Need expert advice on how to handle a seemingly legitimate objection

[fast]

Maybe we're missing a premise? Perhaps:

1. Almost all F are G;
2. a is F;
3. We don't know anything else about a.
4. Therefore, a is probably G.

If something is probably the case, then the fact that it turns out not to be the case doesn't alter the probability of something being the case, so even if a isn't G, the conclusion remains true independent of the facts--so long as the connection between almost all warrants the probability. Right? My cat is probably outside. If it turns out that my cat is inside, was I incorrect? I would have been incorrect had I said my cat is outside...if instead it's inside, but if my conclusion is about probability, then I don't see that what is actually the case is relevant.

 

[Juma]

but if my conclusion is about probability, then I don't see that what is actually the case is relevant.

What you dont realize is that the conclusion of these types of arguments is about your information, not about what is really the case.

 

[Wiploc]

If something is probably the case, then the fact that it turns out not to be the case doesn't alter the probability of something being the case, so even if a isn't G, the conclusion remains true independent of the facts--so long as the connection between almost all warrants the probability. Right? My cat is probably outside. If it turns out that my cat is inside, was I incorrect? I would have been incorrect had I said my cat is outside...if instead it's inside, but if my conclusion is about probability, then I don't see that what is actually the case is relevant.

Picture a man sitting on the sofa in his living room. His cat is on his lap. He is petting his cat. And he explains this theory about the cat: "This is my cat here. Nice kitty. Usually, at this time of day, my cat is outside, not here on my lap as he is today. It stands to reason, then, that my cat is probably outside right now, rather than on my lap. In fact, the force of that logic is so great that I actually believe my cat is outside rather than here. Yes, nice kitty. Daddy loves you, but your purring isn't fooling me into thinking you're really here. Kitchy kitchy."

You can think that's good logic if you want. I'll continue to think it's nuts.

As for your example, when you thought your cat was outside when it really wasn't, I'll assume that that was a good example of when the proposed was reasonable.

- 1. Almost all F are G;
- 2. a is F;
- 4. Therefore, a is probably G.

That is, you didn't have any contradicting evidence.

- 3. We don't know anything else about a.

I'll agree with you that it is sometimes reasonable to conclude that if almost all F are G, and a is an F, that a is probably G. But it seems clear that this isn't always the case.

1. Almost all blacks are Democrats.
2. Colin Powell is a black.
3. Therefore, Colin Powell is probably a Democrat.

That's not good reasoning. If you think it's good reasoning, how do you cope with this:

1. Almost all military types are Republicans.
2. Colin Powell is a military type.
3. Therefore, Colin Powell is probably a Republican.

So now, if the argument is always good, we have proven that Colin Powell is probably both a Republican and a Democrat. But in fact we know that this is improbable. This form of argument could easily be made to produce a multitude of other contradictions and absurdities. Therefore, we know that arguments of that form are not always reasonable.

 

[fast]

If something is probably the case, then the fact that it turns out not to be the case doesn't alter the probability of something being the case, so even if a isn't G, the conclusion remains true independent of the facts--so long as the connection between almost all warrants the probability. Right? My cat is probably outside. If it turns out that my cat is inside, was I incorrect? I would have been incorrect had I said my cat is outside...if instead it's inside, but if my conclusion is about probability, then I don't see that what is actually the case is relevant.

Picture a man sitting on the sofa in his living room. His cat is on his lap. He is petting his cat. And he explains this theory about the cat: "This is my cat here. Nice kitty. Usually, at this time of day, my cat is outside, not here on my lap as he is today. It stands to reason, then, that my cat is probably outside right now, rather than on my lap. In fact, the force of that logic is so great that I actually believe my cat is outside rather than here. Yes, nice kitty. Daddy loves you, but your purring isn't fooling me into thinking you're really here. Kitchy kitchy."

You can think that's good logic if you want. I'll continue to think it's nuts.

As for your example, when you thought your cat was outside when it really wasn't, I'll assume that that was a good example of when the proposed was reasonable.

