Superstrings

[Apolloe]

Penumbra, you are very confused about this issue. You're confusing yourself by talking about "phrases", and "concepts", and similar things. Deal with the proposition, which is something that we can believe, refute, make claims about, etc. Propositions are the things which we believe or not, which are the items of our knowledge.

OP presented a proposition P that he claims is not falsifiable. You respond, saying that is is falsifiable because some other claim Q (where Q is not equal to P) is falsifiable. That makes no sense. You have muddled yourself up by engaging in irrelevant wordplays. I have tried to make it clearer to you by putting into a logical form the argument you are presenting.

I'll try and put it in a formal argument. Let P be the proposition "I exist":
1. It is possible to know P
2. It is not possible to know ~P
3. For P to be falsifiable, it must seem epistemically possible to know that P and possible to know that ~P
4. Therefore, P is not falsifiable (from 2 & 3)
5. Therefore, I can know a proposition, P, that is not falsifiable (from 1 & 4)

Which step in this argument do you think is wrong? Your options are that one of the premises (1, 2, 3) are false, or that I have drawn an invalid inference (4, 5)

To take this from another perspective, you suspect that logic may be possible to know and yet not be falsifiable. Well, your argument works as a demonstration that logic is falsifiable too. I might make the claim that "Modus ponens is a valid logical inference" (google it if you don't know it). I might also say that this claim is not falsifiable (and in fact I DO make this claim). But we can respond like you do. We can say that its negation can be known to be false, ie "It is not the case that modus ponens is a valid logical inference" is false. Since its negation is falsifiable, the proposition is falsifiable. According to you.

It doesn't matter whether the exact statement, "I exist" is falsifiable or not because the concept itself is falsifiable and therefore we can derive knowledge from it.

What concept is falsifiable? Certainly not the one we are talking about. The concept of my personal ability to know whether or not I exist is not falsifiable.

(I know, your answer to this question is that somehow "It is not the case that I exist" is part of the concept. And so again, I say - so what? This new broader concept you're drawing to our attention is not what we're talking about. I talk in terms of specific propositions to make things clearer)

If one proves something true, then they've shown something else to be false, even if that other "something" is simply the negative of their positively proven thing.

Following your reasoning here, we have then in fact shown an infinite number of different propositions to be false, just by showing one proposition true. By showing "I exist" is true, we have shown the following to be false:
~P, ~~~P, ~~~~~P, ~~~~~~P, ((n*2)-1)~P, where n goes from 1 to infinity.

Which is absurd. We're not showing an infinite number of different things as false. We're showing the truth of one proposition that has many (infinitely many) ways of being expressed. It is not, as you say, "something else".

I just don't understand why you can't see this. It's just this: is the proposition "I exist" falsifiable? No it isn't. Can we know "I exist"? Yes. Therefore, we can know something that isn't falsifiable in principle. You then take us off on an irrelevant tangent to say that its negation can be falsified. But that doesn't tell us anything about the falsifiability of the proposition we are actually talking about!

 

[Penumbra]

Penumbra, you are very confused about this issue. You're confusing yourself by talking about "phrases", and "concepts", and similar things. Deal with the proposition, which is something that we can believe, refute, make claims about, etc. Propositions are the things which we believe or not, which are the items of our knowledge.

OP presented a proposition P that he claims is not falsifiable. You respond, saying that is is falsifiable because some other claim Q (where Q is not equal to P) is falsifiable. That makes no sense. You have muddled yourself up by engaging in irrelevant wordplays. I have tried to make it clearer to you by putting into a logical form the argument you are presenting.

I'll try and put it in a formal argument. Let P be the proposition "I exist":
1. It is possible to know P
2. It is not possible to know ~P
3. For P to be falsifiable, it must seem epistemically possible to know that P and possible to know that ~P
4. Therefore, P is not falsifiable (from 2 & 3)
5. Therefore, I can know a proposition, P, that is not falsifiable (from 1 & 4)

Which step in this argument do you think is wrong? Your options are that one of the premises (1, 2, 3) are false, or that I have drawn an invalid inference (4, 5)

To take this from another perspective, you suspect that logic may be possible to know and yet not be falsifiable. Well, your argument works as a demonstration that logic is falsifiable too. I might make the claim that "Modus ponens is a valid logical inference" (google it if you don't know it). I might also say that this claim is not falsifiable (and in fact I DO make this claim). But we can respond like you do. We can say that its negation can be known to be false, ie "It is not the case that modus ponens is a valid logical inference" is false. Since its negation is falsifiable, the proposition is falsifiable. According to you.

You're talking past me. Part of it is my fault, but I've been trying to address it and you don't seem to be listening.

