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Author Topic: Rationality - A purely scientific notion?  (Read 16013 times)
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pck
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« on: January 18, 2010, 07:40:26 PM »

Here I'd like to start a thread dealing with the concepts of rationality, rational thought and rational decisions. What qualifies a thought, action or decision as "rational"?

I want to start by making a point about rationality which I think is not immediately and blindingly obvious but nevertheless easily intelligible and which goes against the notion that all rationality must necessarily involve scientific concepts or even logic/rule-based deduction in formal systems such as mathematics.

(I)

Formal systems like mathematics represent the notion of truth in the sense that those propositions will be labelled "true" which can be derived from a basic set of axioms by certain rules of transformation (axioms = initial propositions taken to be true without appeal to any further reasons).

So math is good for deciding the truth or falsity of certain propositions. What math, or any formal system, does not and cannot represent is the notion of sense. Malformed expressions like "3 5 = +" are not rejected as "false" by the formalism of mathematics, but do not enter the game in the first place. For to be recognized as "false" by the formal system, the opposite, i.e. "NOT 3 5 = +" would have to be provable, but clearly this is impossible since negating a nonsensical statement just produces another nonsensical one, not one capable of being true or false.

(II)

How do we convince someone who we think is talking nonsense of his or her mistake? We have seen that we cannot simply take a nonsensical proposition N and look for proof of its negation. What we can do though is pretend for the moment that N does make sense and derive from it (by logical means) another statement M which is so clearly nonsensical that our "opponent" will have to admit its non-validity. Because M was derived by valid means from N, N will then necessarily have to be judged as nonsensical too.

This could be called "reductio ad absurdum", but the procedure is not to be confounded with a mathematical r.a.a. which involves taking some statement A and deriving from it a contradiction, i.e. the truth of some statement B as well as B's negation. A will then have been shown to be false (not nonsensical).

(III)

Now the procedure described in the first paragraph of (II) is very much a rational way to eliminate errors in our thinking, but it is not analogous to or on the same epistemic level as the r.a.a. as used in formal systems. Thus it follows that some rational arguments indeed transcend reasoning within formal systems. In short, human rational reasoning comprises more than deduction in rule-based systems. The category of sense is what makes all the difference here.

(IV)

If the above argument is sound, then this is a good counterargument against the hypothesis that computers, at least in the way as they are constructed now, will ever be able to match human reasoning. For algorithmic procedures can always be represented by deductive formal systems.


This concludes my point on rational reasoning. Comments and further elaborations are of course very much welcome.
« Last Edit: March 12, 2010, 05:15:50 PM by pck » Logged
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« Reply #1 on: January 18, 2010, 08:21:33 PM »

Rational for me means doing what I feel like or acting as I feel, in that very moment. Very tricky and not so rewarding. Only later (and very few none of) my "opponents" acknowledge that I was right. Looking forward to how others feel about this!  blush
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« Reply #1 on: January 18, 2010, 08:21:33 PM »

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pck
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« Reply #2 on: January 18, 2010, 10:54:00 PM »

Rational for me means doing what I feel like or acting as I feel, in that very moment.[...]

Interesting remark on the subjectivity of rationality. One often accuses others of being irrational and can in retrospect even discern some of one's own actions as irrational, but what we do not have is the feeling that we are acting irrationally right now.

This may perhaps suggest that rationality is something which does not exist "in us", i.e. in our minds, but instead in our language-behaviour, an "after-the-fact" phenomenon.
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« Reply #3 on: January 19, 2010, 04:13:02 PM »

(I)

Formal systems like mathematics represent the notion of truth in the sense that those propositions will be labelled "true" which can be derived from a basic set of axioms by certain rules of transformation (axioms = initial propositions taken to be true without appeal to any further reasons).

So math is good for deciding the truth or falsity of certain propositions. What math, or any formal system, does not and cannot represent is the notion of sense. Malformed expressions like "3 5 = +" are not rejected as "false" by the formalism of mathematics, but do not enter the game in the first place. For to be recognized as "false" by the formal system, the opposite, i.e. "NOT 3 5 = +" would have to be provable, but clearly this is impossible since negating a nonsensical statement just produces another nonsensical one, not one capable of being true or false.

