Doug,

Intersting stuff! Obviously, I haven’t studied any of this formally, as you have, so my “subjectivism” is just an intuitive position I’ve come to over time, and probably not well thought out. Sorry if I’m making you go through a rudimentary philosophy lesson here.

I certainly don’t believe that our thoughts influence how reality is, so the idea that without us to define logic reality would be somehow other than it is makes no sense to me. I tend to think of mathematics (and logic, which I have even less knowledge of) as systems a bit like language. We invented them to describe reality and to allow understanding and prediction of its properties. As such, the systems have a strong connection to what reality actually is. But just as the verbal language by which we describe a thing doesn’t constitute the thing itself, only a representation of it that we can manipulate and that may not embody all of the thing’s properties, so mathematics represents things and processes/rules of reality but of course it cannot be these things.

I would say that we can’t really be sure arithmetic works “all the way up,” as you say, just as we found Newtonian laws didn’t apply “all the way down” to the subatomic scale. A certain amount of uncertainty is built into scientific “truth,” and this is a good thing because it keeps us open to the idea that such truths may need to be revised. A fair degree of certainty can develop when a law we formulate to describe reality proves consistently accurate over time, but a small corner of doubt can remain and be useful. Based on some of your other posts, it would seem that as an “objectivist” you would apply this principle to most empirical science, but stop at the borders of logic, in which the laws we formulate are not simply heuristically useful representations but essentially the truth about the underlying reality. While I would apply a pretty high degree of certainty to such laws, I don’t think I can go as far as to say they really are inviolable principles of reality we have discovered. To me they seem like very useful and reliable descriptions, but still the products of our cognitive systems and so subject to the limitations of those systems, whether we are able to recognize them or not.

For me, as an empirical scientist, the degree of uncertainty here is not great enough to meaningfully affect what I do. But as a philosopher, perhaps your work requires more than just empirically reliable approximations, and you feel you can and should try for the absolutely true. 

[quote author="mckenzievmd"]I certainly don’t believe that our thoughts influence how reality is, so the idea that without us to define logic reality would be somehow other than it is makes no sense to me. I tend to think of mathematics (and logic, which I have even less knowledge of) as systems a bit like language. We invented them to describe reality and to allow understanding and prediction of its properties. As such, the systems have a strong connection to what reality actually is. But just as the verbal language by which we describe a thing doesn’t constitute the thing itself, only a representation of it that we can manipulate and that may not embody all of the thing’s properties, so mathematics represents things and processes/rules of reality but of course it cannot be these things.

Yes, well, certainly we came up with the particular language (terms, names); but this is on all fours with physics. Physics is, in one sense, a purely human invention. But that doesn’t mean it doesn’t reflect objective reality—as though we might not have had the law of gravity if we’d written the rules differently.

Another thought experiment: any other alien intelligence that wanted to describe the world would have come up with substantially the same physical laws as we had. That’s because we would be keying off the same underlying reality.

Now, the difficulty with our notions of physical laws (as embodied in physics, for example) is that they aren’t perfect. They are accurate up to a very high degree, but high accuracy isn’t the same as perfection. And they are always amenable to disconfirmation if further experiments show them to be wrong.

Now, there is no sense to be made of logical theorems being approximately true—either they are proved, in which case they are 100% true, or they are disproved, in which case they are 100% false. (Or, epistemologically, they haven’t been proved or disproved). Now, we could be wrong about any given proof, that’s true, but if the proof is good, the theorem is 100% true. There is never the same degree of certainty about physics, because physical demonstrations aren’t logical demonstrations; they rely either on probabilistic induction or explanatory abduction (inference to the best explanation). Neither of those two latter methods of reasoning is logically valid.

[quote author="mckenzievmd"]I would say that we can’t really be sure arithmetic works “all the way up,” as you say, just as we found Newtonian laws didn’t apply “all the way down” to the subatomic scale. A certain amount of uncertainty is built into scientific “truth,” and this is a good thing because it keeps us open to the idea that such truths may need to be revised.

Hmmm ... so, if you were an engineer working on a large building and had to do some mammoth addition operation, you would then want to be sure that “addition worked that far up” before you’d OK the plans?

How would you go about running that experiment? Surely you’d want then to add numbers a little smaller than your target number, check those results, add numbers a little larger, check those, and do some sort of statistical check? But how could you be sure your statistical check “worked that far up”?

To my mind this looks like an absurd method, and I’d expect that any engineer who started doubting addition with large numbers would be laughed at by his peers ... IMO with good reason ...

[quote author="mckenzievmd"]Based on some of your other posts, it would seem that as an “objectivist” you would apply this principle to most empirical science, but stop at the borders of logic, in which the laws we formulate are not simply heuristically useful representations but essentially the truth about the underlying reality.

