Immaterial aspects of thought

[Bob_Crowley]

Or another point might be: Isn’t memory subject to a similar sort of proof/capable of being the source for a generalization of the proof in question? We generally know what we are remembering, that is, some particular ‘thing’ that is “incompossibly determinate” in relation to anything else, and which cannot be effectively designated as such by the merely formal ‘representations’ of a machine?

Until you have an embolism or a severe head injury, and you can’t remember your tables.

 

[warpspeedpetey]

He put sixteen objects on a table, and divided them up into four equal groups of four. Or he found that if he had four lots of four objects, and lined them up one after the other, he had to count to sixteen to cover them all.

ok, how does this square with the earlier statement “It’s merely a memory exercise”?

 

[AndyT_81]

Thanks all for your comments so far.

hatsoff,

I hesitate to repeat this point, because I doubt it is necessary to discuss the argument, but I feel like I must remind you that modus ponens is not literally a “form] of thought,” but rather a logical inference.

Ok, but what is a logical inference, if not a process/form of thought?

At best you could say that modus ponens models some thinking, but even then you’d be making some steep assumptions with which I for one am not at all comfortable.

I would say that modus ponensIf I’ve understood you correctly (which is not at all certain), then I don’t see how that’s any different from human brains. No matter how unlikely it appears, there’s always the chance that we’re wrong even about something as seemingly straightforward as, say, modus ponens, to extend your analogy. But of course we can still know with as much or nearly as much confidence that a machine operates in a particular way as we can that one’s own mind operates in another particular way.

Is there really a chance that we can be wrong with a formal argument such as modus ponens? Sure, we can substitute incorrect values/states into p and q, but can the form of the argument ever be wrong? I don’t see how it can. Let me try to illustrate. Let p be “I turn a tap on” and q “water comes out”, so via modus ponens:

If I turn a tap on, then water comes out
I turn a tap on
therefore water comes out

Now, of course, it may not be necessary that whenever I turn a tap on water comes out, therefore the argument may fail in certain circumstances, however the form of the argument is truth preserving. If I turned a tap on and water didn’t come out, I wouldn’t doubt the form of the argument, the form is always vaild, rather I would doubt the first premise. Let me try another example, this time with inductive uncertainty removed: p is “Fred is not married” and q is “Fred is a bachelor”

If Fred is not married, then Fred is a bachelor
Fred is not married
Therefore Fred is a bachelor

I would ask you how we could ever be wrong about this? Where could any un-certainty in indeterminate-ness come into this? When we use this form of reasoning, it is definite, there is no ambiguity with regards to the functional form. If you were to say that we are actually indeterminate with regards to the form of this thought process, you would have to be determinate with that thought process in which you issue your denial.

Contrast this with a machine which performs modus ponens. Say this machine consistently spits out a red chip whenever a blue chip is inserted into it. We can never be definite about the truth-preserved-ness of whatever function the machine is performing. One day it may start spitting out blue chips when blue chips are inserted, or blue chips when a red chip followed by a blue chip is inserted, or blue chips when red chips are inserted at a rate of 60 per minute etc. This indeterminism/indefinite-ness is in stark contrast to what we are doing when we think in the form of modus ponens.

I still don’t know what “inherently indeterminate between mutually exclusive functions” is supposed to mean.

Notice all the functions that I listed above:

if Vb > y, Vout > 0V, else Vout=0V
if Vb > y, Vout > 0V, else Vout=0V only if t<1e6 hours after the transistor is created, otherwise Vout < 0V
if Vb > y, Vout >0V, else Vout=0V only if t<1e7 hours after the transistor is created, otherwise Vout = 10V
etc.

These functions cannot all be the case, i.e. only one of them can, therefore they are mutually exclusive. However, we cannot differentiate between them by simply looking at the (name removed by moderator)uts and outputs of the process, as the (name removed by moderator)uts and outputs give equal support for any of these functions (at least, if we are examining the transistor within 1e6 hours after its creation). That is what is meant by indeterminate. Hope that clears things up.

Are you just saying that it’s possible we’re making a mistake in our conception of a calculator’s mechanics?

No. What I am saying is that it is never possible to know which function is actual within the machine, for a finite number of observed (name removed by moderator)uts and outputs.

 

[AndyT_81]

Bob,

I see you hail from Queensland, me to!

So while I have no doubt there is immaterial thought (as the angels and deceased spirits would necessarily do), the above philosophical argument misses the point that all we do when we carry out arithmetic calculations is indulge in recalling our tables. It’s merely a memory exercise.

I would have to disagree here. Sure, we may recall some of the more basic additions, such as 5+5=10, but for more complicated sums, say 123+154, I don’t know about you, but I certainly don’t recall sums like these. When performing this addition, we perform certain formal rules with respect to said addition, all of which are truth-preserving for all numbers. There is no such determinated-ness for machines which perform this operation.