- 1. Almost all F are G;
- 2. a is F;
- 4. Therefore, a is probably G.

That is, you didn't have any contradicting evidence.

- 3. We don't know anything else about a.

I'll agree with you that it is sometimes reasonable to conclude that if almost all F are G, and a is an F, that a is probably G. But it seems clear that this isn't always the case.

1. Almost all blacks are Democrats.
2. Colin Powell is a black.
3. Therefore, Colin Powell is probably a Democrat.

That's not good reasoning. If you think it's good reasoning, how do you cope with this:

1. Almost all military types are Republicans.
2. Colin Powell is a military type.
3. Therefore, Colin Powell is probably a Republican.

So now, if the argument is always good, we have proven that Colin Powell is probably both a Republican and a Democrat. But in fact we know that this is improbable. This form of argument could easily be made to produce a multitude of other contradictions and absurdities. Therefore, we know that arguments of that form are not always reasonable.

I'm going to throw something at you! I said, "if it turns out".

If I reasonably conclude that something is probably the case, then my conclusion wasn't therefore unreasonable simply because I later discover that what I thought was probably the case isn't actually the case.

 

[Wiploc]

Agreed.

 

[fast]

Agreed.

Progress

If my conclusion that says something is probably the case (not, 'is' the case but 'probably' the case), and if there was good reason to think it is probably the case, then wouldn't we say the conclusion was (actually a tenseless 'is', but we'll let that go for now) actually true even though we later discover that it isn't the case and obviously not now probably the case?

 

[Wiploc]

Agreed.

Progress

If my conclusion that says something is probably the case (not, 'is' the case but 'probably' the case), and if there was good reason to think it is probably the case, then wouldn't we say the conclusion was (actually a tenseless 'is', but we'll let that go for now) actually true even though we later discover that it isn't the case and obviously not now probably the case?

Having some trouble understanding your question. I'm guessing that the following scenario will be on point, but you can tell me if I'm wrong about that.


Morning: Fast and wiploc launch into space in a two-man vehicle.

Noon: Joe said, "It will probably rain today." His opinion seemed well-founded. Neither of us would have faulted his reasoning at that time.

Midnight: The day is over, and it never rained. It never rained because, immediately after noon, the earth was demolished to make way for a hyperspace bypass. Joe had no reason to suspect that the earth would be demolished.

Next morning: Fast and wiploc, the only survivors, have the following conversation:


Fast: Joe's opinion was reasonable, right?

Wip: Yes.

Fast: His logic was good?

Wip: Yes.

Fast: It was true that it would probably rain?

Wip: It certainly seemed true at the time.

Fast: If something seems probable, then it is probable, right?

Wip: Uh ...

Fast: I mean, given all the information that we had and should have had at the time, it seemed like it would rain.

Wip: Yes.

Fast: So it was fair to conclude that it was probably going to rain.

Wip: Yes.

Fast: It's true, then, that it was probably going to rain?

Wip: You know that it didn't rain, right?

Fast: And you know that, given all the evidence we had or should have had, it looked like it was going to?

Wip: Yes.

Fast: So it was probably going to rain.

Wip: We can't say that. We already know that it didn't rain.

Fast: So Joe was wrong? It was never true that it was probably going to rain?


So I dunno, Fast, am I on the right track? Does this have to do with what you're asking?

 

[Speakpigeon]

Maybe we're missing a premise? Perhaps:

1. Almost all F are G;
2. a is F;
3. We don't know anything else about a.
4. Therefore, a is probably G.

Exellent. That's it.

I would put it a bit differently:
1. Almost all F are G;
2. a is F;
3. We don't know anything that would entail that a isn't G;
4. Therefore, a is probably G

EB

 

[Speakpigeon]

but if my conclusion is about probability, then I don't see that what is actually the case is relevant.

What you dont realize is that the conclusion of these types of arguments is about your information, not about what is really the case.