Right. Laws of logic are not “approximately true”. They are absolutely true given the axioms. (We may ask, of course, whether the axioms apply in a given situation, but that is a separate question). The point is that we don’t do any sort of empirical experiment to decide whether they are true. Their truth doesn’t rely on experience of the world. They are built into cognition, experience, reality itself.

[quote author="mckenzievmd"]While I would apply a pretty high degree of certainty to such laws, I don’t think I can go as far as to say they really are inviolable principles of reality we have discovered. To me they seem like very useful and reliable descriptions, but still the products of our cognitive systems and so subject to the limitations of those systems, whether we are able to recognize them or not.

Well yes, but I would put the role of our limited cognition into the question of whether we can be certain that any given proof is good or not. We can always sustain doubts—particularly, as I said before, about complex proofs or mathematical operations.

Hmmm ... so, if you were an engineer working on a large building and had to do some mammoth addition operation, you would then want to be sure that “addition worked that far up” before you’d OK the plans?

How would you go about running that experiment? Surely you’d want then to add numbers a little smaller than your target number, check those results, add numbers a little larger, check those, and do some sort of statistical check? But how could you be sure your statistical check “worked that far up”?

To my mind this looks like an absurd method, and I’d expect that any engineer who started doubting addition with large numbers would be laughed at by his peers ... IMO with good reason ...

Well, I believe you orginially said something like number “bigger than we can conceive.” All I was suggesting was that scale seems to make a difference in the extent to which certain physical laws apply, as quantum effects illustrate. However large a building was, I doubt it would be built on scales sufficiently different from the everyday to escape the physical laws that apply at the scales we’re used to since, presumably, it would be built for human beings. Anyway, the example is not important, only the general idea that scale might influence concepts that we see as fundamental and immutable in ways we don’t anticipate. I’m not suggetsing that addition really is different when handling vast numbers.

Anyway, I do see what you’re saying, and of course I can’t offer an example of some situation in which the rules of logic and mathematics don’t apply, since the very heart of my question is how can we know anything about such a circumstance if it is beyond our cognitive capacity. So it gets pretty academic pretty fast when you qualify and “subjunctify” every statement. Thanks for your replies.

[quote author="mckenzievmd"]Well, I believe you orginially said something like number “bigger than we can conceive.”

Quite so, although surely the operation would be equally necessary for numbers larger than we had ever added before. I mean, it would end up being a new experiment, to see if it worked.

[quote author="mckenzievmd"] All I was suggesting was that scale seems to make a difference in the extent to which certain physical laws apply, as quantum effects illustrate.

Well, but in the case of physical objects, we do end up taking them apart in a sense, and it is an empirical question what we find on the inside.

With large numbers, all that is necessary is recursion (like adding one to a previous large number), so there is nothing that is in principle unknown about what large numbers would be like.

There are also well-founded proofs about orders of infinity, that depend on recursion. (E.g., that the real numbers constitute a larger order of infinity than the rational numbers, or than the cardinal numbers, etc.) I can’t see how these sorts of proofs would be valid on a subjectivist interpretation, which is a real problem.

[quote author="mckenzievmd"]Anyway, I do see what you’re saying, and of course I can’t offer an example of some situation in which the rules of logic and mathematics don’t apply, since the very heart of my question is how can we know anything about such a circumstance if it is beyond our cognitive capacity. So it gets pretty academic pretty fast when you qualify and “subjunctify” every statement. Thanks for your replies.

Sure, as I say, I do see a place for our cognitive capacities—it is in whether we have actually got the proofs right. To that extent mathematics is on all fours with physics. We can always be wrong about the validity of a proof just as we can always be wrong about the physical facts.

It’s just that logic is a different sort of enterprise from experimental science. It isn’t empirical, and the proofs it provides, if true, are true always, everywhere and in every conceivable world.

[quote author="dougsmith"]

“Truth” is a property of linguistic items. “Absolute truth” is a confusing thing, since people mean different things by it. Some people mean to make metaphysical claims by the word “absolute”, and others mean to make epistemological claims.

A metaphysical claim:  “Absolute truths” are truths that could not have been false. E.g., 2+2 = 4 is an “absolute truth” since 2+2 could not have equalled anything other than 4. “Bigfoot does not exist” is not an “absolute truth” since bigfoot might have existed, even if in fact he does not. In this sense, all logical and mathematical truths are absolute.

An epistemological claim: “Absolute truths” are truths that we can know are true with 100% probability. But then we get into difficulties, and it is not clear that there are any really “absolute” truths.