Betterave,

Or another point might be: Isn’t memory subject to a similar sort of proof/capable of being the source for a generalization of the proof in question? We generally know what we are remembering, that is, some particular ‘thing’ that is “incompossibly determinate” in relation to anything else, and which cannot be effectively designated as such by the merely formal ‘representations’ of a machine?

Good point.

 

[Bob_Crowley]

ok, how does this square with the earlier statement “It’s merely a memory exercise”?

Because for me, when I want to calculate 4 x 4, I refer to my old tables stuck away in my memory. I have no desire to re-invent the wheel and count out 16 objects every time.

I do not however go through a literal process of “calculating” 4 x 4. I recall that 4x4 give 16 from my memory. And so do you.

 

[Bob_Crowley]

Bob,

I see you hail from Queensland, me to!

I would have to disagree here. Sure, we may recall some of the more basic additions, such as 5+5=10, but for more complicated sums, say 123+154, I don’t know about you, but I certainly don’t recall sums like these. When performing this addition, we perform certain formal rules with respect to said addition, all of which are truth-preserving for all numbers. There is no such determinated-ness for machines which perform this operation.

Betterave,

Good point.

Greetings from Logan.

When we process these larger sums, we recall from memory certain rules that we learnt at school years ago eg. 3 + 4 = 7, with no carry. 2 + 5 = 7, with no carry. 1 and 1 = 2, with no carry, giving the sum of 277. At least I got that far with my Queensland education.

There is such determinedness for machines which perform this operation, as they operate along fixed lines. The (name removed by moderator)ut including the signs, eg. “*” predetermines what they’ll do, along with the circuitry.

The only intelligence which could is not predetermined would have to one which does not owe it’s origin to another intelligence and that is God. Even angels, while they may us intuitive and not deductive reasoning (I don’t see how they could frankly), owe their intelligence to a creator.

However I’ve said on a number of occasions that when my father died in Nundah (in Brisbane - if you’re a Brisbanite, you’ll know where that is) and appeared the same night and probably the very same time, in my bedroom in my flat in Yeronga, several kilometres away. He started with an apology, we argued and conversed, and then he gave this terrifying scream and disappeared. He no longer had a body, and yet not only could he talk but he could see some future events, eg. “You’ll meet a pastor. You’ll think he’s great, but all he’ll do is discourage you even more!” I met the pastor nearly four years later, and he apologised for discouraging me about 8 or 9 years after that. Yet in what would have been no more than a couple of minutes of total “spoken” exchange, he could see me meeting the pastor, and somehow intuitively realise the pastor would discourage me.

So as far as I’m concerned there is an immaterial aspect to mind, but I don’t think the fact we can do arithmetic or mathematics proves it. I think you’d have to look elsewhere for philosophical or metaphysical proof.

 

[warpspeedpetey]

Because for me, when I want to calculate 4 x 4, I refer to my old tables stuck away in my memory. I have no desire to re-invent the wheel and count out 16 objects every time.

I do not however go through a literal process of “calculating” 4 x 4. I recall that 4x4 give 16 from my memory. And so do you.

now im really confused. you dont seee the problem? addition can be pulled ffrom tables you have memorized, but it cannot be unless you have at some point done the actual arithmetic.

i know the times tables from memory, but that memory is from actually working it out in school.

you stated.

So while I have no doubt there is immaterial thought (as the angels and deceased spirits would necessarily do), the above philosophical argument misses the point that all we do when we carry out arithmetic calculations is indulge in recalling our tables. It’s merely a memory exercise.

clearly, arithmetic calculations are not merely a memory exercise.

 

[Bob_Crowley]

now im really confused. you dont seee the problem? addition can be pulled ffrom tables you have memorized, but it cannot be unless you have at some point done the actual arithmetic.

i know the times tables from memory, but that memory is from actually working it out in school.

you stated.

clearly, arithmetic calculations are not merely a memory exercise.

How many times at school did you “prove” 2 plus 2 makes 4? And if you did, what was your method?

For Bertrand Russell to merely prove 1 plus 1 equals 2, he went to quite a long rigorous proof (well beyond my very basic knowledge of philosophy, truth tables etc.) in his work “Principia Mathematica”. The average school kid would not even begin to go to such lengths, and would simply apply the memorised methods and tables he or she had imbibed.

And to say Russell must therefore have used “immaterial” aspects of mind means that Russell had a deeper field of immateriality in his mind than the average school kid. Yet he was a convinced atheist.

 

[hatsoff]

How many times at school did you “prove” 2 plus 2 makes 4? And if you did, what was your method?