In our first post exchange, we were talking past each other, but after you clarified what you meant, I understood your position and understood the differences in our positions, but you still seem to be arguing against a concept that I'm not arguing for. I kind of feel bad that you wrote all this long post out because most of it isn't relevant to what I'm trying to convey. I've moved the parts of your post here that I feel are relevant to your misunderstanding of me so that I can address them again at the bottom of this post here.

Here is how you are talking past me:

In post #21, when I responded to you, we were talking past each other. We were using the term, "I exist" differently- I was using it liberally and you were using it strictly. Meaning, I was asserting that "I exist" was falsifiable because the concept is falsifiable while you were latching onto the exact phrase and saying, "I exist" is not falsifiable (and that's true). Upon seeing how you are using the statement, beginning in my next post #27, I have been trying to be more careful with my wording to ensure we are talking to each other rather than past each other.

-You seem to be under the delusion, which I have tried to dispel multiple times, that I am arguing that the exact phrase "I exist" is a falsifiable claim. It is partly my fault that you are under this delusion, because I was not careful with my words in post 21 where I said just that. Had I the foresight to see how strongly you'd focus on the semantics, I'd have been more careful with my semantics in that post. Since then, I have been attempting to explain what I mean. So, please dispel the notion that I am arguing that the exact phrase, "I exist" is a falsifiable phrase.

-I am arguing that knowledge is only had on concepts that are falsifiable in principle, with the concept consisting of the question and the answer to that question. The concept in this case is self-existence. The question is, "Do I exist"? The answer to that question, if valid, counts as knowledge. Now, how do we arrive at that knowledge? We can either prove the positive, or disprove (falsify) the negative, which are the same thing. The experiment is the same, but how we word the experiment determines whether we have proved a positive or disproved a negative. The important part is not which exact phrase we prove or disprove. (We can't disprove the exact word-for-word phrase, "I exist", and we can't prove the exact word-for-word phrase, "I do not exist." But, we can prove the exact word-for-word phrase, "I exist", and we can disprove the exact word-for-word phrase, "I do not exist." And yet it's all the same knowledge.) Instead, the important part is whether we can obtain knowledge, and whether that knowledge is falsifiable in principle.

So:
The concept is self-existence.
The question is, "Do I exist?"
The answer counts as knowledge and is, "Yes, I exist."

How did I come to that knowledge?
Well, I either proved that I exist by thinking, or I disproved that I do not exist by thinking. The experiment was the same, the wording was different each time, but the same knowledge was obtained. The knowledge is falsifiable even if the exact statement, "I exist" is not falsifiable because the phrase, "I do not exist" is falsifiable. I can't stress this enough- the KNOWLEDGE is falsifiable but the phrase, "I exist" is not falsifiable.

Following your reasoning here, we have then in fact shown an infinite number of different propositions to be false, just by showing one proposition true. By showing "I exist" is true, we have shown the following to be false:
~P, ~~~P, ~~~~~P, ~~~~~~P, ((n*2)-1)~P, where n goes from 1 to infinity.

Which is absurd. We're not showing an infinite number of different things as false. We're showing the truth of one proposition that has many (infinitely many) ways of being expressed. It is not, as you say, "something else".

This would depend on the specific case. If one proves something, then depending on what it is that they have proved, they may have disproved an infinite number of things, but most of them will be irrelevant. What is relevant is one disproved claim: the specific opposite of that which was proven.

So in other words, if I prove that the moon is made of rock (and somehow I examined it completely so the proof is valid), it is true that I may have disproved an infinite number of claims that it is cheese, water, hydrogen, etc, but they aren't important. The disproved claim that is important is the claim that the moon is not made of rock, because proving one or disproving the other is synonymous.

What

concept is falsifiable? Certainly not the one we are talking about. The concept of my personal ability to know whether or not I exist is not falsifiable.

(I know, your answer to this question is that somehow "It is not the case that I exist" is part of the concept. And so again, I say - so what? This new broader concept you're drawing to our attention is not what we're talking about. I talk in terms of specific propositions to make things clearer)

What concept? The concept of self-existence.

The concept you are talking about is, "I exist" which is one half of that concept. "I exist" and "I do not exist" pertain to the same concept. In fact they are the same concept.

You have muddled yourself up by engaging in irrelevant wordplays.

I have not. I have been uninterested in the specific wording and instead was interested in the knowledge behind the wording. You, for some reason I can't understand, have been focusing on the specific wording. That which is important is the knowledge behind the wording.

In regards to the question of whether knowledge can be known without it being falsifiable, I am only focusing on the knowledge, not the precise way that knowledge is worded. You, however, are stressing over exactly how that knowledge is worded.

