Skeptics "reasoning" applied to mathematics

[primemover]

I came up with a parallel of the following skeptic argument and I think it brings to light in a greater contrast the lunacy of such "reasoning".

The argument is that since we cannot know of variables that may affect a situation we cannot be certain of the conclusion we have based on the variables we do know of.

The lunacy of this type of reasoning is exposed in greater contrast when you apply it to mathematics.

We know that 1+1=2. If a skeptic is to be consistent ( I know getting a skeptic to be consistent is far fetched but let's all just pretend for a moment.)..... if the skeptic is to be consistent, he must answer that 1+1 doesn't necessarily equal 2 because there may in fact be an unknown variable in the math problem that he doesn't know about. Such as 1x + 1 = 3. A rational person realizes that we now are no longer be dealing with 1+ 1 = 2 while the skeptic being unable to conceptualize higher than a lobotimized cock roach considers this proof that we can't be certain of anything.

Edited April 30, 2007 by primemover

[Dragonfly]

This is not a good argument. In mathematics we know that there are no unknown variables, as we define the number of variables. When we describe the real world we use a model with a certain finite number of variables, but we can never be sure that this number of variables is sufficient for a correct description. Of mathematical statements we can be certain, as they are derived from the definitions; of statements about the real world we can never be 100% certain, as we never can learn all the variables and we never can be sure that our model is correct. That is in a nutshell the difference between analytical statements and synthetic statements. Welcome to the real world.

[primemover]

This is not a good argument. In mathematics we know that there are no unknown variables, as we define the number of variables.

I was aware of this difference when I formulated the parallel and it completely misses the point.

You admit that we can be certain that 1+1=2 yet you cannot admit that we can be certain that when two (lets keep it simple for discussions sake and say two) variables interact within reality we can be certain of their consequence. Rather or not there are unknown variables in either case misses the fundamental point. In one case you are allowing for contextual certainty and in another you are not.

When we describe the real world we use a model with a certain finite number of variables, but we can never be sure that this number of variables is sufficient for a correct description.

In other words, because we are not omniscient, we can never be certain. Or in contrast, because we are not omnipotent, we can never do anything.

[Dragonfly]

You admit that we can be certain that 1+1=2 yet you cannot admit that we can be certain that when two (lets keep it simple for discussions sake and say two) variables interact within reality we can be certain of their consequence. Rather or not there are unknown variables in either case misses the fundamental point. In one case you are allowing for contextual certainty and in another you are not.

No you cannot be certain of their consequence, as you never can be certain that these are the only variables influencing the outcome. In mathematics you can isolate that what you want to study, but if you isolate certain parts in real life you do that at your own peril. Mathematics is certain, reality is not.

In other words, because we are not omniscient, we can never be certain. Or in contrast, because we are not omnipotent, we can never do anything.

The first part is correct with respect to reality, we can never be certain. The second part is nonsense, you don't have to be omnipotent to do something.

[Brant Gaede]

You admit that we can be certain that 1+1=2 yet you cannot admit that we can be certain that when two (lets keep it simple for discussions sake and say two) variables interact within reality we can be certain of their consequence. Rather or not there are unknown variables in either case misses the fundamental point. In one case you are allowing for contextual certainty and in another you are not.

No you cannot be certain of their consequence, as you never can be certain that these are the only variables influencing the outcome. In mathematics you can isolate that what you want to study, but if you isolate certain parts in real life you do that at your own peril. Mathematics is certain, reality is not.

In other words, because we are not omniscient, we can never be certain. Or in contrast, because we are not omnipotent, we can never do anything.

The first part is correct with respect to reality, we can never be certain. The second part is nonsense, you don't have to be omnipotent to do something.

Well, I'm certain I'm not omnipotent. I'm also certain that no one else is, was or ever will be. Am I deluded about the latter?

--Brant

Edited April 30, 2007 by Brant Gaede

[Dragonfly]

Well, I'm certain I'm not omnipotent. I'm also certain that no one else is, was or ever will be. Am I deluded about the latter?

That is of course not the kind of certainty we're talking about. I'm also fairly certain that I'm not a teapot, but that is not the problem. That is our knowledge about the physical world, where the point is not what it is not (an infinite set), but what it is. Our knowledge of the latter may continually increase and become more accurate, but will never be exhaustive. Otherwise we would be omniscient, and you're probably also certain that that is not possible.

[Daniel Barnes]

primemover:

>In other words, because we are not omniscient, we can never be certain. Or in contrast, because we are not omnipotent, we can never do anything.

And primemover thinks skeptics are bad at reasoning! Hilarious!

[primemover]

No you cannot be certain of their consequence, as you never can be certain that these are the only variables influencing the outcome. In mathematics you can isolate that what you want to study, but if you isolate certain parts in real life you do that at your own peril. Mathematics is certain, reality is not.

