence" is actually used (things become more likely to exist when you receive evidence more likely to be observed in worlds containing those things). So "existence" is simply a proposition/function of a predicate whose probability marginalises like that over your distribution over possible worlds, and never mind trying to define exactly when it's true or false, since you don't need to. Or something like that.

Comment author: shminux 28 April 2013 03:10:55AM 1 point [-]

RobbBB, in my experience, tends to give pseudo-precise answers like that. It seems like a domain confusion. You are asking about observable reality, he talks about mathematical definitions.

Comment author: [deleted] 28 April 2013 04:34:34AM 4 points [-]

I'm not a frequent poster here, and I don't expect my recommendations carry much weight. But I have been reading this site for a few years, and offline I deal with LWish topics and discussions pretty regularly, especially with the more philosophical stuff.

All that said, I think RobbBB is one of the best posters LW has. Like top 10. He stands out for clarity, seriousness, and charity.

Also, I think you shouldn't do that thing where you undermine some other poster while avoiding directly addressing them or their argument.

Comment author: shminux 28 April 2013 04:57:50AM * 0 points [-]

All that said, I think RobbBB is one of the best posters LW has. Like top 10. He stands out for clarity, seriousness, and charity.

It certainly has not been my impression. I found my discussion with him about instrumentalism, here and on IRC, extremely unproductive. Seems like a pattern with other philosophical types here. Maybe they don't teach philosophers to listen, I don't know. For comparison, TheOtherDave manages to carry a thoughtful, polite and insightful discussion even when he disagrees. More regulars here could learn rational discourse from him.

Or maybe I'm falling prey to the Bright Dilettante trap and the experts in the subject matter just don't have the patience to explain things in a friendly and understandable fashion. I'm not sure how to tell.

Also, I think you shouldn't do that thing where you undermine some other poster while avoiding directly addressing them or their argument.

I take back the "pseudo-" part. His answers were precise, but from a wrong domain.

Comment author: wedrifid 28 April 2013 08:26:54AM 3 points [-]

Seems like a pattern with other philosophical types here. Maybe they don't teach philosophers to listen, I don't know. For comparison, TheOtherDave manages to carry a thoughtful, polite and insightful discussion even when he disagrees. More regulars here could learn rational discourse from him.

Agree on both counts. I'll second your advocacy of a TheOtherDave as a posting style role model. In particular he conveys the impression that he is far better than the average lesswrong participant at understanding what people are saying to him. (Rather than the all to common practice of pattern matching a few keywords to the nearest possible stupid thing that can be refuted.)

Comment author: [deleted] 28 April 2013 06:31:03PM 1 point [-]

Maybe they don't teach philosophers to listen, I don't know.

I can tell you from experience that 'they' don't. Do you know who does teach this?

Comment author: shminux 28 April 2013 07:36:59PM 1 point [-]

I don't know. Certainly there is some emphasis on charitable reading and steelmanning on this forum, but the results are mixed. Maybe it's taught in psychology, nursing and other areas which require empathy.

continue this thread »

Comment author: RobbBB 28 April 2013 10:35:18AM * 1 point [-]

I'm a little unclear on what your criticism is. Is one of these right?

You're being too precise, whereas I wanted to have an informal discussion in terms of our everyday intuitions. So definitions are counterproductive; a little unclarity in what we mean is actually helpful for this topic.
There are two kinds of existence, one that holds for Plato's Realm Of Invisible Mathy Things and one that holds for The Physical World. Your definitions may be true of the Mathy Things, but they aren't true of things like apples and bumblebees. So you're committing a category error.
I wanted you to give me a really rich, interesting explanation of what 'existence' is, in more fundamental terms. But instead you just copy-pasted a bland uninformative Standard Mathematical Logician Answer from some old textbook. That makes me sad. Please be more interesting next time.

If your point was 1, I'll want to hear more. If it was 3, then my apologies! If it was 2, then I'll have to disagree until I hear some argument as to why I should believe in these invisible eternal number-like things that exist in their own unique number-like-thing-specific way. (And what it would mean to believe in them!)

Comment author: itaibn0 28 April 2013 01:37:35PM * 0 points [-]

How about this: Mathematicians have a conception of existence which is good enough for doing mathematics, but isn't necessary correct. When you give a mathematical definition of existence, you are implicitly assuming a certain mathematical framework without justifying it. I think you would consider this criticism to be a variant of #2.

In particular, I also think about things mathematically, but when I do so, I don't use first-order logic, but rather intuitionistic type theory. Can you give a definition for existence which would satisfy me?

Comment author: RobbBB 29 April 2013 12:54:40AM 0 points [-]

I'm a mathematical fictionalist, so I'm happy to grant that there's a good sense in which mathematical discourse isn't strictly true, and doesn't need to be.

Are you asking for a definition of an intuitionistic 'exists' predicate, or for the intuitionistic existential quantifier?

Comment author: itaibn0 29 April 2013 11:16:59AM 0 points [-]

(Note: I added a link in my previous comment)

First, if you accept that mathematical constructs are fictional, why do you consider it valid to define a concept in terms of them? Second, I admit I wasn't clear on this issue: The salient part of intuitionistic type theory isn't intuitionism, but rather that it is a structural theory. This means that statements of the form "exists x, P(x)" are not well defined, but rather only statements of the form "exists x in A, P(x)" can be made.

Comment author: shminux 28 April 2013 08:39:45PM * 1 point [-]

Thank you, this framework helps. Definitely no to 1. Definitely yes to 2, with some corrections. Yes to some parts of 3.

