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05-15-2003, 03:39 PM | #241 | |
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05-15-2003, 03:42 PM | #242 | |
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05-15-2003, 03:57 PM | #243 |
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yguy:
It's not just unlikely that the people I see are aardvarks in human suits, its impossible. Only in the realm of imagination is it logically possible. It's only "impossible" if you use impossible in a sort of vague real-world sense of "so far beyond a reasonable doubt that it'd be totally stupid to give it any serious consideration." But "impossible" in the absolute sense that 1+1=3 is impossible? Of course not. For instance, I'd guess you'd acknowledge that it is within God's power to create a sentient aardvark in an incredibly realistic human suit. Perhaps with genetic engineering and robotics it would even be possible for humans to do such a thing in a few centuries (If you believe humans have a soul but animals don't, I suppose you'd disagree--if that's the case though, do you think animals have any free will? Do you think they have conscious experiences, and that it is wrong to torture them?) yguy: I mean fer cying out loud, Jesse, is it really so unreasonable to assert that some ideas are too idiotic to give a second thought to? Of course not. But if you're interested in the philosophical question of what you can really know with absolute certainty (this question was the basis of Descarte's entire philosophical system, for example), then these sorts of practical considerations are totally irrelevant. To me it's obvious that, in the context of a philosophical discussion, there is a fundamental qualitative difference between my "certainty" that the earth is round and my "certainty" that 1+1=2. |
05-15-2003, 05:07 PM | #244 | |
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A question for the math/physics experts: How would this basic math we're discussing change under extreme conditions, such as the event horizon of a black hole, or at the Planck scale? Does 1+1 still equal 2 in six or ten dimensional space? Tenspace |
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05-15-2003, 05:11 PM | #245 | |
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05-15-2003, 05:17 PM | #246 | |||||
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Thinking is an action. To perform an action, an entity must exist. I think, therefore I act, therefore I am. Done deal, right? Wrong - because there is no apparent means by which even such fundamentally simple and seemingly unassailable logic can be verified. We are essentially left saying we know it to be veridical because it is self-evident. |
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05-15-2003, 06:38 PM | #247 |
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yguy:
It would appear then, that whether there are actually any aardvarks dressed in suits which make them indistinguishable from humans on the planet is irrelevant to the proposition being possible in the absolute sense. Have I got that right? Right. yguy: OK, the drift I'm getting here is that you cannot know any proposition to be absolutely true unless you can be assured that it is neither based on a faulty premise, nor can contradictory consequences be derived from it. In this regard, the problem with "Cogito ergo sum" is the same as we encounter with the Peano postulates: there is no way to be assured of this logical perfection. Thinking is an action. To perform an action, an entity must exist. I think, therefore I act, therefore I am. Done deal, right? Wrong - because there is no apparent means by which even such fundamentally simple and seemingly unassailable logic can be verified. We are essentially left saying we know it to be veridical because it is self-evident. Yes, but in almost all cases you can at least try to argue why a contradiction would follow from assuming some proposition is false. That argument itself may rest on even simpler assumptions that you take to be self-evident, like "a proposition cannot be simultaneously true and false", but the idea is to reduce it to the most basic set of assumptions possible, assumptions that you believe no reasonable person could deny are necessarily true (as opposed to assumptions that no reasonable person would deny are true in the real world, like 'the earth is round'). You did something like this above with your defense of "cogito ergo sum"--your argument did not directly say how a contradiction would result from assuming the contrary, but it was implicit (thinking is an action, an entity must exist to perform an action, but if you assume I don't exist but can still think, you contradict one of those first two assumptions). You haven't even tried to explain why a contradiction would follow from assuming God doesn't exist or that humans evolved naturally, as far as I can see. |
05-15-2003, 08:41 PM | #248 | |||
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05-15-2003, 10:48 PM | #249 |
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yguy:
I infer from this that the logical possibility of any proposition is entirely the product of the mind which confers said possibility upon it, and is completely irrelevant to any objective reality. I don't know quite what you mean by "the product of the mind which confers said possibility upon it"--that sounds more subjective than what I'm talking about. Think of logical/metaphysical possibility as being similar to physical possibility--to say that a particular phenomena is permitted by the laws of physics is not to say any instances of this phenomena exist in the real world. A black hole 10 billion light years in diameter might be allowed by the laws of physics as we understand them, but that's no guarantee that any exist. On the other hand, an object that accelerates past the speed of light is not allowed by the laws of physics as we understand them, and thus unless our understanding of physics is wrong, no such object will be found in our physical universe. Jesse: Yes, but in almost all cases you can at least try to argue why a contradiction would follow from assuming some proposition is false. That argument itself may rest on even simpler assumptions that you take to be self-evident, like "a proposition cannot be simultaneously true and false", but the idea is to reduce it to the most basic set of assumptions possible, assumptions that you believe no reasonable person could deny are necessarily true (as opposed to assumptions that no reasonable person would deny are true in the real world, like 'the earth is round'). yguy: I find truly awe-inspiring the extent to which reasonable people are able to deny the obvious. In this very thread, we have an intelligent poster claiming that 1+1=2 is a tautology If you're making a statement about what is true within a particular axiomatic system, it is. yguy: and another one claiming that flowers make themselves beautiful by being beautiful. I haven't seen the quote you're referring to, but I suspect you're taking it out of context. Jesse: You haven't even tried to explain why a contradiction would follow from assuming God doesn't exist or that humans evolved naturally, as far as I can see. yguy: But according to your own logic as displayed in the case of the aardvarks, any such logical construction would be independent of reality anyway, so what good would it be if I were able to produce such a thing? Your "independent of reality" comment is too vague. It's true that deciding whether something is necessarily true should not depend on knowing in advance whether it happens to be true in our reality. But once you can show that something is necessarily true, that means it absolutely must be true in all possible realities, including this one. So, your conclusions about whether a truth is necessary or not do have a bearing on what you should believe is true in the real world. Most theistic philosophers want God to be a necessary being that would exist in all possible realities rather than a contingent being who just happens to exist in our reality, so they obviously agree with me that this is an important distinction, even if you don't. Perhaps you should read up on modal logic if you still don't understand the distinction between necessary truths and possible truths which happen to be true in our reality. |
05-16-2003, 10:36 AM | #250 | ||||||
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2. Logic. An empty or vacuous statement composed of simpler statements in a fashion that makes it logically true whether the simpler statements are factually true or false; for example, the statement Either it will rain tomorrow or it will not rain tomorrow. By this definition, it appears to me that "1+1 is either equal or to not equal to 2" is tautological, but that 1+1=2 is not. If it is, than all expressions of arithmetic addition are equally so, are they not? By extension then, all true equations are tautological. Quote:
tenspace(5/14/03 @9:03 PM): If beauty is truth, then yes, the flower contrived its own beauty, through its ability to attract pollinators better than they less beautiful flowers, in the population of these flowers you mention. y: So let me get this straight: a flower's beauty comes from the fact that it is beautiful? tenspace: <crickets.wav> Quote:
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