I'm not talking about isolating anything. If I'm driving and I see a river I am certain that I am seeing a river.

What would the conversation with you and your wife sound like as you crossed the mississippi river.

Wife:Oh wow honey look it's the Mississippi river.

you: Well it may be the Mississippi river but you can never be sure about that you know.

Do you talk like that? Whos philosophy you more closely emulate in your day to day life?

The first part is correct with respect to reality, we can never be certain. The second part is nonsense, you don't have to be omnipotent to do something.

And I don't have to be omniscient to know something.

Edited April 30, 2007 by primemover

[primemover]

primemover:

>In other words, because we are not omniscient, we can never be certain. Or in contrast, because we are not omnipotent, we can never do anything.

And primemover thinks skeptics are bad at reasoning! Hilarious!

When someone says we can't be sure of anything what they are saying is that ultimately we can know nothing.

IOW's because we are not omniscient we can't know anything.

We are condemned for having senses and rational faculties that each has a specific identity.

Are you with me so far?

Edited April 30, 2007 by primemover

[Daniel Barnes]

Primemover:

>because we are not omnipotent, we can never do anything.

Once again: why should we listen to you lecture on sound reasoning when you come out with hilarious illogic like this, Prime?

Or, if this is meant to be an opponent's argument, can you give us an actual example of someone using this? I've never heard anyone say this. It sounds like a strawman of your own invention to me.

If you have no example of anyone who ever actually claimed this, what is the point of offering it for debate?

[primemover]

Primemover:

>because we are not omnipotent, we can never do anything.

Once again: why should we listen to you lecture on sound reasoning when you come out with hilarious illogic like this, Prime?

Or, if this is meant to be an opponent's argument, can you give us an actual example of someone using this? I've never heard anyone say this. It sounds like a strawman of your own invention to me.

If you have no example of anyone who ever actually claimed this, what is the point of offering it for debate?

is it a strawman? I'm simply carrying over his reasoning to another area. It's his reasoning. I just changed the subject matter.

Now of coarse he doesn't say that about omnipotence but if he were to be consistent he would.

Edited April 30, 2007 by primemover

[Daniel Barnes]

>is it a strawman? I'm simply carrying over his reasoning to another area. It's his reasoning. I just changed the subject matter.

>Now of coarse he doesn't say that about omnipotence but if he were to be consistent he would.

But your example doesn't actually follow unless you use "knowledge" in a ridiculously limited sense.

For example, just because I know my bus timetable, doesn't mean I am certain that the bus will always be there!

You seem to think that if knowledge isn't certain, it doesn't exist, or is entirely useless! This is obviously a fallacy.

Actually, you can have knowledge that is approximately correct, and generally reliable - just like my bus timetable. And you can strive to improve it, or make it better (I might go and get a copy of the latest bus timetable, which takes into account a few new schedule changes).

"Absolute certainty" is simply unnecessary, even if we could get it. Which we can't - unless we resort to mere word-play, and invent a self-contradictory oxymoron like "contextual absolute".

[Dragonfly]

When someone says we can't be sure of anything what they are saying is that ultimately we can know nothing.

IOW's because we are not omniscient we can't know anything.

Whoever said that we can't know anything?

[primemover]

>is it a strawman? I'm simply carrying over his reasoning to another area. It's his reasoning. I just changed the subject matter.

>Now of coarse he doesn't say that about omnipotence but if he were to be consistent he would.

But your example doesn't actually follow unless you use "knowledge" in a ridiculously limited sense.

For example, just because I know my bus timetable, doesn't mean I am certain that the bus will always be there!

You seem to think that if knowledge isn't certain, it doesn't exist, or is entirely useless! This is obviously a fallacy.

Actually, you can have knowledge that is approximately correct, and generally reliable - just like my bus timetable. And you can strive to improve it, or make it better (I might go and get a copy of the latest bus timetable, which takes into account a few new schedule changes).

"Absolute certainty" is simply unnecessary, even if we could get it. Which we can't - unless we resort to mere word-play, and invent a self-contradictory oxymoron like "contextual absolute".

Strawman.

I wouldn't pretend to know the future and say that the bus will arrive at x time. I would say that I know for certain what time THEY SAY the bus will arrive. So you admit that you know for certain when they say the bus will arrive?

"But your example doesn't actually follow unless you use "knowledge" in a ridiculously limited sense."

Knowledge means to know something about reality. You position seems to be that anything we know can be overturned at any moment therefore how can you assert that we know anything?

[primemover]

When someone says we can't be sure of anything what they are saying is that ultimately we can know nothing.

IOW's because we are not omniscient we can't know anything.

Whoever said that we can't know anything?

Your position is that what we "know" as true can be overturned at any moment. If something you "knew" as true is latter false then all along you did not really know it. Thus we can't know anything.

