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awatkins69
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You’ll have to help me here because I’m not a mathematician at all. But ultrafinitists deny the set of natural numbers?? How does this affect closure with all the basic operations?
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Moonstruck888
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Prove it, if you can. I dare you. I double dare you. Prove it.
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awatkins69
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Well, the only way to disprove it is to say that, for some reason, one of those things would be incomprehensible.
But all we’d have to say is that, if there were an actual infinite set of comprehensible things, necessarily the intellect could comprehend each of these things.
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Moonstruck888
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The human mind is grossly inefficient in many respects and starkly limited. Our ability to reason and think critically is stunted by instinctive and emotional imperatives and insurmountable mental limitations.This is begging the question. The argument is directed against the assertion that “the intellect is a property of matter” and here you’re arguing that the since the intellect is a property of matter, then it has a storage limit.
But this argument is not about long-term storage anyway, but the capability of the mind to process, calculate, apprehend and generate a potential infinite number and kind of concepts.
Where computers have limits, for example, the mind can transcend those (by observing the computer’s limitations).
awatkins69 distinction on the “potential” infinite is a very good one. Thanks!
(… that’s what I was looking for in developing this argument).
To assert, with no accompanying evidence, that the human mind is infinite in faculty is to say the least a bit of a stretch.
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Moonstruck888
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I didn’t ask you to evade it, I asked you to prove it. You can’t. No problem. I knew you wouldn’t be able to.
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awatkins69
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Chill out my friend. I didn’t evade it. It’s very simple:
If there were an actual infinite amount of comprehensible things, the intellect could potentially comprehend each of them.
What’s wrong with that statement? It’s necessarily true. It doesn’t need to be proven since it is an analytic statement.
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Just_Lurking
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Exponentiation is explicitly acknowledged to not be closed. That is, if a and b are numbers, then a**b (a to the b-th power) might not exist if the result would be too large.
It seems to me that this means that the other more basic operations, such as multiplication, addition, or even successor, must also be partial (not closed), but there seems to be some kind of philosophical tap dancing in order to avoid coming to that conclusion.
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sidbrown
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I think it will depend on what is meant by infinite. The real numbers are infinite. the natural numbers are infinite. The interval of real numbers from 0 to 1 is infinite. And we have a pretty good understanding of these concepts which involve infinite quantities.
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sidbrown
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How do you define too large here?
Suppose it were M. Then we are able to know M-1. But if we know M-1, we can just add 1 to that quantity and presto, we know M already.
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Just_Lurking
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That’s what I think too, so I can’t be an ultrafinitist.
The actual size of “too large” is unknown, but 2**1000 is definitely too large since it is more than the number of electrons in the universe.
See here for some mathematical work on ultrafinitism.
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reggieM
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First, I think you’ll have a very difficult time providing evidence that the mind is not infinite. In fact, I don’t think you’ll be able to even give a reasonable guess at what the storage and processing capability of the mind is at all. When is a mind half full?
These capacities are different from the ability to retrieve all of the information stored. In the same way that we know the capacity of a computer hard-drive (and how much is stored) without having to retrieve it, or retrieve it correctly.
As for positive evidence of the infinite capacity of the mind … we could start with the information storage and retrieval that we can observe.
It’s very common to find an elderly person, even up to 90 years of age – who can remember details of childhood with perfect clarity.
So, that’s 80 years of sensory data stored. To remember a particular event with clarity of detail, that means that it’s possible that every second of the person’s life is stored in the mind.
How many bits of information are captured in a second? That can vary, but think about the audio, tactile, visual and symbollic information – as well as the information generated internally to interpret, compare, categorize all of this. Not to mention the emotional information that is generated in a response of feelings. How many bits of information is this per second?
Even if it was only one bit per second. That would be 60 bits per minute. 3,600 bits per hour. 86,000 bits per day. 31,536,000 bits per year. 31.5 million bits per year. Now, we have a person who lived 90 years. 2,838,240,000 bits of information in a lifetime. 2.8 billion and information still streaming in, being processed, generating emotional information, interpretations and new ideas.
Now, take that 2.8 billion and multiply it by a more reasonable factor on bits of information per second. Obviously, it’s not one bit per second. But how many? Look at a walk in a garden – colors, scents, sounds – a thousand bits of information per second? A hundred thousand?