I'm missing something here, which is that a formal system usually (always?) also has a defined language (grammar and syntax). The above statement 3 5 = + can then be labeled as making no sense, as it's not an allowed expression in the mathematical language. In a formal language, this is a purely rational process, so actually, I think mathematics as a formal system with a formal language, can tell us that the statement makes no sense.
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« Reply #4 on: January 19, 2010, 04:48:02 PM »

Quote
some rational arguments indeed transcend reasoning within formal systems


does not testing by paradox work in both maths and formal language?

Quote
One often accuses others of being irrational and can in retrospect even discern some of one's own actions as irrational, but what we do not have is the feeling that we are acting irrationally right now.


i wanted to substitute "irrational" above with "being critical of others", and that  often this is a mirror of our own shortcomings, which we subconsciously see in others but often fail to see in our selves..

or that their "irrational" behaviour in our eyes, suggests that our own stance is rational (ie what we do is ok with ourselves, makes sense by our selftesting, but that 'their behaviour fails our testing'

it would then seem important for us to use other criteria to 'test' their behaviour, so as to try and find a mechanism for understanding the rationality of their behaviour, or stance on a subject.

it is thus incumbant on us to test fully what others say/do and not just accept that we necessarily have sufficient experience or 'testing proceedures' to pass judgement. (or indeed that simply we have the full facts or at least sufficient info)

eg the full picture example below


Quote
This may perhaps suggest that rationality is something which does not exist "in us", i.e. in our minds, but instead in our language-behaviour, an "after-the-fact" phenomenon.


interesting and i agree but also,
i'm sure i've heard myself say, either aloud, or internally, "this isn't making sense", as i'm actually saying something, or just after..

in fact i feel myself saying it right now !


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pck
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« Reply #5 on: January 19, 2010, 06:45:57 PM »

I'm missing something here, which is that a formal system usually (always?) also has a defined language (grammar and syntax). The above statement 3 5 = + can then be labeled as making no sense, as it's not an allowed expression in the mathematical language. In a formal language, this is a purely rational process, so actually, I think mathematics as a formal system with a formal language, can tell us that the statement makes no sense.


Using mathematical proof (= symbolic transformations) we can only decide whether a proposition is true of false (derivable from the basic axioms or not), but this presupposes that the proposition in question is syntactically well-formed.

The point is that math has no inner method of finding a statement nonsensical. It is a human being which must decide whether the formal rules of proposition-forming were correctly applied or not. The concept of mathematical nonsense is not expressible using mathematical language, but shows itself when the mathematician fails to be able to handle a nonsensical statement correctly according to the rules of math. So it is not in the formal language that you label the statement as nonsensical, but outside of it.

(Neither is the concept of proof expressible in the language of math. However, proofs show themselves when one does math - you get a string of symbols as the expression of the proof you're working on.)

Every formal system needs someone to apply it and to check whether the rules have been obeyed or not. In the end, it always comes down to human beings doing something with a formalism. I believe it is one of the confusions of our overly scientificially minded age to forget that and somehow think that math exists by itself, or could even do itself.
« Last Edit: January 20, 2010, 12:16:40 AM by pck » Logged
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« Reply #6 on: January 23, 2010, 12:36:45 AM »

that makes sense Smiley
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pck
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« Reply #7 on: January 24, 2010, 12:28:13 PM »

does not testing by paradox work in both maths and formal language?

It does, I'm treating math as a special case of a formal language here ("formal language" as opposed to "natural language"). What I tried to point out was that reduction to absurdity within the category of sense works differently compared to r.t.a. within a system of logic.

Nitpick corner: The term "paradox" is often used interchangeably with "contradiction". A mathematical paradox however is an apparent contradiction, i.e. a true statement which defies intuition. A real contradiction in math is sometimes also called an "antinomy". The use of "paradox" in the colloquial sense with its double-meaning can lead to some very "interesting" talk at cross purposes...

[...]
it would then seem important for us to use other criteria to 'test' their behaviour, so as to try and find a mechanism for understanding the rationality of their behaviour, or stance on a subject.

it is thus incumbant on us to test fully what others say/do and not just accept that we necessarily have sufficient experience or 'testing proceedures' to pass judgement. (or indeed that simply we have the full facts or at least sufficient info)
[video]

Agreed. I believe that the most basic prerequisite for understanding each other is agreement in behaviour (including but not limited to language-behaviour). If this is true, it might to some extent explain why we find foreign cultures, or even the behaviour of people in our own neighbourhood (those which we do not appreciate), so strange. The more we are able to "sync" with them, the less alienated we will feel. Obviously, this will not always be easy or even possible. It would be interesting to hear about this from Diane who is currently going through a process of cultural change.