Agreed.
EB

 

[Speakpigeon]

Going back to one of the other argument discussed:

P1: Almost all Americans are poorer than Bill Gates.
P2: Bill Gates is an American.
C: Therefore, Bill Gates is probably poorer than Bill Gates.

Here we know Bill Gates is not poorer than himself.

So, with the additional premise P3, we can say that the conclusion doesn't follow because P3 is false:
P1: Almost all Americans are poorer than Bill Gates;
P2: Bill Gates is an American;
P3: We don't know anything that would entail that Bill Gates is not poorer than Bill Gates;
C: Therefore, Bill Gates is probably poorer than Bill Gates.

Any objection?
EB

 

[Wiploc]

Maybe we're missing a premise? Perhaps:

1. Almost all F are G;
2. a is F;
3. We don't know anything else about a.
4. Therefore, a is probably G.

Exellent. That's it.

I would put it a bit differently:
1. Almost all F are G;
2. a is F;
3. We don't know anything that would entail that a isn't G;
4. Therefore, a is probably G

EB

Good, that's better than mine.

 

[fast]

Agreed.

Progress

If my conclusion that says something is probably the case (not, 'is' the case but 'probably' the case), and if there was good reason to think it is probably the case, then wouldn't we say the conclusion was (actually a tenseless 'is', but we'll let that go for now) actually true even though we later discover that it isn't the case and obviously not now probably the case?

Having some trouble understanding your question. I'm guessing that the following scenario will be on point, but you can tell me if I'm wrong about that.


Morning: Fast and wiploc launch into space in a two-man vehicle.

Noon: Joe said, "It will probably rain today." His opinion seemed well-founded. Neither of us would have faulted his reasoning at that time.

Midnight: The day is over, and it never rained. It never rained because, immediately after noon, the earth was demolished to make way for a hyperspace bypass. Joe had no reason to suspect that the earth would be demolished.

Next morning: Fast and wiploc, the only survivors, have the following conversation:


Fast: Joe's opinion was reasonable, right?

Wip: Yes.

Fast: His logic was good?

Wip: Yes.

Fast: It was true that it would probably rain?

Wip: It certainly seemed true at the time.

Fast: If something seems probable, then it is probable, right?

Wip: Uh ...

Fast: I mean, given all the information that we had and should have had at the time, it seemed like it would rain.

Wip: Yes.

Fast: So it was fair to conclude that it was probably going to rain.

Wip: Yes.

Fast: It's true, then, that it was probably going to rain?

Wip: You know that it didn't rain, right?

Fast: And you know that, given all the evidence we had or should have had, it looked like it was going to?

Wip: Yes.

Fast: So it was probably going to rain.

Wip: We can't say that. We already know that it didn't rain.

Fast: So Joe was wrong? It was never true that it was probably going to rain?


So I dunno, Fast, am I on the right track? Does this have to do with what you're asking?

Yes, very much on track.

I think the probability is independent of actuality. The probability that a die will land on an odd number is independent of the fact of what it lands on. Knowledge after the fact along with the language we use misleads us into thinking we're saying one thing when we're not

Let's say we're in the front yard and take a quarter and throw it across the top of a house and it lands normally on one of it's sides in the back yard. What's the probability that it'll land on tails? Now that it's landed, what's the probability that it landed on tails? You can't go look. Of course, there's no chance it landed on tails if it landed on heads and vice versa, so it's not knowledge itself (should you go look) that determines the probability, for our knowledge or lack thereof won't change the facts. Recall earlier I mentioned something about the tenseless 'is'. When we speak of the probability of something happening, we can't treat the truth of the matter as if it's temporal in nature. When I say my car is in the parking lot, it's either true or false, but don't confuse the utterance of that truth with another identical sentence made at a later time, for although the sentence remains the same, the proposition changes, for the sentence is actually shorthand for a much more precise sentence that includes things like temporal and spatial qualities, to name a couple.

The problem is magnified when speaking of probabilities, and I'm typing one letter at a time on an iPad mini.

 

[Speakpigeon]

Fast, Juma already put it in a nutshell:

but if my conclusion is about probability, then I don't see that what is actually the case is relevant.