And again, this is just information received through the senses and not the trillions of bits of information generated by thoughts, dreams, emotional experiences, logical deductions and other internal processes.
The number is incalculably large. And, there is no evidence that this information has “filled” any capacity of the mind at all. Why is that the case? Why is it so difficult to know what the information capacity of the mind is? The fact that this task is so difficult (and most likely impossible) is another strong evidence for the immateriality of the mind and it’s infinite capacity.
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Moonstruck888
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Exactly.
I can’t guess when a mind is half full, and neither can you, so you’re resorting to speculation based on wild surmise.
“I don’t know the capacity of the human mind, therefore the capacity of the human mind is infinite.”
That’s your argument, but for it to be any more than mere speculation, you must have evidence.
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Moonstruck888
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It is not an analylitic statement, it is a flawed, half baked proposition which actually doesn’t say anything at all. You have absolutely no method by which you can hope to guage the capacity of the human mind, so you’ve just said, maybe aye, maybe no.
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awatkins69
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You can’t “prove” that the intellect can comprehend all comprehensible things. It follows necessarily by definition. By definition, comprehensible things are things that can be comprehended. If you deny that the intellect can comprehend any and every comprehensible thing, you’re saying that there are incomprehensible comprehensible things!
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Moonstruck888
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You’re missing out the rather salient point about “an infinite amount” here, which is very disingenuous of you. Of course all comprehensible things can be comprehended. The question was whether an infinite amount can be comprehended by one brain at one time.
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awatkins69
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If that’s the question, then I already answered it in my very first reply to you.
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Moonstruck888
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And I told you that your answer was an absurd fallacy based on an assumption.
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awatkins69
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Ok. Let’s look this over. You said: “The question was whether an infinite amount can be comprehended by one brain at one time.”
I never said that the intellect could hold an infinite amount of concepts at one time. I said it could hold a potentially infinite amount of different concepts, each of them *individually *, not *all *of them at one time.
We agreed that anything that is comprehensible can be comprehended (obviously). So if there was an infinite amount of comprehensible things, the intellect could grasp each of these. Otherwise there would be an incomprehensible comprehensible concept, which is absurd. Thus, the intellect can grasp a potential infinite amount of concepts (*not *an actual infinite). Best.
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Moonstruck888
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To grasp each of these infinite number of comprehensible concepts, if it could not be done simultaneously, would take an infinite amount of time. Whatever way you look at this, no matter how long you spend grasping concepts, you’re always an infinite number away from grasping an infinite number of concepts.Ok. Let’s look this over. You said: “The question was whether an infinite amount can be comprehended by one brain at one time.”
I never said that the intellect could hold an infinite amount of concepts at one time. I said it could hold a potentially infinite amount of different concepts, each of them *individually *, not *all *of them at one time.
We agreed that anything that is comprehensible can be comprehended (obviously). So if there was an infinite amount of comprehensible things, the intellect could grasp each of these. Otherwise there would be an incomprehensible comprehensible concept, which is absurd. Thus, the intellect can grasp a potential infinite amount of concepts (*not *an actual infinite). Best.
If you want to get round this by inserting the word “potentially” in, that’s fine. All your doing is making a statement that doesn’t actually say anything.
It boils down to anything comprehensible can be comprehended. Well done Sherlock. Thank the Lord you were here to point out the obvious.
What you have failed utterly to do is provide a shred of evidence that the intellect is not physical. Comprehensible things can be comprehended, therefore the intellect is definitely supernatural? I’m sorry, I really don’t see how that follows.
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awatkins69
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That’s the point. It’s a potential infinite. Do you not understand the distinction? Do you think there is no distinction between a potential and actual infinite? If *you *do not understand the distinction, because you don’t understand what these basic concepts mean, you have no right to go around demeaning people with your sarcasm and mean rhetoric.
I’ll tell you what. Tell me how you understand the distinction between an actual and potential infinite, and I’ll continue to reply to your posts. If you do not understand the distinction, learn about it, give some constructive comments, and I’ll be happy to continue to reply. Otherwise, I’m not going to bother with your mockery just because of your unwillingness to understand.
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