With regard to the video, another thing that strikes me as important here is that in many cases we can never know when the film truly ends. There may be another twist we just haven't seen yet. So we have reason to remain sceptical about what we think we know and must continue to try and get more support for our beliefs.

interesting and i agree but also,
i'm sure i've heard myself say, either aloud, or internally, "this isn't making sense", as i'm actually saying something, or just after..

in fact i feel myself saying it right now !

Right now after you gave it some thought Smiley
« Last Edit: January 24, 2010, 08:35:42 PM by stog » Logged
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« Reply #8 on: January 24, 2010, 08:20:03 PM »

Quote
Every formal system needs someone to apply it and to check whether the rules have been obeyed or not. In the end, it always comes down to human beings doing something with a formalism. I believe it is one of the confusions of our overly scientificially minded age to forget that and somehow think that math exists by itself, or could even do itself.
pck above

further from the above pck.. i am posting a youtube link which appeared at the bottom of a wiki link vic suggested we saw.
if anyone knows of any other allied audio video pls let us know thx

here is the clip - english with dutch subtitles, that appears to be a sort of preamble to your discussion/quote pck - at least this section certainly could be...




for those who don't know, homunculi  mentioned is a physiological 'sensory' little man ie he has big lips genitals and hands -- i'll dig out a diagram shortly

"here from wiki A homunculus (Latin for "little human", plural is "homunculi"; the diminutive of homo, "human") is, most generally, any representation of a human being. It is often used to illustrate the functioning of a system. In the scientific sense of an unknowable prime actor, it can be viewed as an entity or agent."
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« Reply #9 on: January 24, 2010, 08:50:33 PM »

also further from pck's
Quote
Every formal system needs someone to apply it and to check whether the rules have been obeyed or not. In the end, it always comes down to human beings doing something with a formalism. I believe it is one of the confusions of our overly scientificially minded age to forget that and somehow think that math exists by itself, or could even do itself.
above

i wonder how far a computer can be programmed to apply the formal language of testing known as maths such that it can make rational decisions
it already 'knows' that 6+5=12 is incorrect/irrational...

as the man in the clip says above about our 32 vision centres - they are all 'ours'from the beginning and have instilled our progressive/evolutiv judgement testing and they continue to gain experience along with the conscious us and all the other areas - or are these all what make up the 'conscious us'?

does not the computer - by virtue of its human programming similiarly gain an evolving structure /or is that evolving structure 'staccatto' -- ie is it not incremental, only as much as someone 'adds' or programs it more?

it cannot innately organise all its different parts/areas, as the living organism can, and thus  smooth totally interactive geometric judgement learning is not as easily achieved.  are neural net setups a way? what other examples are there? maybe i could ask inim?
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« Reply #10 on: January 25, 2010, 03:39:01 PM »

This is a nice article on just that subject , may get some of you to think...

http://www.nytimes.com/1997/04/22/science/evolutionary-necessity-or-glorious-accident-biologists-ponder-the-self.html?pagewanted=3
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« Reply #11 on: February 01, 2010, 04:36:30 PM »


i wonder how far a computer can be programmed to apply the formal language of testing known as maths such that it can make rational decisions
it already 'knows' that 6+5=12 is incorrect/irrational...

It is quite possible to formalize/algorithmicize the process of checking the validity of equations or mathematical statements in general (although it can be shown that no single algorithm can exist which is able to decide the truth of any statement). Endeavours of this sort have been called "meta-mathematics", "proof theory", etc. While such meta-theories and/or algorithms implementing them undoubtedly have their use, they do not and cannot eliminate the need for a human being as the last instance in the chain of reasoning. For meta-theories work according to their rules which means that someone must check whether the rules of the meta-theory have been applied correctly (and/or whether the algorithm implementing it has no errors). So all that is achieved is a deferral of the problem to another level. A meta-meta-theory would produce yet another deferral, and so on ad infinitum. We are looking at a limit of rule-based reasoning here.