What you dont realize is that the conclusion of these types of arguments is about your information, not about what is really the case.

In other words, probability is based on the information you have. New information, new probabilities.

Further, since you hold that what matters are not sentences but context-dependent propositions, the same set of sentences will point at a different argument each time you happen to access new information. So, the following four sentences will point to a true argument when we don't know anything that entails that a isn't G, even if in fact a is not G, and to a false argument otherwise, even if in fact a is G. So, these arguments are not about the fact of the matter but about our being justified in assuming the conclusion, which sounds in effect a lot like validity to me:

1. Almost all F are G;
2. a is F;
3. We don't know anything that would entail that a isn't G;
4. Therefore, a is probably G

EB

 

[Wiploc]

Yes, very much on track.

I think the probability is independent of actuality.
...

Recall earlier I mentioned something about the tenseless 'is'.

Before I roll the dice, I can say, "I probably won't roll snake eyes."

After I roll, I can say, "Wow, I rolled snake eyes even though it was improbable." But I can't say --- if I did roll snake eyes --- "I probably didn't roll snake eyes."

 

[fast]

Yes, very much on track.

I think the probability is independent of actuality.
...

Recall earlier I mentioned something about the tenseless 'is'.

Before I roll the dice, I can say, "I probably won't roll snake eyes."

After I roll, I can say, "Wow, I rolled snake eyes even though it was improbable." But I can't say --- if I did roll snake eyes --- "I probably didn't roll snake eyes."

i agree.

The probability of rolling snake eyes doesn't change even after one rolls and lands. Recall, "wow, I rolled ... Was improbable"

 

[fast]

Fast, Juma already put it in a nutshell:

but if my conclusion is about probability, then I don't see that what is actually the case is relevant.

What you dont realize is that the conclusion of these types of arguments is about your information, not about what is really the case.

In other words, probability is based on the information you have. New information, new probabilities.

Further, since you hold that what matters are not sentences but context-dependent propositions, the same set of sentences will point at a different argument each time you happen to access new information. So, the following four sentences will point to a true argument when we don't know anything that entails that a isn't G, even if in fact a is not G, and to a false argument otherwise, even if in fact a is G. So, these arguments are not about the fact of the matter but about our being justified in assuming the conclusion, which sounds in effect a lot like validity to me:

1. Almost all F are G;
2. a is F;
3. We don't know anything that would entail that a isn't G;
4. Therefore, a is probably G

EB

i somehow think there are some disconnections in the form of that argument, but either way, I think it's the wording of the conclusion that's problematic. The underlying assumption is that the likelyhood of something is increased by the fact something is almost always the case. The probability that something would have happened given the conditions isn't altered by the fact things didn't turn out as we thought they probably would. Perhaps the conclusion should read differently to reflect that.

Back to the coin toss. Anna tosses a coin and doesn't know what it lands on, but Bob does know what it lands on. The probability of what it might have landed on isn't changed by Bob's knowledge of what it landed on. Sure, if Bob says there's a 50% possibility that it's on heads when he clearly sees that it's on tails, he's wrong, but guess what, if it's on tails, Anna is also wrong to say there's a 50% chance that it's on heads. Her lack of knowledge doesn't alter the possibility of what it's on. Again, the probability is in regards not to what is actually the case but of what might or may happen.

 

[Speakpigeon]

Yes, very much on track.

I think the probability is independent of actuality.
...

Recall earlier I mentioned something about the tenseless 'is'.

Before I roll the dice, I can say, "I probably won't roll snake eyes."

After I roll, I can say, "Wow, I rolled snake eyes even though it was improbable." But I can't say --- if I did roll snake eyes --- "I probably didn't roll snake eyes."

And I also can't say, "So snake eyes were probable after all"! Instead, it's still true that snake eyes were improbable.