Right, so as I think you’ve previously stated, what I have been doing is mixing up metaphysical truth with epistemological truth.

in my mind I have been logical and coherent and in a way I have but only because I’ve been switching between these two modes of thinking automatically without knowing I’ve been doing it This could only look incoherent to any one reading my posts.

It is that which has made me incoherent as I need to stick to a mode of logic or be clear when switching between modes.

So It is true that big foot does not exist cannot be an absolute truth but never the less if it is true then there is zero probability of his existing or it is impossible for him to exist and this is correct as long as I use the correct mode of logic.

It is true that big foot does not exist and it is true that he might exist can also be coherent as long I use the correct mode of logic.

It is impossible for big foot to exist and he might exist could both be true but I’d have to explain which mode of logic I was using in each case. Not that I’d want to now I know where the confusion lies but it clears up what the confusion has been.

Do you think this suming up of the situation so far is about right?

Stephen

[quote author="StephenLawrence"]Do you think this suming up of the situation so far is about right?

Well, you know better what you were trying to say. But it certainly could be.

The issue isn’t so much of logic per se as of clarity. That is, getting clear on whether what we’re discussing is an issue of metaphysics (the way the world is) or epistemology (the way we learn about the world).

[quote author="dougsmith"][quote author="StephenLawrence"]
The issue isn’t so much of logic per se as of clarity. That is, getting clear on whether what we’re discussing is an issue of metaphysics (the way the world is) or epistemology (the way we learn about the world).

Sorry I’m afraid I still haven’t got this.

Thanks for the two definitions that helps.

1)Big foot does not exist, if true can mean there is a 0 in a million possibility that he exists or in fact a zero possibility that he exists or put in another way that it is impossible that he exists.

2)But another way of looking at it, is that big foot does not exist but he might.

I hope my thought of having a bet helps.

There is a sense in which I would be wasting my money if I bet. We have agreed on that and that is how I mean ‘impossible’ in 1) (this is leaving aside the fact big foot does not exist is not an absolute truth)

2) is also true and so it is possible that big foot exists.

I thought what I was doing was mixing up modes of logic?

Stephen

Good morning Doug,

There is something I’m trying to find out which I’m sure is very simple but somehow I must be making a hash of trying to explain myself.

I’ll have another go today.

Mr Jones arrives home from work to find Mrs Jones waiting on the doorstep.

He says “good evening dear” opens the door and they walk in.

He asks her why she didn’t let herself in with her own key.

She explains that she COULDN’T open the door with her key because she forgot to put her key in her purse this morning and it was left on the dining room table.

Mr Jones agrees that she couldn’t but points out that she COULD if she had remembered to put the key in her purse.

Mrs Jones agrees with Mr Jones.

What Mr Jones and Mrs Jones have done is agreed that she could and agreed that she couldn’t.

But Doug surely this is not a contradiction?

Surely both are right?

I wondered if these different ways of looking at it were different modes of logic perhaps?

If not what is the explanation?

Imagine Mr Jones came home from work and asks Mrs Jones to put her key in the lock. She explains that she can’t. He asks her again, again she says she can’t. He starts to get very angry, “it is possible for you to put your key in the lock, now do it!”

Now we can both see Mr Jones would be wrong.

He might be right to say that it is possible for Mr Jones to put the key in the lock.

But Mrs Jones surely knows that it is impossible for her, she couldn’t do it even if her life depended upon it because her key is inside the house on the dining room table.

Surely Mrs Jones can say she is unable to put her key in the lock without this meaning she believes everything happens necessarily and without it being a contradiction or incoherent?

Stephen

[quote author="StephenLawrence"]He asks her why she didn’t let herself in with her own key.

She explains that she COULDN’T open the door with her key because she forgot to put her key in her purse this morning and it was left on the dining room table.

Mr Jones agrees that she couldn’t but points out that she COULD if she had remembered to put the key in her purse.

Mrs Jones agrees with Mr Jones.

What Mr Jones and Mrs Jones have done is agreed that she could and agreed that she couldn’t.

But Doug surely this is not a contradiction?

It certainly appears to be a contradiction, however there is a suppressed conversational implication here—one is saying, “I couldn’t because X”, the other is saying, “You could because Y.” And these aren’t contradictory.

“Could” and “couldn’t” here are basically tracing the causal antecedents to the proposed action. One says, “I couldn’t GIVEN the fact that the key is in a location I cannot access.” (Or something like that). The other says, “You could GIVEN the possibility that you had caused the key to be in your possession.” (Or something like that).

[quote author="StephenLawrence"]Surely both are right?

Yes.

[quote author="StephenLawrence"]I wondered if these different ways of looking at it were different modes of logic perhaps?