It is interesting that you put "knows" in quotes, which suggests that we aren't really prepared to credit a machine with having knowledge. Why is that? Software which can check equations for validity has been available for many years. But can a computer program be said to have "knowledge" about what it does in the same way a human knows something? I don't think so. Someone who has knowledge about some subject S is able to describe S and explain it to others, and can argue cogently about S in connection with, or comparison to, other subjects. These abilities are partially constitutive of the meaning of the term "know". Computers fail at all of these, they do not and cannot show knowledge-behaviour. So when we say the computer "knows" something we use "know" metaphorically. We have created a second meaning of "know" which does not share all of its logical features with the original, garden-variety "know". That is not a bad thing or a practice to be abolished but must be kept in mind when one wants to derive logical conclusions from statements such as "The computer knows that 6+5=11". Not all conclusions logically derivable from "I know that 6+5=11" will also follow logically from "My computer knows that 6+5=11". When I say "I know that 6+5=11", more is expected of me than the mere ability to reply "11" whenever someone asks "What is 6+5?".

I believe there is more to calculation than putting down symbols on paper using a mechanical procedure or having it done by electrical circuits. If the wind sweeps together two leaves on the street, has it calculated that 1+1=2? We answer "no" here. What if a teacher had a machine enabling him to control the wind and thus put one and one leaf together by operating the machine, in order to demonstrate an example of "1+1=2" to his students? In that case we would call it an addition of 1+1. This suggests that "calculating", "adding", etc. are terms which require human involvement, certain types of behaviour and intent.

I think that all this points to the notion that looking at brain or silicon structures alone is not going to give us the understanding we seek here. We have to look at behaviour and capabilities too. Surely these are correlated with certain material structures, but I doubt they are logically reducible to them. Material structures are at best only partially constitutive of the meaning of terms of mental ability and action such as "know", "calculate", etc. To see this, think of our distant ancestors and how they used those terms sensibly and intelligibly, all the while knowing little or nothing about brain physiology. Even today we most certainly do not refer to brain physiology or parts of our brains when we say things like "I understand", "I know that..", etc. in everyday speech. It follows that an understanding of which physical structure must be present in order for it to be possible that "someone knows something" does not give us a complete picture or understanding of the phenomenon of knowledge. What is instead called for is a linguistic analysis of our patterns of speech, an investigation into our use of language, which is the true place where meaning is located. (A locative concept different from that of "physical location" is at work here.) Meaning is not located within physical structures on the insides of our skulls, even though it is true that without those structures no such thing as meaning would exist. (The notion that a complete description of a human brain is logically equivalent to the brain described - and/or the abilities its owner has - is one of the views of "hard AI" which scientists such as Douglas Hofstaedter have advanced (this was one of his views in the 70s, he may have changed it in the meantime).)

The previous argument contains a strong case against materialism without the need to resort to "supernatural" phenomena.

does not the computer - by virtue of its human programming similarly gain an evolving structure /or is that evolving structure 'staccatto' -- ie is it not incremental, only as much as someone 'adds' or programs it more?

I think a computer does not acquire human features or abilities because it was programmed by humans any more than a canvas acquires human features because a human created a painting on it. Neither does any complex mechanical system acquire human abilities because humans constructed it and/or set it in motion. The fact that some systems designed by humans are too complex to allow for a complete prediction of their behaviour in all possible cases does not make them "intelligent" or license the notion that they have "a mind of their own". As mentioned above, the ascription of properties like that to said systems would require the systems to be equivalent in behaviour, abilities, etc. to human beings.
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« Reply #12 on: February 08, 2010, 11:21:33 AM »

Using mathematical proof (= symbolic transformations) we can only decide whether a proposition is true of false (derivable from the basic axioms or not), but this presupposes that the proposition in question is syntactically well-formed.

The point is that math has no inner method of finding a statement nonsensical. It is a human being which must decide whether the formal rules of proposition-forming were correctly applied or not. The concept of mathematical nonsense is not expressible using mathematical language, but shows itself when the mathematician fails to be able to handle a nonsensical statement correctly according to the rules of math. So it is not in the formal language that you label the statement as nonsensical, but outside of it.

(Neither is the concept of proof expressible in the language of math. However, proofs show themselves when one does math - you get a string of symbols as the expression of the proof you're working on.)

Every formal system needs someone to apply it and to check whether the rules have been obeyed or not. In the end, it always comes down to human beings doing something with a formalism. I believe it is one of the confusions of our overly scientificially minded age to forget that and somehow think that math exists by itself, or could even do itself.