[Dragonfly]

Your position is that what we "know" as true can be overturned at any moment. If something you "knew" as true is latter false then all along you did not really know it. Thus we can't know anything.

We don't need 100% certainty to know something. That absolute knowledge about the world is not possible does not imply that no knowledge is possible. A sufficiently high probability is in practice good enough. Knowledge is that what makes our living possible, even if it is not 100% certain. Your error is to equate knowledge with 100% certainty, implying that everything you "know" is 100% certain and that you never err. Yeah, sure.

[Daniel Barnes]

Primemover:

>Your position is that what we "know" as true can be overturned at any moment. If something you "knew" as true is latter false then all along you did not really know it. Thus we can't know anything.

Sure, but only if you insist on "know" meaning omniscient certainty! Because obviously only ominscience, where all possible future circumstances and possibilities are known, can never be overturned.

I don't agree with this, clearly. I don't think you need to have ominscient certainty of all future possibilities to say you "know" something.

However, what you're saying above is, despite your protestations to the contrary, that you do. Knowledge that can never be overturned the only type of knowledge that you say qualifies to be called such! In your supposed criticism of skepticism, I think you might be projecting, as they say.

It's not just you, BTW. Ayn Rand seems to have the same problem - or at least Fred Seddon seems to think so. Towards the end of his lengthy essay here, he argues the following:

"In defense of Nyquist, I do think that Rand is really a radical here. Her notion of certainty is one that challenges the usual definition of knowledge as “justified true belief,” a notion that probably goes back to Plato. This definition insists that in order to know P, P must be true. Rand, for better or worse, sees this as a variant of intrinsicism and rejects it. Therefore, and Nyquist is quite right about this, you can know P, yet P may be false. " (emphasis DB)

So: according to Seddon, Rand reckons "you can know P, yet P may be false."

Whodathunkit?

Edited April 30, 2007 by Daniel Barnes

[Michael Stuart Kelly]

We don't need 100% certainty to know something. That absolute knowledge about the world is not possible does not imply that no knowledge is possible.

Dragonfly,

Please forgive the lapse but I can't resist. Are you absolutely 100% certain about what you are proposing? You seem emotionally committed to it.

Michael

[Daniel Barnes]

Michael:

>Please forgive the lapse but I can't resist. Are you absolutely 100% certain about what you are proposing?

Michael, just so we can retire this naiive line of argument once and for all - skepticism is itself not 100% certain! It may, in fact, turn out to be false. Thus we can hold it without falling into logical error.

This is Skepticism 101, BTW. Can't believe I keep hearing this over and over again as if it was somehow a clever criticism!

[Michael Stuart Kelly]

skepticism is itself not 100% certain!

Daniel,

Damaamm!!! I can't resist this one either.

Are you certain of what you just said?

Michael

[Dragonfly]

Please forgive the lapse but I can't resist. Are you absolutely 100% certain about what you are proposing? You seem emotionally committed to it.

You seem to see a bit too often all kinds of emotions in other people, do you think it would invalidate their arguments, while you have no emotional commitments at all?

In this case my statement is just the advice to use a sensible definition of "knowledge". You shouldn't take words like "certain" out of their context, which is the common error in this kind of (hardly original) questions.

[Daniel Barnes]

Michael:

>Are you certain of what you just said?

Have you never made an error typing a post, and not realised it?

[Michael Stuart Kelly]

You shouldn't take words like "certain" out of their context, which is the common error in this kind of (hardly original) questions.

Dragonfly,

Woah theah!

You just chided me on another thread for establishing context for certainty (except we were calling it by another name).

So you would agree with Rand about contextual certainty, then?

Michael

[primemover]

Sure, but only if you insist on "know" meaning omniscient certainty! Because obviously only ominscience, where all possible future circumstances and possibilities are known, can never be overturned.

Again with your strawmen. Has any Objectivist claimed to know the future?

I don't agree with this, clearly. I don't think you need to have ominscient certainty of all future possibilities to say you "know" something.

Again with your future business!

However, what you're saying above is, despite your protestations to the contrary, that you do. Knowledge that can never be overturned the only type of knowledge that you say qualifies to be called such! In your supposed criticism of skepticism, I think you might be projecting, as they say.

are you sure?

It's not just you, BTW. Ayn Rand seems to have the same problem - or at least Fred Seddon seems to think so. Towards the end of his lengthy essay here, he argues the following:

"In defense of Nyquist, I do think that Rand is really a radical here. Her notion of certainty is one that challenges the usual definition of knowledge as “justified true belief,” a notion that probably goes back to Plato.

Yea a great indicator of the truth of something is how old it is or by how many people think it is true.:thumbsup:

[Michael Stuart Kelly]

Have you never made an error typing a post, and not realised it?

Daniel,

I do remember typing a friendly post on your blog. I might have been mistaken, though.

Michael