Also, discovering the results of coin-tossing and dice-rolling is something different from knowing something about the conclusion which is already the case, as with the 1000kg-dog or Bill Gates. I think the equivalent would be to know in advance that the dice are loaded so that the conclusion "I probably won't roll snake eyes" is not only wrong from the start but we know it's wrong.
EB

 

[Speakpigeon]

In other words, probability is based on the information you have. New information, new probabilities.

Further, since you hold that what matters are not sentences but context-dependent propositions, the same set of sentences will point at a different argument each time you happen to access new information. So, the following four sentences will point to a true argument when we don't know anything that entails that a isn't G, even if in fact a is not G, and to a false argument otherwise, even if in fact a is G. So, these arguments are not about the fact of the matter but about our being justified in assuming the conclusion, which sounds in effect a lot like validity to me:

1. Almost all F are G;
2. a is F;
3. We don't know anything that would entail that a isn't G;
4. Therefore, a is probably G

EB

i somehow think there are some disconnections in the form of that argument, but either way, I think it's the wording of the conclusion that's problematic. The underlying assumption is that the likelyhood of something is increased by the fact something is almost always the case. The probability that something would have happened given the conditions isn't altered by the fact things didn't turn out as we thought they probably would. Perhaps the conclusion should read differently to reflect that.

I don't see any disconnection here. Remember, given the premises, the conclusion follows (as far as I can see).

And again, the argument is time-stamped. It's valid at the moment it's asserted. But we can make another argument once we know a isn't a G after all:

1. Almost all F were G;
2. a was F;
3. We didn't know anything that entailed that a wasn't G although we now know it isn't;
4. Therefore, a was probably G (at the time)

However, it does hinge on our theory of probabilities. Here, "a was probably G" means that at the time stating that a was G was our most rational choice given what we knew at the time. If we switch to an absolute perspective (God's view) then we have to ditch the word "probably" and take the argument as an invalid deduction:
1. Almost all F are G;
2. a is F;
3. Therefore, a is G.

EB

 

[Speakpigeon]

Back to the coin toss. Anna tosses a coin and doesn't know what it lands on, but Bob does know what it lands on. The probability of what it might have landed on isn't changed by Bob's knowledge of what it landed on. Sure, if Bob says there's a 50% possibility that it's on heads when he clearly sees that it's on tails, he's wrong, but guess what, if it's on tails, Anna is also wrong to say there's a 50% chance that it's on heads. Her lack of knowledge doesn't alter the possibility of what it's on. Again, the probability is in regards not to what is actually the case but of what might or may happen.

That's a God's view of probabilities. But probabilities are based on what we think we know. Given what she thinks she knows, Anna is correct to say there a 50% chance it's "head". Our best scientists would do the same. Bod however knows it's "tail" so he would be wrong to maintain the same claim as Anna.

I think that if you switch to absolute probabilities based on what is the case rather than on what we know or think we know then you have to ditch all inductive arguments because they will be always wrong.
EB

 

[fast]

Back to the coin toss. Anna tosses a coin and doesn't know what it lands on, but Bob does know what it lands on. The probability of what it might have landed on isn't changed by Bob's knowledge of what it landed on. Sure, if Bob says there's a 50% possibility that it's on heads when he clearly sees that it's on tails, he's wrong, but guess what, if it's on tails, Anna is also wrong to say there's a 50% chance that it's on heads. Her lack of knowledge doesn't alter the possibility of what it's on. Again, the probability is in regards not to what is actually the case but of what might or may happen.

That's a God's view of probabilities. But probabilities are based on what we think we know. Given what she thinks she knows, Anna is correct to say there a 50% chance it's "head". Our best scientists would do the same. Bod however knows it's "tail" so he would be wrong to maintain the same claim as Anna.

I think that if you switch to absolute probabilities based on what is the case rather than on what we know or think we know then you have to ditch all inductive arguments because they will be always wrong.
EB

What I would like to see is the wording of a true conclusion such that it's identical for both Anna and Bob. What it's on needs to go out the window. Bob needs to be more concerned about future throws and not let his knowledge of the first throw lead him to think that knowledge of what happened somehow has an effect on probabilities.