I don't think I completely agree with this. A formal language comes with an unambiguous grammar/syntax, it's an integral part of the whole system. If a statement cannot be parsed, this is within that whole system even if it's not in the language as such. The rules for parsing a formal language should be completely rational (one could say: mathematical in a broad sense), and as such don't need any human beings to interfere; a turing machine will do. The system-at-large (math's formal language plus the parser) can tell you a statement is nonsensical, without any human interference. In a running computer, one can argue math does exist by itself, and does itself.

Of course, the system itself was set up by humans, but one could say that about everything we study, model, etc. There's usually the condition that both input and output have to be understandable by humans.

The real point for me here is, that there's no significant difference with natural language when it comes to labelling a statement nonsensical. If I say "table tomorrow breakfast jump", we label that as nonsense because our natural language parser rejects it.

The difference being that natural language is "fuzzy", meaning we can say some sentences are slightly sensical, or slightly nonsensical, etc.

But we could create fuzzy math language too, if we wanted to. We probably don't want to, because we want math sentences to be parsed rationally, independently of and not needing a human's subjectivity.
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« Reply #13 on: February 10, 2010, 03:03:26 AM »

I don't think I completely agree with this. A formal language comes with an unambiguous grammar/syntax, it's an integral part of the whole system. If a statement cannot be parsed, this is within that whole system even if it's not in the language as such. The rules for parsing a formal language should be completely rational (one could say: mathematical in a broad sense), and as such don't need any human beings to interfere; a turing machine will do. The system-at-large (math's formal language plus the parser) can tell you a statement is nonsensical, without any human interference. In a running computer, one can argue math does exist by itself, and does itself.

I cannot see how adding the rules of parsing to the system does in any way affect my point. It is still a human being which must pass judgement whether the rules have been applied correctly. In the same way, any computer program designed to help with such a task must be checked for correctness by some human agent.

It is not the formal system that is rational, but the human being which applies it. To ascribe the property of rationality to a formal system makes no sense, since a formal system cannot act rationally. Indeed, it cannot act at all. Neither does a computer programmed according to the rules of a formal system act rationally. It does not act at all. It merely runs instruction sets according to its programming.

As you note, the parsing of a formal language FL does not take place within the language itself. Parsing is something done in addition to the definition of FL (which obviously also occurs outside of FL). Parsing is a part of the application of FL. No language can check the grammatical correctness of its own statements. Only the users of a language can do that. It is not by a linguistic act that an ungrammatical statement is found to be lacking in sense. (Though you can use language to express the fact that you have found a statement to be devoid of sense. And the same language can also be used to show why a statement is to be regarded as senseless.) It is me, not the English language or the grammar of English, who discovers "giraffe blunt cellar works" to be ungrammatical. In order to make that discovery, I apply the rules of English grammar.

A Turing machine will not do at all here, since it cannot find any statement whatsoever to be grammatical or ungrammatical. It can only generate strings of symbols according to the rules it was programmed with. "Sense" doesn't even enter the picture here. Only a human being can find a statement to be grammatical or ungrammatical - if aided by a Turing machine, by making sense of what the TM has put out.

The system-at-large cannot "tell" me anything at all. As Wittgenstein once noted, all mathematical statements say exactly the same, namely nothing. Note I had to put "tell" in quotes because of its metaphorical use. This is not nitpicking but an important distinction, since a formal system "telling" me something is just a figure of speech which is used to convey the notion of me using the formal system, applying it, to hopefully make discoveries which can answer the questions I am trying to resolve. It is me who can make discoveries with the aid of formal systems. Formal systems do not have the ability to discover. To ascribe to them the power of making discoveries is obviously completely nonsensical. In the same way, a computer running a program cannot be said to be "doing math", for it cannot "do" anything.

I can switch on a computer and have it execute computations. It will however only do (metaphorical "do" here) so on my instigation. The mere flowing of electrical currents within silicon structures does not constitute "doing math". That is not how we use that expression normally. You will probably call this nitpicking, but it is actually a very important distinction which I explained above and in my previous posting. What is happening inside computers is quite different from "doing math". Only when a human operates the machine can "doing math" be intelligibly said to be happening, and even then it's the human who does it with the aid of the machine, it is not the machine itself doing it.