The knowledge is whether we exist or not. We can phrase it several ways, but the important thing is the knowledge itself. The concept is provable and disprovable depending on how it is worded because proof and disproof are two sides of the same coin.

So how does this differ from that which is not falsifiable? Because it can be tested, and depending on how we word the test, it is either proved or the opposite is disproved, and they are synonymous.

In contrast, an example of something that is not falsifiable is an invisible and undetectable dragon in my garage. It is made out of "dragon-ether", which I define as something non-physical that cannot be detected by physical means. It has no measurable effect on the garage or anything outside of the garage. This being the case, you cannot test my claim at all. You can't prove or disprove "the dragon exists" or "the dragon does not exist", so you cannot obtain knowledge as to the existence of the dragon in my garage, and the claim that the dragon exists in my garage is not a falsifiable claim.

So, one last time:

I just don't understand why you can't see this. It's just this: is the proposition "I exist" falsifiable? No it isn't. Can we know "I exist"? Yes.

Good so far.

Therefore, we can know something that isn't falsifiable in principle. You then take us off on an irrelevant tangent to say that its negation can be falsified. But that doesn't tell us anything about the falsifiability of the proposition we are actually talking about!

Invalid conclusion, and no tangents are necessary. The proposition I am actually talking about is the knowledge of self-existence, not the word-for-word claim, "I exist". The knowledge itself rests on that which can be proved or disproved (falsified) with the same exact experiment depending on how we word it. How we word the knowledge is largely irrelevant (which is why it confuses me as to why you focus on the wording so much).

So, in summary, I have knowledge of my own existence and it's based on falsifiability and proof via the same method. If thinking requires existence, and I can think, then I've simultaneously proved that I exist and falsified that I don't exist, because it's the same knowledge to be had. Whether I word it as "I exist" or "It is not true that I do not exist" is irrelevant because it pertains to the same knowledge, which is testable, provable, and falsifiable. In contrast, something that is not falsifiable is like the ether-dragon that is not testable in any way no matter how it's worded.

-Lyn

 

[Wiccan_Child]

*jumps right in*

I'll try and put it in a formal argument. Let P be the proposition "I exist":
1. It is possible to know P
2. It is not possible to know ~P
3. For P to be falsifiable, it must seem epistemically possible to know that P and possible to know that ~P
4. Therefore, P is not falsifiable (from 2 & 3)
5. Therefore, I can know a proposition, P, that is not falsifiable (from 1 & 4)

Which step in this argument do you think is wrong? Your options are that one of the premises (1, 2, 3) are false, or that I have drawn an invalid inference (4, 5)

I would say premise (2). Before any proof is given that we do indeed exist, person X has no idea whether P or ¬P are true, or even possible. Thus, to him, both P and ¬P are possibilities: perhaps someone will prove to him that he doesn't, in fact, exist. Obviously, we can prove that, so no one will ever prove ¬P, but probabilities arise from ignorance: the more we know, the more remote the alternate possibilities are.

Consider something more mathematical. Suppose there is some mathematical statement which is as yet unproven; all we know is that it is either true or false. Modern mathematicians can neither prove nor disprove this statement, so they have to say that both alternatives are possible: it's possible that the statement is true, it's possible that the statement is false. However, the statement is either true or false. Eventually, the mathematicians come up with a proof: the statement is false. The statement was always false. So was there any possibilities that the statement could have been proven true?

Following your reasoning here, we have then in fact shown an infinite number of different propositions to be false, just by showing one proposition true. By showing "I exist" is true, we have shown the following to be false:
~P, ~~~P, ~~~~~P, ~~~~~~P, ((n*2)-1)~P, where n goes from 1 to infinity.

Which is absurd. We're not showing an infinite number of different things as false. We're showing the truth of one proposition that has many (infinitely many) ways of being expressed. It is not, as you say, "something else".

I would have to disagree. Two statements may be equivalent, but not necessarily identical. 1/2 is a mathematical term, as is 2/4, but they are fundamentally different. They may have the same numerical evaluation, but they're as different as "I have a cat" and "У меня есть кошка": ostensibly the same, but undeniably different.

It all boils down to whether you consider p and ¬¬p to be identical, or merely equivalent. 1 = 4/4, but is 1 the same thing as 4/4?

Also, Apolloe, I remember having a nice big discussion with you earlier, and I've been meaning to reply to your latest post, but I can't remember which thread it was in! You don't happen to remember, do you?