I don’t know what you mean by “modes of logic”. These can both be formalized using something called “modal logic”, but I don’t think that’s what you mean.

[quote author="StephenLawrence"]Imagine Mr Jones came home from work and asks Mrs Jones to put her key in the lock. She explains that she can’t. He asks her again, again she says she can’t. He starts to get very angry, “it is possible for you to put your key in the lock, now do it!”

Now we can both see Mr Jones would be wrong.

He might be right to say that it is possible for Mr Jones to put the key in the lock.

But Mrs Jones surely knows that it is impossible for her, she couldn’t do it even if her life depended upon it because her key is inside the house on the dining room table.

Surely Mrs Jones can say she is unable to put her key in the lock without this meaning she believes everything happens necessarily and without it being a contradiction or incoherent?

Obviously. It’s possible GIVEN certain antecedent conditions. Had these conditions been such-and-so she would have been able to do it. Had she been in the closest possible world to this one where she’d remembered to take the key, she’d have been able to open the door.

Her husband can be annoyed at her that she forgot, but GIVEN that she’s forgotten (I.e. given that she’s not in the world where she’d remembered), it will be impossible for her to unlock the door without a lockpick.

Where we are now in the world is the result of a very long causal chain stretching into the past. That causal chain could have been different at any point along its path. Further, it could have been different at each point in many different ways. All of those different paths (and more) constitute different possible worlds. When we talk about non-actualized physical possibility we are talking about these paths-not-taken. Hence on one path something might have been possible while on another path it might not. There is no contradiction here.

[quote author="dougsmith"]

I don’t know what you mean by “modes of logic”. These can both be formalized using something called “modal logic”, but I don’t think that’s what you mean.

Modes of logic is a concept which exist in all possible worlds where I invented it :oops:

I doubt whether it will catch on.

Stephen

[quote author="dougsmith"]

Obviously. It’s possible GIVEN certain antecedent conditions. Had these conditions been such-and-so she would have been able to do it. Had she been in the closest possible world to this one where she’d remembered to take the key, she’d have been able to open the door.

Her husband can be annoyed at her that she forgot, but GIVEN that she’s forgotten (I.e. given that she’s not in the world where she’d remembered), it will be impossible for her to unlock the door without a lockpick.

Where we are now in the world is the result of a very long causal chain stretching into the past. That causal chain could have been different at any point along its path. Further, it could have been different at each point in many different ways. All of those different paths (and more) constitute different possible worlds. When we talk about non-actualized physical possibility we are talking about these paths-not-taken. Hence on one path something might have been possible while on another path it might not. There is no contradiction here.

Ok, so this is where I get stuck.

Mrs Jones has the ability to put her key in the door lock.

Trouble is she can’t.

That is why I would call this an unusable ability.

Now if an unusable ability looks like a contradiction it is not, if we take it to mean able to but can’t in this case because the key is on the dining room table.

What I can’t understand is what use is this ability to mrs Jones? Or any of us?

Stephen

[quote author="StephenLawrence"]Mrs Jones has the ability to put her key in the door lock.

Trouble is she can’t.

Without the key, she doesn’t have the ability to put the key into the lock. What she has is the ability to put the key into the lock given that she has the key. But she doesn’t have the key.

(When we say “she has the ability to put the key into the lock” it is understood that we believe she already has the key).

Put another way, if her husband were to learn that she didn’t have the key, and nonetheless say to her, “Go ahead, put the key into the lock, you have the ability!” we would think he was crazy.

[quote author="dougsmith"]

Put another way, if her husband were to learn that she didn’t have the key, and nonetheless say to her, “Go ahead, put the key into the lock, you have the ability!” we would think he was crazy.

I must apologise to my wife for an incident that happened the other day when I came home and found her waiting on the doorstep..................

Stephen

[quote author="StephenLawrence"]I must apologise to my wife for an incident that happened the other day when I came home and found her waiting on the doorstep..................

[quote author="dougsmith"]
Without the key, she doesn’t have the ability to put the key into the lock. What she has is the ability to put the key into the lock given that she has the key. But she doesn’t have the key.

I thought she had the ability to put the key in the lock because she could do so in other possible worlds.

So she had the ability to do otherwise even though in this case she couldn’t because the keys were on the dining room table.

If we go back to the man drinking tea from the FW thread.

I would say he didn’t have the ability to drink coffee because he didn’t have a bad experience with tea when he was a boy.

And you would say that he did have the ability and if I thought he didn’t it meant I believed everything happened necessarily.

The way I think he didn’t have the ability is the same as the way we both think Mrs Jones didn’t have the ability.

If I could understand the difference between the Mrs Jones case and the man who drank tea’s case, then we could really make some progress.

Stephen