Could someone with no formal mathematical training read a textbook full of formulas and proofs and figure out what it is good for? The answer is no, not because the symbolic transformations shown would be too cryptic, but because he or she was never shown how to apply it. The symbolic manipulations and transformations of math can be learned by rote with little or no understanding of what use they have. But if the relation the formalism stands in with the rest of the world is not explained, it will be just ink on paper. The explanation of its use is something which has to be given in addition to the formal system. I mention this to emphasize the importance of the difference between algorithmic procedures (= following rules) and using algorithmic procedures to achieve some end. Computers can be programmed so they will "follow" certain rules (metaphorical use of "follow" here, since the computer has no concept of what is happening when it is running programs). But they can not be made to set out to achieve ends of their own, since they are incapable of showing the appropriate behaviour which would warrant the ascription of volition and/or goal-oriented action to them.

Of course, the system itself was set up by humans, but one could say that about everything we study, model, etc. There's usually the condition that both input and output have to be understandable by humans.

I think there is no "but" here. This is actually the crux of the problem. All of our searching for truth, knowledge, facts, etc. hinges on human capacities, not the least of which is our language. Our understanding of the world, including our own capacities, is often crucially dependent on that. There could not be any notion of "truth" without language. The belief that our use of the word "truth" makes sense because there is some kind of independent, "absolute truth" "out there" which our term "truth" refers to is part of the philosophy of Plato. This is a metaphysical notion (one which I do not subscribe to), not a scientific one, which is nonetheless clandestinely applied in many "scientific" arguments, especially those about the nature of reality.

The real point for me here is, that there's no significant difference with natural language when it comes to labelling a statement nonsensical. If I say "table tomorrow breakfast jump", we label that as nonsense because our natural language parser rejects it.

Very interesting twist of logic here. You assume that human beings have a "natural language parser" which decides whether a statement is grammatical ("parses") or not. So you are from the start taking the view that man's capacity for language can be modelled on a computer paradigm using algorithms. This is a self-defeating move, since the difference between formal languages and natural languages is precisely what is at stake here. You're presupposing the result you want to argue for.

The difference being that natural language is "fuzzy", meaning we can say some sentences are slightly sensical, or slightly nonsensical, etc.

Putting "fuzzy" in quotes once more signifies metaphorical use. It isn't really clear what is supposed to be meant by the term here. What exactly is "fuzzy" about natural language? Of course you could hope that certain ambiguities of colloquial expressions can be eliminated by replacing them with more strictly defined terms in a formal language. But the definitions of those terms will, naturally, have to use natural language. Natural language is always what it comes down to in the end. We simply do not have anything else we can use or appeal to. There is no way around it, and I think it's actually easy to see that there isn't. The final link in the chain is always a human being. So if you think natural language is somehow tainted by "fuzziness", then so is any formal language, since it must necessarily appeal to and build on natural language.

The notion of a statement being "slightly sensical" is equally unclear. A statement either makes sense or it doesn't. There are no shades of grey in the category of sense.

But we could create fuzzy math language too, if we wanted to. We probably don't want to, because we want math sentences to be parsed rationally, independently of and not needing a human's subjectivity.

The fact that rationality cannot be equated with algorithmic procedures was what I tried to show at the beginning of this thread. There is no such thing as "rational parsing". "Rational parsing" as opposed to what? Whether a "parsing violation" has occured or not is for a human being to say, not for some set of rules, since rules can a) say nothing and b) are no use in the task of checking whether they were applied correctly. (What do you do if your task is to check whether "come home every tuesday" was applied correctly? You go to the person's home on tuesday and see if he is there. The rule itself will not help you with looking around and identifying the person in question. The act of checking is one thing. The rule prompting you to do so is another.)

"Subjectivity" is another term which I find hard to understand in this context. How could rules be parsed or followed "objectively"? As explained above, computers cannot follow rules, only humans can.
« Last Edit: February 13, 2010, 10:31:30 AM by pck » Logged
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« Reply #14 on: February 21, 2010, 05:40:46 PM »

I find the subject interesting but this is getting way too long!  Wink

I seem to disagree with you mostly on the many (implicit) assumptions in your posts, and the assumptions are mostly what lead to conclusions and arguments here.

The implicit assumptions I see are all of the "only a human can do this in the end"-type.

For example, if your assumption is that "judgement" about grammatical correctness can only be passed by humans (in the end), then we differ completely just on that alone. You say any machine would have to be checked for correctness by a human, but you don't tell us why. Do we also check human's verdicts on correctness by other humans? Why, or why not? And then who checks all these humans for correctness? This seems to me like an unworkable assumption, and rather anthropocentric.