 

[Apolloe]

Penumbra, just rewording what you have said before I respond further. You seem to be claiming that falsifiability is an essential aspect of knowledge. ie, that we can't have knowledge without there being falsifiability present, even if the falsifiability is only in principle. And that in this particular case falsifiability is present (as you require) because one can demonstrate the truth of the proposition by falsifying its negation. Does that sound accurate?

ie, we need falsifiability for knowledge, and falsifiability is present (even if not necessarily used) via the falsifying of the claim "I do not exist"?

 

[Apolloe]

*jumps right in*

Hope you landed on your feet

I would say premise (2). Before any proof is given that we do indeed exist, person X has no idea whether P or ¬P are true, or even possible. Thus, to him, both P and ¬P are possibilities: perhaps someone will prove to him that he doesn't, in fact, exist. Obviously, we can prove that, so no one will ever prove ¬P, but probabilities arise from ignorance: the more we know, the more remote the alternate possibilities are.

These are excellent considerations. What you refer to here are "epistemic possibilities". Indeed, someone may not have thought about it clearly and might (without thinking) reply, "Why couldn't I know that I don't exist?" You spend a short time explaining it to them, and they'll realise how silly their question was. But for a moment before hand, it did indeed seem epistemically possible to them. More to say below:

Consider something more mathematical. Suppose there is some mathematical statement which is as yet unproven; all we know is that it is either true or false. Modern mathematicians can neither prove nor disprove this statement, so they have to say that both alternatives are possible: it's possible that the statement is true, it's possible that the statement is false. However, the statement is either true or false. Eventually, the mathematicians come up with a proof: the statement is false. The statement was always false. So was there any possibilities that the statement could have been proven true?

I have bolded two important sentences in the quote just above. Here you refer to "epistemic possibility", which you then do not qualify and simply call "possible". It's possible, as far as we know.

Now, when we talk about possible worlds, we talk about worlds which are logically possible. This point may be a little tricky to make, so pay attention if you can to what I'm trying to say, to try and look past the clumsiness of my presentation(!):
A mathematical statement of the like you propose is either true or false by necessity. We don't *know* what the truth is, but presumably whatever is true is true in every possible world. Let's say that this hypothetical mathematical statement turns out to be true in our world, and we have a proof that demonstrates it. Proofs deal with logical certainty - if there's any possibility that your "proof" might be wrong, you don't have a proof after all. So, if we have proven that statement true, then we will say that there is no other possible world in which the statement is false. So while there are possible worlds in which there are unicorns (while there are none in our world), there are no possible worlds in which this mathematical statement has the opposite truth value to the one it has in our world (at least for some mathematical statements).

Like you said (and I bolded above), we know that it is either true or false. And the statement is true or false by logical necessity - we just don't know which way.

Statements about unicorns, or city names, or other contingent facts do not just have various epistemic possibilities, but they have various subjunctive probabilities too. There are possible worlds in which cities are named differently to our world, and possible worlds in which cities that do not yet exist will be named differently than in our world.

Now going back specifically to your objection of my argument - you rejected premise 2. But I have given an argument earlier in this thread that establishes the truth of premise 2. We don't care about the ignorant man who has not yet seen that 2 is true - that only deals with an epistemic possibility. Since *you* have seen the truth of premise 2, you should have no problem with it in the argument.

I would have to disagree. Two statements may be equivalent, but not necessarily identical. 1/2 is a mathematical term, as is 2/4, but they are fundamentally different. They may have the same numerical evaluation, but they're as different as "I have a cat" and "У меня есть кошка": ostensibly the same, but undeniably different.

It all boils down to whether you consider p and ¬¬p to be identical, or merely equivalent. 1 = 4/4, but is 1 the same thing as 4/4?

They share the same referent, and in that sense they are identical, yes.
4/4 is the same as 1
But:
"4/4" is not the same as "1"

I don't see how this distinction is relevant here.

Penumbra agreed with me that "I exist" being true is the same as "I do not exist" being false. Yet she said that by showing one thing true, we've shown "something else" to be false. I was disagreeing with this claim that it is "something else". Here I am concerned about the things these sentences refer to, and not the form of sentences themselves. ie, how the world is or is not.

And this may be one (or the) source of the disagreement between myself and penumbra. When I talk about "falsifiability" as a requirement, I'm referring to a Popparian view of science. The first post in this thread was with regards to an objection of string theory that "it's not falsifiable". This objection is raised precisely because someone holds a Popparian view of science. It seems to me now that Penumbra was not in fact defending such a view. Perhaps Penumbra is not even aware of the history of science and what it is that was being referred to. Summary: Penumbra may be using the requirement of falsifiability in a very different sense to that which was originally being used.

Also, Apolloe, I remember having a nice big discussion with you earlier, and I've been meaning to reply to your latest post, but I can't remember which thread it was in! You don't happen to remember, do you?

