I go 1 at 60, 2 at 30, etc.

Name the first number that I fail to count

Third time I'm asking you the question.

This is a standard inductive argument. If it's impossible to name the first natural number at which a property fails to hold, the property must hold for all natural numbers.

Please give this argument some thought. — fishfry

It begs the question. Your premise is necessarily false. Such a supertask is impossible, even in principle, to start.

In your opinion. But you have no proof or evidence. On the contrary, the mathematics is clear. — fishfry

You just listed five rational numbers and are claiming that this is proof of you reciting all the natural numbers in descending order? You're talking nonsense.

But counting backward from infinity is always finite! I showed you how that works, counting backward from 1 in the ordered set <1/2, 3/4, 7/8, ..., 1> — fishfry

What number do you recite after 1?

Did I not move you, surprise you, convince you, that if you count 1, 2, 3, ... successively halving the time intervals, that you will indeed count every single natural number in finite time? If not, why not? — fishfry

Because it begs the question.

But counting backward from infinity is always finite! I showed you how that works, counting backward from 1 in the ordered set <1/2, 3/4, 7/8, ..., 1> — fishfry

What number do you recite after 1?

It's easy, I'll do it right here on a public Internet forum.

1, 15/16, 7/8, 3/4, 1/2. Done.

That's because the first step backward from any limit ordinal necessarily jumps over all but finitely members of the sequence whose limit it is. — fishfry

That's not counting down from infinity. That's just reciting five rational numbers.

I don't know what you mean that supertasks are nonterminating by definition. — fishfry

Tasks are performed ad infinitum. I never stop counting. There's always another number to count.

You did lose me when you said that counting 0, 1, 2, ... is "counting down from infinity." I did not understand that example when you gave it earlier. Mathematically, the ordered set <1, 2, 3, ...> exists, all at once. Its counting is completed the moment it's invoked into existence by the axiom of infinity. — fishfry

I'm talking about reciting the numbers. So imagine someone reciting the natural numbers up to infinity. Now imagine that process in reverse. That's what I mean by someone counting down from infinity.

It is a non sequitur to argue that because we can sum an infinite series with terms that match the proposed time intervals that it is possible to have counted down from infinity. It is impossible, even in principle, to start such a count. The maths of an infinite series doesn't change this.

And it is a non sequitur to argue that because we can sum an infinite series with terms that match the proposed time intervals that it is possible to have counted up to infinity. It is impossible, even in principle, to stop such a count. The maths of an infinite series doesn't change this.

Well ok, then why don't I complete a supertask when I walk across the room, first going halfway, etc.? Can you distinguish this case from your definition? — fishfry

If supertasks are impossible and motion is possible then motion isn't a supertask.

* You have not convinced me or even made me understand your reasoning that supertasks are "metaphysically impossible" or that they entail a logical contradiction. — fishfry

By definition supertasks are non-terminating processes, therefore you've gone wrong somewhere if you conclude that they can terminate after 2N seconds.

Also I think the clearest example I gave was that of having counted down from infinity. We can assert (explaining what happened in reverse) that I recited 0 after 60 seconds, recited 1 after 30 seconds, recited 2 after 15 seconds, recited 3 after 7.5 seconds, etc., and we can say that we can sum an infinite series with terms that match the described (and implied) time intervals, but it doesn't then follow that we can have counted down from infinity; we can't even start such a count. The mathematics is evidently a non sequitur, and so it's a non sequitur in the case of having counted up to infinity as well (and so for any proposed supertask).

In the case of Thomson's lamp, nothing ever happens to the lamp except as described by this process: I turn it on after 30 seconds, turn if off after 15 seconds, turn it on after 7.5 seconds, etc. It cannot be on after 60 seconds because I always turn it off after turning it on and it cannot be off after 60 seconds because I always turn it on after turning it off, but it must be either on or off after 60 seconds, and so therefore there is a contradiction.

If you want to say that such a supertask is possible then the burden is on you to explain the state of the lamp after 60 seconds, and your answer must follow from the description of the supertask. If nothing follows then the supertask is impossible.

He does. Most of the paper focuses on rationalizing low probabilities for the first two premises to the point of 3 being likely. — noAxioms

What paper are you reading? From the conclusion to Are You Living in a Computer Simulation?:

A technologically mature “posthuman” civilization would have enormous computing power. Based on this empirical fact, the simulation argument shows that at least one of the following propositions is true: (1) The fraction of human‐level civilizations that reach a posthuman stage is very close to zero; (2) The fraction of posthuman civilizations that are interested in running ancestor‐simulations is very close to zero; (3) The fraction of all people with our kind of experiences that are living in a simulation is very close to one.