To me, a much better working assumption would be to either allow both humans and machines to make a verdict on some sentence's grammatical correctness, or disallow both as they could both be incorrect...

A lot of your other points, I would make the same comments on, mutatis mutandis. Maybe I'll get back to some later.
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« Reply #15 on: February 21, 2010, 05:56:00 PM »

It is not the formal system that is rational, but the human being which applies it. To ascribe the property of rationality to a formal system makes no sense, since a formal system cannot act rationally. Indeed, it cannot act at all. Neither does a computer programmed according to the rules of a formal system act rationally. It does not act at all. It merely runs instruction sets according to its programming.

I think this might show our differences in assumptions clearest. You make a few important statements here, but to me they seem nothing more than assumptions. Like, "a formal system cannot act". What if human beings are in fact formal systems? Then you would be saying humans can't act. Someone might say "Humans, they merely are a bunch of particles interacting according to the laws of nature". So it seems like you're ruling out the possibility that humans would be formal systems, however, you don't provide any evidence for this statement.
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« Reply #16 on: February 21, 2010, 06:27:49 PM »

Computers can be programmed so they will "follow" certain rules (metaphorical use of "follow" here, since the computer has no concept of what is happening when it is running programs). But they can not be made to set out to achieve ends of their own, since they are incapable of showing the appropriate behaviour which would warrant the ascription of volition and/or goal-oriented action to them.

This is another assumption for which there just isn't any evidence, AFAIK. Why would a human be capable to achieve ends of his own, and a machine not? And how do we know that humans aren't "following" certain rules?

And even more interesting: how do we determine a certain machine has no concept of what is happening, compared to a human which supposedly does have this concept? Do humans have this concept at all times, or is it limited? How do we test humans for having a concept of what's happening? I suggest using a computer for that  Wink just to be objective.
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« Reply #17 on: February 22, 2010, 07:15:33 AM »

I think this might show our differences in assumptions clearest. You make a few important statements here, but to me they seem nothing more than assumptions. Like, "a formal system cannot act". What if human beings are in fact formal systems? Then you would be saying humans can't act. Someone might say "Humans, they merely are a bunch of particles interacting according to the laws of nature". So it seems like you're ruling out the possibility that humans would be formal systems, however, you don't provide any evidence for this statement.

This is interesting topic, so I just have to comment. I don't see rationality primeraly as a matematical or logical concept as it's discussed in this topic. I see it more of a biological or economic concept. In short to me rationality means that somebody (he, she or it) does what is best to it with the abilities and knowledge it has. This requires at least three things from the rational agent.

1- Rational agent has to be independent and it's actions can't be entirely determined by somebody else.

2. Rational agent has to have some sort of goal it's trying to achieve.

3. Rational agent has to be able to adjust it's behavior if the environment changes and new behavior is needed for best result.

In this sense even a worm could be said to be rational, but computer program fails in every one of the requirements. Computer programs are only tools for humans even though they are complex tools.





« Last Edit: February 22, 2010, 07:21:10 AM by blitzxz » Logged
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« Reply #18 on: February 22, 2010, 05:13:35 PM »

I think this might show our differences in assumptions clearest. You make a few important statements here, but to me they seem nothing more than assumptions. Like, "a formal system cannot act". What if human beings are in fact formal systems? Then you would be saying humans can't act. Someone might say "Humans, they merely are a bunch of particles interacting according to the laws of nature". So it seems like you're ruling out the possibility that humans would be formal systems, however, you don't provide any evidence for this statement.

I think your focus on scientific thinking misleads you into a misunderstanding of my main point. I'll try to clarify again:

A formal system cannot act any more than an idea or a concept can act. A formal system has no capacities to do anything. What you are thinking of instead are material systems which can be described using formal systems. To say that "human beings are formal systems" is to bend language, to invent a metaphorical, secondary meaning of a term which is not normally used like that. It is to ignore substantial parts of what must obtain in order for us to use the term "formal system". Similarly for "act". Why do we laugh when someone says "the computer doesn't like me" or "the computer has tricked me" or "the computer is acting up today". Because here the words "like" and "tricked" and "act" are used in a way not compatible with our everyday usage of them. You are free to invent new meanings of course. But obviously if we deviate from the standard usage of "act" or "formal system", we can argue for or against pretty much anything we like. The resulting statements would simply reflect the changes in meaning we have applied, and not any kind of truth about the nature of humanity.