I did wonder Do you get email alerts for thread replies? Perhaps your email history could direct you there. At any rate, this link should get you there:
Deism! - Page 6 - Christian Forums

 

[Wiccan_Child]

These are excellent considerations. What you refer to here are "epistemic possibilities". Indeed, someone may not have thought about it clearly and might (without thinking) reply, "Why couldn't I know that I don't exist?" You spend a short time explaining it to them, and they'll realise how silly their question was. But for a moment before hand, it did indeed seem epistemically possible to them.

'Epistemic possibility'. Well, that's my phrase for the day!

I have bolded two important sentences in the quote just above. Here you refer to "epistemic possibility", which you then do not qualify and simply call "possible". It's possible, as far as we know.

Now, when we talk about possible worlds, we talk about worlds which are logically possible. This point may be a little tricky to make, so pay attention if you can to what I'm trying to say, to try and look past the clumsiness of my presentation(!):
A mathematical statement of the like you propose is either true or false by necessity. We don't *know* what the truth is, but presumably whatever is true is true in every possible world. Let's say that this hypothetical mathematical statement turns out to be true in our world, and we have a proof that demonstrates it. Proofs deal with logical certainty - if there's any possibility that your "proof" might be wrong, you don't have a proof after all. So, if we have proven that statement true, then we will say that there is no other possible world in which the statement is false. So while there are possible worlds in which there are unicorns (while there are none in our world), there are no possible worlds in which this mathematical statement has the opposite truth value to the one it has in our world (at least for some mathematical statements).

Like you said (and I bolded above), we know that it is either true or false. And the statement is true or false by logical necessity - we just don't know which way.

Statements about unicorns, or city names, or other contingent facts do not just have various epistemic possibilities, but they have various subjunctive probabilities too. There are possible worlds in which cities are named differently to our world, and possible worlds in which cities that do not yet exist will be named differently than in our world.

Now going back specifically to your objection of my argument - you rejected premise 2. But I have given an argument earlier in this thread that establishes the truth of premise 2. We don't care about the ignorant man who has not yet seen that 2 is true - that only deals with an epistemic possibility. Since *you* have seen the truth of premise 2, you should have no problem with it in the argument.

To be honest, I haven't read the entirety of this thread. As I said, I jumped in . Your proof concludes that it is not possible to falsify the claim "I exist", but your proof only proves this true for people who already know that it is, in fact, true: as you said, it is an epistemic possibility that we can know our own non-existence. I know I exist, and you know you exist, but some ignorant third-party might well be unaware of the certainty with which an individual can assert their own existence - thus, they violate your second premise. Your third premise agrees with this: to ignorant person, it is epistemically possible that either P is true, or ¬P is true.

They share the same referent, and in that sense they are identical, yes.
4/4 is the same as 1
But:
"4/4" is not the same as "1"

I don't see how this distinction is relevant here.

The distinction is to highlight the difference between P and ¬¬P. Semantically equivalent, but fundamentally different.

Penumbra agreed with me that "I exist" being true is the same as "I do not exist" being false. Yet she said that by showing one thing true, we've shown "something else" to be false. I was disagreeing with this claim that it is "something else". Here I am concerned about the things these sentences refer to, and not the form of sentences themselves. ie, how the world is or is not.

Nonetheless, I would say that p is different to ¬¬p, at least as far as the claim "Proving p proves ¬¬p as well" goes. If you prove p but not q, you don't know the truth of q - because you don't yet know that q is semantically equivalent to p (because, for example, they're in different languages). A proof of p works for q as well, but not automatically so.

So I would say that not only is ¬¬p different to p with regard to working out how many things you've really proven, but also that different wordings if p are as well: "I exist" and "I exist here and now", "x = -1" and "2x = 2", are the same for all intents and purposes, but a strict treatment requires they're different.

And this may be one (or the) source of the disagreement between myself and penumbra. When I talk about "falsifiability" as a requirement, I'm referring to a Popparian view of science. The first post in this thread was with regards to an objection of string theory that "it's not falsifiable". This objection is raised precisely because someone holds a Popparian view of science. It seems to me now that Penumbra was not in fact defending such a view. Perhaps Penumbra is not even aware of the history of science and what it is that was being referred to. Summary: Penumbra may be using the requirement of falsifiability in a very different sense to that which was originally being used.

That's entirely possible. I'll let her comment

I did wonder Do you get email alerts for thread replies? Perhaps your email history could direct you there. At any rate, this link should get you there:
Deism! - Page 6 - Christian Forums

Ah, thanks! I don't get e-mail alerts, just the standard Control Panel things.