If (1) is true, then we will almost certainly go extinct before reaching posthumanity. If (2) is true, then there must be a strong convergence among the courses of advanced civilizations so that virtually none contains any relatively wealthy individuals who desire to run ancestor‐simulations and are free to do so. If (3) is true, then we almost certainly live in a simulation. In the dark forest of our current ignorance, it seems sensible to apportion one’s credence roughly evenly between (1), (2), and (3).

Point is, you are misstating Bostrom's premises. Item 3 doesn't follow from the premises as you word them. — noAxioms

They are not premises. (3) isn't intended to follow from (1) and (2).

Could you give me an example of two incompatible mathematical systems? — Tarskian

There is a universal set in New Foundations but not in ZFC.

The surreal number line, unlike the real number line, includes infinity and infinitesimals.

There are many different, incompatible, mathematical systems. Assuming Platonism, which mathematical system is "correct", and how is this determined?

But I couldn't see why Bostrom thought that one of those three must be true. — Ludwig V

If lots of civilisations are capable of and willing to make simulations then they will, and so simulated persons will greatly outnumber non-simulated persons.

Therefore, if simulated persons do not greatly outnumber non-simulated persons then most civilisations are either incapable of or unwilling to make simulations.

I find both these to be highly unlikely, for the reason stated in this topic and mine. Bostrom of course has motivation to rationalize a higher probability for both of these, but rationalizing is not being rational. — noAxioms

I'm confused by what you're saying.

Bostrom is saying that one of these is almost certainly true:

1. Almost every intelligent civilisation is incapable of creating simulations
2. Almost every intelligent civilisation doesn't want to create simulations
3. Almost every conscious person is living in a simulation

Because if lots of civilisations are capable of and willing to make simulations then they will, and so simulated persons will greatly outnumber non-simulated persons.

Therefore, if simulated persons do not greatly outnumber non-simulated persons then most civilisations are either incapable of or unwilling to make simulations.

He doesn't say which of the three is most likely to be true.

Artificial consciousnesses programmatically fed phenomenal experience, e.g. man-made brains-in-a-vat.

Well between the two of you I have no idea what a supertask is anymore. — fishfry

A supertask is "a countably infinite sequence of operations that occur sequentially within a finite interval of time."

Bostrom's Simulation Argument is that one of these is almost certainly true:

1. The fraction of human-level civilizations that reach a posthuman stage (that is, one capable of running high-fidelity ancestor simulations) is very close to zero, or
2. The fraction of posthuman civilizations that are interested in running simulations of their evolutionary history, or variations thereof, is very close to zero, or
3. The fraction of all people with our kind of experiences that are living in a simulation is very close to one.

He then argues that if (3) is true then we are almost certainly living in a simulation.

I'm only asking how far 1,1 is from 1,2 in a discrete space system. As far as I can tell, it's 0 units, right? — Hanover

I don't think the question makes sense, but you'll have to ask a physicist who knows more about quantum gravity to explain it. I can only point out to you that there are physical theories that take spacetime to be discrete.

The problem is adjacency. If object A is adjacent to object B on a finite grid, what is the distance from A to B? If it's 0 units, then A and B occupy the same space and A = B. — Hanover

You seem to be imagining a model of discrete space overlaying some model of continuous space and then pointing out that in continuous space there is always more space between two discrete points.

That seems to be begging the question.

Best I can do is point you to something like quantum spacetime and quantum gravity.

There are physical theories that treat spacetime as discrete. They are not supported to the extent that General Relativity is, but given that quantum mechanics and General Relativity are known to be incompatible, it would seem that at least one of them is false, and my money is on General Relativity being false.

Given the logical paradoxes that continuous space and time entail, I think that discrete spacetime is not just a physical fact but a necessity.

However, the thing measured is the passage of time which occurs. — Metaphysician Undercover

And the passage of time that we would measure as being 60 seconds occurs even when we don't measure it.

If it's at L-1 at T-1 and L-2 at T-2, how long did it take to get from L-1 to L-2? — Hanover

The question makes no sense. You're asking for some second "level" of time to define the time between T1 and T2. There's no such thing. The only time is T1, T2, T3, etc.

Assuming at the most microscopic level, the object is on an 8x8 chessboard. The pawn moves from e2 to e3. There is no e2.1 or other smaller increments in this finite world. At T1 it's at e2 and T30 it's at e3. The assumption is that at some point in time, it was no where while transitioning (moving?) from e2 to e3. — Hanover

We can't examine this at the macroscopic scale. At whatever the smallest scale is: at Time1 it's at Location1 and at Time2 it's at Location2. There's no intermediate Time1.5 where it doesn't exist or Location1.5 that it moves through.

And you're just making the same mistake again and falsely claiming that indirect realists believe that our eyes respond to light reflected by sense data. They don't. If you're going to continue to argue against this strawman then I'm out.