A very good question. I can picture a room full of third-graders engaging the Peano axioms and difference relations. I doubt that picture has ever been instantiated in reality, however.

 

[warpspeedpetey]

How many times at school did you “prove” 2 plus 2 makes 4? And if you did, what was your method?

For Bertrand Russell to merely prove 1 plus 1 equals 2, he went to quite a long rigorous proof (well beyond my very basic knowledge of philosophy, truth tables etc.) in his work “Principia Mathematica”. The average school kid would not even begin to go to such lengths, and would simply apply the memorised methods and tables he or she had imbibed.

And to say Russell must therefore have used “immaterial” aspects of mind means that Russell had a deeper field of immateriality in his mind than the average school kid. Yet he was a convinced atheist.

i didnt need a mathematical proof, i was a kid. it was obvious to me that 2+2=4. simply gather 2 of this and 2 of that and count. just as the first person did. bertrand russel didnt invent mathematics. im not arguing for the immaterial aspects of mind. for me that is an obvious consequence of the appearance of free will. but thats another thread.

but as to his atheism, ive always questioned the rational depth of his rejection. in the debate with Fr. Copleston, he essentially dodges hierarchical causality. as intelligent as he was. i get the impression that he must have known it was a dodge. Copleston even said something to that effect. after reading the ‘mathematical experience’, ive come to realize that mathematicians are no more sure of their field than any other. i always thought it was ironclad.

 

[Betterave]

I didnt need a mathematical proof, i was a kid. it was obvious to me that 2+2=4. simply gather 2 of this and 2 of that and count. just as the first person did. bertrand russel didnt invent mathematics.

That sounds right to me. You objectors don’t really want to say that before one can properly be said to know that 1+1=2 (and that ‘1+1=2’ is just ‘1+1=2’ and nothing else) one must be familiar with the work of people like Russell and/or Peano? That strikes me as way absurd!

 

[Ghosty]

To this day I don’t use multiplication tables; I never memorized them as a kid and never bothered to as an adult.

When I calculate 4 x 4, I add four 4s in my mind, going 4 to 8 to 12 to 16. Oddly enough I’m faster at arithmatic than most folks I know.

Just thought I’d throw that out there.

 

[Bob_Crowley]

To this day I don’t use multiplication tables; I never memorized them as a kid and never bothered to as an adult.

When I calculate 4 x 4, I add four 4s in my mind, going 4 to 8 to 12 to 16. Oddly enough I’m faster at arithmatic than most folks I know.

Just thought I’d throw that out there.

Multiply 1575439543.65371 by 98560431.2589.

By the time you finish with your method, I should be on the pension. If you still want tutoring in maths tables, I might have the time to do some.

 

[Ghosty]

Multiply 1575439543.65371 by 98560431.2589.

By the time you finish with your method, I should be on the pension. If you still want tutoring in maths tables, I might have the time to do some.

I doubt you know the table for that one, either. Besides, I never said I multiplied everything in my head, I said when I do 4 x 4 I work it out each time (and same for most multiplication around the same level).

I just thought it was funny that you were so insistant that others use tables to work with problems as simple as 4 x 4, as you yourself do (nothing wrong with tables, either, they’re just not used by everyone). I do have a friend who does complex equations in his head in a split second (and says he’s not even concious of the process, it just kind of “comes out” correctly), faster than I can type it into a calculator, but his brain seems to wired in an unusual way. I’m tempted to put your math problem to him and see what happens.

How did we go from 4 x 4 to millions and billions?

Peace and God bless!

 

[AndyT_81]

Thanks for the further comments all.

Bob,

Multiply 1575439543.65371 by 98560431.2589.

By the time you finish with your method, I should be on the pension. If you still want tutoring in maths tables, I might have the time to do some.

I’m not sure what you mean by “maths tables”? To calculate the product of those two numbers, we would certainly need some sort of formal method to do so, is that what you mean by maths tables? The point I am trying to make in this thread (perhaps poorly!) is that the formal method you use is definite, by doing so you know that you are performing this method or function and no other. You also know that substituting any other number into this formal method, if done correctly, will give you a correct or truthful answer. In other words, your method is determinate amongst mutually exclusive methods, and is truth preserving for all (name removed by moderator)uts.

Contrast this with a multiplication machine. We can (name removed by moderator)ut numbers and get outputs which seem to simulate what we do with our formal methods, but there are an infinite number of functions, all mutually exclusive, that would still give the same results. This is true of any physical process. Therefore the machine/physical process is indeterminate amongst mutually exclusive functions/methods.

This is in stark contrast to our thoughts of formal methods, and therefore, these thoughts at least can not be wholly the result of physical processes.

That’s the argument anyway.

 

[hatsoff]

Thanks for the further comments all.