Re 2. First, let me adopt bounded realism here, with physics (external reality or territory) + logic (human models of reality, or maps). Let me ignore the ultraviolet divergence of decompartmentalization (hence "bounded"), where Many Words, Tegmark IV and modal realism are considered "territory". To this end, let me put the UV cutoff on logic at the Popper's boundary: only experimentally falsifiable maps are worth considering. A map is "true" means that it is an accurate representation of the piece of territory it is intended to represent. I apologize in advance if I am inventing new terms for the standard philosophical concepts -- feel free to point me to the standard terminology.

Again, "accurate map", a.k.a. "true map" is a map that has been tested against the territory and found reliable enough to use as a guide for further travels, at least if one does not stray too far. Correspondingly, a piece of territory is said to "exist" if it is described by an accurate map.

On the other hand, your "invisible mathy things" live in the world of maps. Some of them use the same term "true", but in a different way: given a set of rules of how to form strings of symbols, true statements are well-formed finite strings. They also use the same term "exist", but also in a different way: given a set of rules, every well-formed string is said to "exist".

Now, I am not a mathematician, so this may not be entirely accurate, but the gist is that conflating "exist" as applied to the territory and "exist" as applied to maps is indeed a category error. When someone talks about existence of physical objects and you write out something containing the existential quantifier, you are talking about a different category: not reality, but a subset of maps related to mathematical logic.

I am not sure whether this answers your objection that

why I should believe in these invisible eternal number-like things that exist in their own unique number-like-thing-specific way. (And what it would mean to believe in them!)

but I hope it makes it clear why I find your replies unconvincing and generally not useful.

Comment author: RobbBB 29 April 2013 12:28:43AM * 0 points [-]

You've redefined 'x exists' to mean 'x is described by a map that has been tested and so far has seemed reliable to us', and 'x is true' correspondingly. One problem with this is that it's historical: It commits us to saying 'Newtonian physics used to be true, but these days it's false (i.e., not completely reliable as a general theory)', and to saying 'Phlogiston used to exist, but then it stopped existing because someone overturned phlogiston theory'. This is pretty strange.

Another problem is that it's not clear what it takes to be 'found reliable enough to use as a guide for further travels'. Surely there's an important sense in which math is reliable in that sense, hence 'true' in the territory-ish sense you outlined above, not just in the map-ish sense. So perhaps we'll need a more precise definition of territory-ish truth in order to clearly demonstrate why math isn't in the territory, where the territory is defined by empirical adequacy.

I think your view, or one very close to yours, is actually a lot stronger (can be more easily defended, has broader implications) than your argument for it suggests. You can simply note that things like Abstract Numbers, being causally inert, couldn't be responsible for the 'unreasonable efficacy of mathematics'; so that efficacy can't count as evidence for such Numbers. And nothing else is evidence for Numbers either. So we should conclude, on grounds of parsimony (perhaps fortified with anti-Tegmark's-MUH arguments), that there are unlikely to be such Numbers. At that point, we can make the pragmatic, merely linguistic decision of saying that mathematicians are using 'exists' in a looser, more figurative sense.

Perhaps a few mathematicians are deluded into thinking that 'exists' means exactly the same thing in both contexts, but it is more charitable to interpret mathematics in general in the less ontologically committing way, because on the above arguments a platonistic mathematics would be little more than speculative theology. Basically, we end up with a formalist or fictionalist description of math, which I think is very plausible.

You see, we aren't so different, you and I. Not once we bracket whether unexperienced cucumbers exist out there, anyway!

Comment author: shminux 29 April 2013 03:55:16AM 0 points [-]

You've redefined 'x exists' to mean 'x is described by a map that has been tested and so far has seemed reliable to us', and 'x is true' correspondingly.

I disagree that this is a redefinition. You believe that elephants exists because you can go and see them, or talk to someone you trust who saw them, etc. You believe that live T-Rex (almost surely) does not exist because it went extinct some 60 odd million years ago. Both beliefs can be updated based on new information.

'Newtonian physics used to be true, but these days it's false

That's not at all what I am saying. Consider resisting your tendency to strawman. Newtonian physics is still true in its domain of applicability, it has never been true where it's not been applicable, though people didn't know this until 1905.

'Phlogiston used to exist, but then it stopped existing because someone overturned phlogiston theory'

Again, a belief at the time was that it existed, a more accurate belief (map) superseded the old one and now we know that phlogiston never existed. Maps thought of as being reliable can be found wanting all the time, so the territory they describe is no longer believed to exist, not stopped existing. This is pretty uncontroversial, I would think. Science didn't kill gnomes and fairies, and such. At least this is the experiment-bounded realist position, as far as I understand it.

You can simply note that things like Abstract Numbers, being causally inert, couldn't be responsible for the 'unreasonable efficacy of mathematics'; so that efficacy can't count as evidence for such Numbers.

I can't even parse that, sorry. Numbers don't physically exist because they are ideas, and as such belong in the realm of logic, not physics. (Again, I'm wearing a realist hat here.) I don't think parsimony is required here. It's a postulate, not a conclusion.

Perhaps a few mathematicians are deluded into thinking that 'exists' means exactly the same thing in both contexts, but it is more charitable to interpret mathematics in general in the less ontologically committing way

Then I don't understand why you reply to questions of physical existence with some mathematical expressions...

You see, we aren't so different, you and I. Not once we bracket whether unexperienced cucumbers exist out there, anyway!

I'm not nearly as optimistic.

continue this thread »

Comment author: MugaSofer comment score below threshold [+] (0 children)

Comment author: shminux 13 February 2013 07:19:49AM 2 points [-]

Required reading.

Comment author: Qiaochu_Yuan 13 February 2013 07:32:02AM * 4 points [-]

How much of the Sequences have you read? In particular, have you read 37 Ways That Words Can Be Wrong?

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