Acquaintance primarily concerns knowledge. — Luke

Yes, hence the epistemological problem of perception.

The direct/indirect realism dispute primarily concerns sensory perception — Luke

It concerns whether or not sensory perception provides us with direct knowledge of distal objects.

Naive realists claim that sensory perception does provide us with direct knowledge of distal objects because distal objects are literal constituents of conscious experience, and so we are acquainted with distal objects.

Indirect realists claim that sensory perception does not provide us with direct knowledge of distal objects because distal objects are not literal constituents of conscious experience, and so we are only acquainted with mental phenomena.

My usage is consistent. Indirect realists equivocate over the meaning of "perception", using it to mean both the sensory perception of external objects and the Russellian acquaintance of mental representations. — Luke

It's only equivocation if they start from the premise that we are acquainted with mental phenomena and then conclude that our eyes respond to light reflected by mental phenomena, but they never make this conclusion. This is the strawman conclusion that you are fabricating.

Except your explanation of what indirect realists believe is that our perceptions of material objects are not mediated by the perception of some other entity, which is therefore not indirect realism. — Luke

What indirect realists mean by "perception of some other entity" isn't what you mean by "perception of some other entity". You're equivocating.

Indirect realists do not and never have believed or claimed that our eyes respond to light reflected by sense data.

That our perceptions of material objects are mediated by the perception of some other entity, such as sense-data. — Luke

Except by this you mean "our eyes respond to light reflected by sense data" which isn't what indirect realists believe.

It's something I do not accept.

According to what I mean by it, it is that we have sensory perceptions of sense-data. but you have been telling me that that's not what you mean by it. — Luke

By "we do not perceive some other entity, such as sense-data" you mean "our eyes do not respond to light reflected by some other entity, such as sense-data".

Indirect realists agree with you that our eyes do not respond to light reflected by some other entity, such as sense-data.

So what is it that indirect realists believe that you do not?

As I've stated several times now, it is over part (2) of Fish's definition: — Luke

Except according to what you mean by "perceive some other entity, such as sense-data", (2) is something that indirect realists accept.

Otherwise, I don't know what indirect realists mean by indirect perception. — Luke

I have spent 70 pages explaining it.

I don't think there's much point in continuing since you refuse to acknowledge that my position is even possible: that one can reject naive realism without being an indirect realist. — Luke

As has been established, your position misunderstands indirect realism. You think that by "we perceive mental phenomena" the indirect realist means "our eyes respond to light reflected by mental phenomena". They don't.

So given that neither non-naive direct realism nor indirect realism believe that our eyes respond to light reflected by mental phenomena; given that both groups believe that some distal object reflects light, that this light stimulates the sense receptors in our eyes, that this then triggers activity in the visual cortex, and that distal objects and their properties are not literal constituents of the resulting conscious experience, where is it that non-naive direct realism and indirect realism diverge?

Some things can be dismissed on logical grounds, like the notion of continuous motion and the infinitely divisible half-way points an object in motion must then move through.

But one cannot use armchair philosophy to determine the smallest unit of space/time/movement.

Light is color. — creativesoul

No it's not. Light often causes us to see colours, but they are not the same thing, as evidenced by the obvious fact that I can see colours when I dream and my eyes are closed in a dark room.

Arguing for them both results in saying incompatible things when compared to one another. Have you been arguing for both throughout this thread, at different times arguing for one, and then the other later? — creativesoul

I have only been arguing that distal objects are not constituents of conscious experience given that conscious experience does not extend beyond the head. This is impartial to which of property dualism and eliminative materialism is correct.

How is Russellian acquaintance with mental representations of external objects an indirect perception? Russellian acquaintance is not a perception, so it cannot be an indirect perception of an external object. — Luke

This is where you're getting confused by grammar. The words "see" and "experience" and "perceive" and "aware" are all being used ambiguously and interchangeably.

Naive realists claim that distal objects and their properties are literal constituents of conscious experience and that as such we are acquainted with distal objects and their properties, and so our knowledge of them is direct and there is no epistemological problem of perception. The external world just is as it appears. They call this "direct perception of distal objects".

Indirect realists claim that distal objects and their properties are not literal constituents of conscious experience – that the constituents of conscious experience are something like sense data/qualia/mental representations – and so that we are not acquainted with distal objects and their properties – only this sense data/qualia/mental representations – and so our knowledge of them is indirect and there is an epistemological problem of perception. The external world might not be as it appears. They call this "indirect perception of distal objects".

That's all there is to it. You're misunderstanding indirect realism if you think it's saying something else, e.g. that our eyes respond to light reflected by mental phenomena and that our ears respond to sound emitted by mental phenomena.

Are you asking if I'm aware that eliminative materialism and property dualism are incompatible? Yes, I'm aware. I'm undecided between them, but my inclination favours property dualism although I'm open to eliminative materialism.

