Aaron Cotnoir has suggested that people think that paradoxes are meaningless. I think they are lucky that they hadn’t suggested that to me unless they wanted to see me freak out.
It was my good fortune to have my first real exposure to the work of Frege, Russell and Wittgenstein be from Thomas Ricketts. I can’t remember verbatim what he said, but this is close:
No one knows how long it took Frege to understand what Russell had written in his letter (Russell’s Paradox), be it a few seconds, a minute, ten minutes or a few hours. But we do know that at that moment his entire universe collapsed.
Only out of gross ignorance of history can anyone believe that paradoxes are meaningless. Frege’s project up until Russell came along and spoiled everything was, at least in part, to give a firm foundation for mathematics based solely upon logic. With just a few laws coupled with his newfound quantification he was able to provide a seemingly consistent theory and then also provide sophisticated philosophy of language to bolster his views.
There was probably a moment when Frege allowed himself to dare to think he’d solved one of the greatest mysteries of the universe. Not only had he legitimately and demonstrably changed mathematics forever, but the ramifications of his theory were obviously far-reaching into philosophy and science. Then Russell sent him that letter that struck at the very axioms of his theory. It was a jugular shot and I can’t see Frege feeling other than like all the blood had been drained from his body. Everything he had worked for was put in jeopardy.
So if anyone believes that paradoxes are meaningless, I suggest to go read some history. Paradoxes can destroy. Any theory that comes along and says paradoxes are meaningless, is garbage.
2 thoughts on “Are Paradoxes Meaningless?”
I’m glad we agree on the fact that the ‘meaningless’ view isn’t exactly as promising as most people suppose. However, I don’t think your argument shows that. I think you’re equivocating on ‘meaningful’ and ‘meaningless’ in the post. No one who endorses the view would contend that the paradoxes don’t have important historical consequences, or force a revision of theories. So, in a sense they can be ‘meaningful’ to the process of philosophical or mathematical inquiry. But that’s entirely beside the point of whether they have content.
And I don’t think there’s any reason to think that anything that has meaningful (read: important) consequences to inquiry must itself be meaningful (read: has content).
Example: suppose a semantic theory entails (by composition principles, etc) that the sentence “Colorless green ideas sleep furiously” is true (or whatever). That seems to be a decent candidate for a meaningless sentence, and it might thereby lead to a revision of the semantic theory. It might even be a historically important revision. But why should that entail that the sentence is meaningful?
Thanks for the comment.
I figure if someone actually believed your example semantic theory, then that apparently meaningless (to us) sentence would have meaning (content) for that person. Then that person would have to square the common sense belief that the offending sentence is meaningless (contentless) with the theory that attributed meaning. At this point whether or not the sentence has meaning is in limbo: either common sense needs a revision or the theory does, and there is no simple way to choose.
So the sentence does have meaning (content) for one person or a small group of people, kind of like spies talking in code: their sentences are apparently meaningless, but really are not because we just don’t use the same principles. If these peoples’ theory is correct, then colorless green ideas do sleep furiously. If they choose to revise their theory to square with common sense, then it is *because* that sentence had content, content that they did not like.
When we look back at problems in theories we did not create, it is all too easy to scoff at the old difficulties. I recall doing it quite often as an undergrad (and later unfortunately). I suspect that this is why so many people just assume paradoxes to be meaningless. They did not put the effort in and are just seeing the apparently meaningless consequences of debunk theories. Because something has no content now doesn’t mean it didn’t in the past or will not in the future.
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