Undoubtedly, there are many aspects of human life which can be adequately and cogently described using formal systems. However it does not follow that formal descriptions are all there is to it. Indeed, my initial argument at the beginning of this thread was just about that, I tried to show that what we call rational reasoning includes, but is not limited to, rule-based deduction in formal systems. There I provided the "evidence" that human beings are not formal systems. "Evidence" in quotes here because I did not conduct an experiment which discovered that fact. I didn't turn over a stone only to find that humans aren't formal systems. That human beings are not formal systems is not some contingent fact which could be otherwise: It is logically impossible (unthinkable) that humans could be formal systems, given our standard use of "rationality", "reasoning", "rule", "formal systems", etc.

In the same way, there can neither be any evidence in favour of the statement "a formal system cannot act" nor can there be any against it. The problem is not scientific. It is conceptual, a question of whether it does or does not make sense to say that. Sense is about our conceptional use of language and what linguistic pictures we can possibly construct. It is not about "whatever seems plausible to me" (except in the colloquial phrase "this makes sense to me", which is a figure of speech we use to convey our belief that some statement S is true). "Pigs can fly" is a false statement which nevertheless has sense, since it is actually imaginable that pigs might fly (if certain facts in the world were different). Contrarily, "the world exists" is a non-sensical statement since its opposite "the world doesn't exist" is not even imaginable. The existence of the world is a precondition for there to be any statement at all, so the assertion "the world exists" is logically incapable of containing any information. It is incapable of saying anything which would make me understand more than I did before.

Likewise, "a formal system can act" is incapable of saying anything at all since it violates our standard use of "act", which is reserved for living entities. To extend the notion of acting to computers is a move which stands in need of conceptual justification (for which I see no chances at all).
« Last Edit: February 24, 2010, 09:31:23 PM by pck » Logged
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« Reply #19 on: February 22, 2010, 05:40:12 PM »

I find the subject interesting but this is getting way too long!  Wink

Please tell me you are not really surprised.

The implicit assumptions I see are all of the "only a human can do this in the end"-type.

Actually I'm not making any assumptions at all here. Again, I believe you're being misled by scientific thinking. Almost all my points are about the sense of certain terms, not about theories in which they are used.

For example, if your assumption is that "judgement" about grammatical correctness can only be passed by humans (in the end), then we differ completely just on that alone. You say any machine would have to be checked for correctness by a human, but you don't tell us why. Do we also check human's verdicts on correctness by other humans? Why, or why not? And then who checks all these humans for correctness? This seems to me like an unworkable assumption, and rather anthropocentric.

I don't say why because there is no why. "Checking for correctness" is an expression originally invented to refer to human beings exclusively. So anthropocentrism is just what is called for here. If you want to extend the notion to computers (i.e. use it when you talk about computers) you are free to do so. But obviously this will not automatically shed insight on how humans check for correctness. The difference between computer parsing and evaluation of grammatical structures by humans is just what is at stake here. As argued in a posting above, you must not presuppose that which you want to demonstrate.

Calling that what the computer does "parsing", and then going on to claim that humans "parse" as well proves nothing and is bound to lead us into confusions about the nature of the human capability to understand language.

To me, a much better working assumption would be to either allow both humans and machines to make a verdict on some sentence's grammatical correctness, or disallow both as they could both be incorrect...

Machines can produce results, which may help a human reach a verdict. Passing verdicts is not something that we normally ascribe to non-living entities. If you want to call a computer running a program until it stops "reaching a verdict", you are free to do so. But this will reveal nothing about the nature of verdict-reaching of human beings. Again, that difference is precisely what is at stake here.

A machine working according to the rules of a formal system could never find itself to be incorrect. It can only produce output according to its design or programming. We get into an infinite regress of demands for justification if we continue to ask "and how do you know this is correct" since the same question can be asked about any possible answer one might give. So "checking for correctness" by humans or machines in whatever sense can never come to an end in the "objective manner" you seem to be looking for. I think this is a confusion which arises from applying the linguistic picture of "checking for correctness" ("cfc") in an illogical way: It makes no sense to ask whether my cfc-procedure checks out correctly itself. For it is the measure by which I judge correctness. To ask whether that measure is "correct" in itself makes no sense in the same way it makes no sense to ask about the price of a coin (except in the case of the coin being regarded as a collector's item). Logically, judgement of correctness comes down to "this is simply how I do it". Emphasis on "I" and "do". Very anthropocentric indeed.
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