tag:blogger.com,1999:blog-1860307875990258501.post8528889281175328090..comments2013-03-21T09:05:35.143-05:00Comments on Non-Kantradiction: Reconciling Rationalism and Empiricism: the Infinite, Finite and IndefiniteErik Christiansonhttp://www.blogger.com/profile/15747258914239065813noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-1860307875990258501.post-12490999449331365822012-12-31T17:46:24.402-06:002012-12-31T17:46:24.402-06:00I think I am better understanding the difficulty n...I think I am better understanding the difficulty now.<br /><br />When I said, "we think the finite in contrast with the infinite", I didn't mean to suggest that the infinite is the opposite of every individual natural number in terms of a negation. I apologize for the confusion. I am suggesting that Rationalists think natural numbers as finite relative to a ground, and not to the series.<br /><br />Using the Principle of Sufficient Reason (PSR) we could argue that there must be a ground (reason) for why natural numbers are finite. No natural number has a relation to another as ground, so it must be something else outside the sequence that grounds it - something not limited by the series, something in-finite. The reality (or lack thereof) attributed to this ground I can leave aside for now.<br /><br />An Empiricist will argue, correctly, that no matter how far we count we feel like we can count further, and that we cannot justify the infinite <i>a priori</i> with our inability to reach the end. The emphasis here is on the series as indefinitely great, and not the nature of the members of the series. The PSR tries to address a concern with the nature of any member of the series.<br /><br />We can ask, and should ask, what grounds the PSR, or other similar Rationalist procedures. Here I was just concerned with opening up the possibility that a great deal of difference perceived between Rationalists and Empiricists is simply the result of failing to understand the strategies employed by either side. Perhaps the Rationalists didn't even understand their own procedure as well as they could have.Erik Christiansonhttps://www.blogger.com/profile/15747258914239065813noreply@blogger.comtag:blogger.com,1999:blog-1860307875990258501.post-53241334239637224392012-12-31T17:01:52.580-06:002012-12-31T17:01:52.580-06:00I understand you to be saying that we need to comp...I understand you to be saying that we need to comprehend infinity in order to count to 1 (i.e., finitude = not infinity, or finitude = infinity + limits, or some such derivation). Of course this will not appeal to an empiricist who claims it is the other way around.<br /><br />One reason is that the argument seems to equate finitude with countability. It is easy to say that "infinite" is the opposite of "finite," but uncomfortable to say it is the opposite of 1 (and every other natural number). Even assuming we need to comprehend finitude "distinctly," that seems like a category error.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1860307875990258501.post-76329743440887801592012-12-31T10:30:37.506-06:002012-12-31T10:30:37.506-06:00Thanks for your comment. I hope I can clarify som...Thanks for your comment. I hope I can clarify some of this and revise in light of it.<br /><br />1) I'm happy formulating laws the way you do as explaining a temporal connection. I am trying to consider how the 'lawfulness' is also thought in terms of the ground for thinking the connection. So, we experience gravitation (temporally), but we also think gravity in a way where it is not given (as an appearance) in the sequence. Gravity (as opposed to gravitation) is only intelligible (we don't know how to tell if it is a possible or impossible object of experience, since we just think it). Gravitation is experienced as the sequence comprehended in a certain orderly way.<br /><br />2) I didn't mean to suggest that an empiricist considers himself limited to however high he has actually counted. We have a sense of being able to go on; it was this sense that I was calling into question. <br /><br />Empiricists do say there is no ground for deducing the existence of the infinite from the finite, just as you cannot deduce a necessary connection of events. The Empiricist does abstract a notion of infinity, but we need to consider how one performs such an abstraction. I am basically suggesting that the manner in which this abstraction works for empiricists is best explained by the Rationalist treatment of the infinite. I am also suggesting that the limits the Empiricists recognize for deduction of the infinite be applied to the understanding of the Rationalists. Erik Christiansonhttps://www.blogger.com/profile/15747258914239065813noreply@blogger.comtag:blogger.com,1999:blog-1860307875990258501.post-37401810541352827992012-12-31T09:26:43.605-06:002012-12-31T09:26:43.605-06:00It seems you are assuming that laws are static (no...It seems you are assuming that laws are static (not implying temporality). But if laws are formulated as "if x [happens], then y [happens]," then this argument loses force. Furthermore it is problematic to discuss the meaning (or ontological status, as it were) of a law in absence of its operation. For instance, what is a mathematical limit if not a law "of movement?" The same could be said of infinity. If we conceive of natural numbers as the output of a "+1 generator," then I don't think an empiricist needs to posit a limited number of them. (He can continue counting even after all the jelly beans are exhausted from the jar.) Perhaps he needs to abstract from temporality in order to make that "leap" from indefinite to infinite, but that is not the same as saying that the finite meaningfully "depends" on the infinite.Anonymousnoreply@blogger.com