Bob,

I’m not sure what you mean by “maths tables”? To calculate the product of those two numbers, we would certainly need some sort of formal method to do so, is that what you mean by maths tables? The point I am trying to make in this thread (perhaps poorly!) is that the formal method you use is definite, by doing so you know that you are performing this method or function and no other. You also know that substituting any other number into this formal method, if done correctly, will give you a correct or truthful answer. In other words, your method is determinate amongst mutually exclusive methods, and is truth preserving for all (name removed by moderator)uts.

Contrast this with a multiplication machine. We can (name removed by moderator)ut numbers and get outputs which seem to simulate what we do with our formal methods, but there are an infinite number of functions, all mutually exclusive, that would still give the same results. This is true of any physical process. Therefore the machine/physical process is indeterminate amongst mutually exclusive functions/methods.

This is in stark contrast to our thoughts of formal methods, and therefore, these thoughts at least can not be wholly the result of physical processes.

That’s the argument anyway.

It sounds like you recognize the argument is hogwash, which is to your credit. I would go a bit further and argue that this sort of argument is downright incoherent. The language used in the paper reminds me of Platonic (or, perhaps more accurately, Thomistic) roots. Since Platonism and Thomism are both incoherent (a harsh judgment, I know, but appropriate), then that could be the underlying problem.

The idea that we can never be sure what a machine is doing sounds somewhat mystical. Are we not to trust our own senses? Are we to allow ourselves to be paralyzed by the problem of induction? And whatever the rub, why is it ignored in our own self-reflection?

This is a bizarre argument, to be sure. I have to say, though, I’m glad to have become aware of it. So thanks to the OP for that.

 

[warpspeedpetey]

Thomism …incoherent

care to back that wild assertion up?

 

[Betterave]

It sounds like you recognize the argument is hogwash…

I predict that the claim above is hogwash. (I suspect hatsoff’s reading comprehension is not quite all there, but I await confirmation from Andy.)

 

[AndyT_81]

hatsoff,

It sounds like you recognize the argument is hogwash, which is to your credit.

No, I don’t think it’s hogwash. I’m not 100% for it, as I am still trying to understand it fully, but from what I can see so far it is good.

I would go a bit further and argue that this sort of argument is downright incoherent.

If you believe you can argue that this argument is coherent, please go ahead and do so. I am looking for critical analysis of this argument, and I have found that this is best achieved when well thought out to-and-fros occur.

The idea that we can never be sure what a machine is doing sounds somewhat mystical.

It shouldn’t, Ross or myself haven’t appealed to anything mystical. Rather, this argument is apparently based on some of the big findings of analytic philosophy of recent years, namely the “new riddle of induction” (look it up, along with philosopher Nelson Goodman).

Are we not to trust our own senses?

Yes, we certainly are to trust our senses. The only thing is, our senses don’t show us anything about functions. Our senses show us (name removed by moderator)uts and outputs and the functions that produce said (name removed by moderator)uts and outputs are completely unknown to us. We can formulate abstractions based on said (name removed by moderator)uts and outputs (abstractions which are definite in our thoughts), or conversely, design machines that simulate our abstractions, but we can never know what function is actually taking place within the machine (if any are). An infinite number of functions, all mutually exclusive to one another, are possible. This indeterminate-ness is something completely foreign to our formal thoughts.

Are we to allow ourselves to be paralyzed by the problem of induction?

I see no reason why the argument should “paralyze” us.

And whatever the rub, why is it ignored in our own self-reflection?

I’m not sure what you mean by this, could you expand further?

This is a bizarre argument, to be sure. I have to say, though, I’m glad to have become aware of it. So thanks to the OP for that.

You’re very welcome. It is a complicated argument, but quite fascinating I think.

 

[hatsoff]

No, I don’t think it’s hogwash. I’m not 100% for it, as I am still trying to understand it fully, but from what I can see so far it is good.

Oh, I see now that you are the OP. Okay…

If you believe you can argue that this argument is coherent, please go ahead and do so. I am looking for critical analysis of this argument, and I have found that this is best achieved when well thought out to-and-fros occur.

Ross seems to conflate actual mental computation with self-reflection on our own mental computation. For example, he writes,

“…the ‘function’ does not consist in the array of (name removed by moderator)uts and outcomes. The function is the form by which (name removed by moderator)uts yield outputs.”

Now, if our conceptualization of computational exercises is what Ross has in mind when he talks about “the form,” then he’s begging the question by assuming that it’s not a physical process. In that case, his argument would be coherent, but useless. However, I suspect he’s referring to some reified versions of computational concepts, which would make his argument unintelligible. This is what I meant when I said that his argument reminds me of Platonism and its variants. Either way, though, we have a serious problem.