And this seems like a fun read as well http://www.amazon.com/gp/product/0262562359/ref=ox_sc_act_title_1?ie=UTF8&smid=ATVPDKIKX0DER
Cheers, ~PM From: [email protected] To: [email protected] Subject: [agi] Database Semantics Date: Thu, 8 Nov 2012 14:06:31 -0800 As regards natural language, Roland Hausser's work might be useful http://www.amazon.com/Computational-Linguistics-Talking-Robots-Processing/dp/3642224318 Cheers ~PM Date: Thu, 8 Nov 2012 10:48:23 -0600 Subject: Re: [agi] Randomness: Mathematics as Perceptual Bias From: [email protected] To: [email protected] When using natural language, most people will shift their interpretation of a statement to the nearest neighbor that makes sense to them, or they will keep the meaningful part of the interpretation and disregard the part that makes no sense. In dealing with the Barber's Paradox, we can still count on the fact that the Barber shaves all those other than himself that do not shave themselves, and we leave the question as to whether he shaves himself open for further evidence. In logic and mathematics, however, these sorts of partial interpretations are disallowed, not because we're intellectually unable to resolve them, but because the way we resolve them might vary from person to person, and the logical or mathematical language is designed to minimize ambiguities and miscommunications at the expense of brevity. So while in natural language, we can still assign a (partial) meaning to the statement, in logic we must (in most systems) throw out the whole thing. Statements in any language are "things", which can be described by other statements in the same or another language, provided it is sufficiently general. The statement "P(X)" is not the same as the statement "P(X) is true". The meaning of "P(X) is meaningless" is distinct from the (potential absent) meaning of the statement "P(X)" that is being referred to. So while "P(X)" as a statement may play a role in determining the truth value of referring statements such as "P(X) is true" and "P(X) is meaningless", it still does not have meaning in and of itself. Nonsense is nonsense, even when we identify it as such. Logic systems are typically constructed using a simplified metalogic, which is somewhat circular, but unavoidable because we must describe the new language with the only tool we have for describing things: language. I'm pretty familiar with this idea of using logical statements that assign truth values to other logical statements. There is definitely utility in this syntactic/formal approach to logic, since it helps us design languages that are highly regular and analytic in their structure. However, the purpose of a language is not to follow rules, but to describe things, and this applies to logic just as well as any other language. The strict syntactical rules are an additional constraint we place on formal, as opposed to natural, languages. Meaning, which is universal to language and is fundamental to its purpose, is a mapping from language terms onto reality (or at least our internal representation of it), allowing us to describe those things. Without meaning, language is useless, and so I see the arbitrary assignment of a truth value to a meaningless statement as an exercise in futility, unless that truth value is the Meaningless truth value I already described, which serves as a label to tell us not to invest further time trying to assign meaning to it (and not to apply the principle of the excluded middle to it). In natural language, we can take an alternate route, and assign meaning and truth values to individual cases the statement maps to which happen to be consistent. In formal logic, we are not permitted to do this because it violates the regularity constraints we place on logic as a regular/analytic alternative to natural language, and so we throw out the entire statement. The problem I am pointing out is not about whether the statement should be thrown out, but rather how. In "standard" logic, this is done by assigning a value of False to the statement. But for a Meaningless statement, this act of assigning False works together with the principle of the excluded middle to produce an error: claiming that the negation of the Meaningless statement is in True, when in fact it is also Meaningless. Most incarnations of logic fail to distinguish between the cases where an un-True statement can be negated to get a True one, and cases where the negation of the un-True statement is also un-True. So either we don't get to use the power of the excluded middle where it is appropriate, or we are at risk of using it where it is inappropriate. AGI | Archives | Modify Your Subscription ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