Either way, distal objects and their properties are not constituents of experience. Naive realism would seem to require some sort of substance dualism, as only that would seem to allow for experience to "literally extend beyond the subject's head, to encompass what the experience is of".

Have you abandoned the eliminative materialist approach in favor of a sense data theorist one? — creativesoul

As I've said before, I'm undecided between eliminative materialism and property dualism. If eliminative materialism is true then experience and its constituent properties (e.g. smells, tastes, colours) are reducible to physical phenomena like certain brain states. If property dualism is true then experience and its constituent properties are non-physical emergent phenomena.

Are those constituents of experience? — creativesoul

Yes.

Hence, we've arrived at incoherency/self-contradiction. — creativesoul

How so?

How much time elapses from travel to point a to point b and where is the object located during that time lapse?

Does the object leave existence between a and b and if it does, what maintains its identity during that interval? — Hanover

That’s a question for physicists to answer.

What is color again? — creativesoul

Qualia/sense-data/mental phenomena.

Yes, I think something along these lines is required when talking about perceiving something, especially since the main point of contention in this debate is whether our sensory perception of external objects is direct or indirect. — Luke

Indirect realists don't believe or claim that our eyes respond to light reflected by mental phenomena and that our ears respond to sound emitted by mental phenomena, so you clearly misunderstand indirect realism and are arguing against a strawman.

Who did that? Are they in the room with us right now? — fishfry

See here:

As Salmon (1998) has pointed out, much of the mystery of Zeno’s walk is dissolved given the modern definition of a limit. This provides a precise sense in which the following sum converges:

$\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \ldots$

Although it has infinitely many terms, this sum is a geometric series that converges to 1 in the standard topology of the real numbers. A discussion of the philosophy underpinning this fact can be found in Salmon (1998), and the mathematics of convergence in any real analysis textbook that deals with infinite series. From this perspective, Achilles actually does complete all of the supertask steps in the limit as the number of steps goes to infinity.

...

Suppose we switch off a lamp. After 1 minute we switch it on. After ½ a minute more we switch it off again, ¼ on, ⅛ off, and so on. Summing each of these times gives rise to an infinite geometric series that converges to 2 minutes, after which time the entire supertask has been completed.

I have been arguing that it is a non sequitur to argue that because the sum of an infinite series can be finite then supertasks are metaphysically possible. The lack of a final or a first task entails that supertasks are metaphysically impossible. I think this is obvious if we consider the supertask of having counted down from infinity, and this is true of having counted up to infinity as well.

We can also consider a regressive version of Thomson's lamp; the lamp was off after 2 minutes, on after 1 minute, off after 30 seconds, on after 15 seconds, etc. We can sum such an infinite series, but such a supertask is metaphysically impossible to even start.

Do you hold the view that we must perceive mental phenomena in order to perceive real objects? If so, then this is where our positions differ and we have more than a grammatical dispute, since it is not my position that we must perceive mental phenomena in order to perceive real objects. If not, then you are not an indirect realist. — Luke

What do you think "perceive mental phenomena" means? Do you think it means that my eyes respond to light reflected by mental phenomena? Do you think it means that my ears respond to sound emitted by mental phenomena?

I think you're reading something into the meaning of "perceive mental phenomena" that just isn't there. Indirect realists probably aren't saying what you think they're saying when they say that we perceive mental phenomena. Acquaintance with mental phenomena is the appropriate interpretation. This is how to interpret the meaning of "feel" in "I feel pain" and the meaning of "hear" in "the schizophrenic hears voice" and the meaning of "see" in "I see colours".

This sense of acquaintance with mental phenomena occurs also in veridical perception, and this is all that is meant when the indirect realist says that awareness of distal objects is mediated by awareness of mental phenomena. The former sense of "awareness" is the sense of intention and the latter sense of "awareness" is the sense of acquaintance. And it is for precisely this reason that, as argued in Semantic Direct Realism, the intentional theory of perception (a non-naive direct realism) is consistent with the sense datum theory of perception (an indirect realism).

But if we admit that time is infinitely divisible, counting to infinity doesn't seem to amount to a logical impossibility, and so we reverse the time of the task. — Lionino

And that's where you're being deceived by maths. We can't have counted down from infinity because there is no first number and so we can't have counted up to infinity because there is no last number.

The fact that an infinite series can have a finite sum is a red herring in both cases.

But to talk about what the brain is doing when presented with a cow... — Mww

Brains aren't presented with cows. Brains respond to signals sent by the body's sense organs. But most importantly, the phenomenal character of conscious experience – which as a property dualist I take to be a non-physical emergent phenomenon – is ontologically distinct from the cow.

So what’s your third-person account of belief and what it seems like?