I'm looking for info. on Boolean logic in relation to human reasoning, the similarities and differences. Everything I turn up by search is too technical for me and tends to AI oriented rather than focussing on minds and human epistemology. Anybody know of some straightforward discussions of this issue? Thanks in advance Canute
well, basic boolean reasoning as I understand it is this: if/not else. combined with OR, AND, and NOT, allow for the logical elimination of possible solutions one factor at a time, until a solution or solutions which fit the logic can be found. IF me.age=10 AND you.age=20 THEN print 'I am half as old as you are' ELSE IF me.age=20 OR you.age=10 THEN print 'you may be half as old as I am' The noticable difference between that and the human brain is parrallelisation. this method requires a one-item-at-time aproach, whereas the brain is able to handle more than one item at a time. Studies during the mid-nineties suggested that the average human brain can activly consider 7 things at once. Through personal study, I have decided that I can only consider 4 things actively, but I have been diagnosed with ADD and low-level dyslexsia, so I'm not average. However, we as humans are capable of using boolean logic to come to conclusions; these two things are not mutually exclusive.
River-Wind I don't really see how parallelism affects whether our thinking is Boolean or not (any more than it affects the nature of a computer's logical processes). I'm impressed if you can consider four things at once. Are you sure you really mean 'at once'? Canute
Parrallelism: I bet the brain does work on a boolean-like proccess (nueron on/off), but the pattern of the nueron firings has as much to do with the data in question as does the actual current state of the nueron in question. SO it's not just on/off, but a pattern of on/offs over a period of time. This must be interpreted by other brain cells, so they must also be active to recieve the pattern information. As for keeping multiple things in mind at once, I did a number of experiments over the past 7 years or so, trying to determine the accuracy of that "the average erson has 7 things" number, which I read in some textbook. I would mentally focus on a number of items, and then try and decern how many of them were actually "in focus", as opposed to "readily accessable info". For instance, I would visualise a row of 10 numbers, then take a step back from myself viewing that row. I would see how many were really there, and how many were hazy - only in place by logical formula. ie, If I have 10 numbers, I know that 0,1,2,3,4,5,6,7,8,and 9 are all in line. However, ignoring that knowledge, how many can I actually see? How many can I, by shifting my focus, make myself aware of (evidence that they were origanally not in focus). Usually it was 3 or four. I recently verified this test by also testing my automatic counting ability. Taking numerous series of objects in the real world, and seeing how many there could be in a group before I had to actively count them. I've found that I can see four objects and say to myself "that's four" without any intermediate thought, whereas if there are five items, I have to divide the group into two or more subgroups, and then add the totals of those subgroups to find the final answer. It appears that this is a limitation in my spacial abilities; I tend to imagine lines connecting the objects, and then I'm able to identify the number of "corners" which the shape that they create has. If the object is more complex than a square, I have to count, I can't simply identify. I asked my Dad these questions, and he has told me that he can recognise 5 items at a time this way, and given my knowledge of his cognitive abilities, that seems to support my limited testing. An interesting point to note on this topic is that differene between having something going on in your brain and being able to focus on an item. I, while counting these things, also have part of my brain flying around, thinking about random crap, plus a part of my brain thinking about the actual results of the testing procedure. So while I have 400 things going on in my head, I only have 5 awareness points - the four on the topic of my focus, and the one which is aware of the functioning of my brain as it works.
This is a sorta complicated topic, as you probably know. There's not going to be a succinct discussion of how well Boolean logic maps onto the function of the human brain because, well, nobody knows. So... I'll be as helpful as I can, but I'm warning you in advance. Computers all effectively run off of Boolean logic, since all of the operations in most forms of processor assembly language act pretty much directly on the binary data types within the system. This may actually mean that an assembly command acts on bits in groups of 8, or 16, or 32 at a time. All the same, the commands are generally representable in simple Boolean logic. In the simple analysis, the human brain represents a very large number of synapses which can either be active or inactive. As such, people claim that the brain is also binary and essentially like a computer but this is not necessarily the case. There are two reasons why not: 1) I understand that neurons are not just "on" and "off", but rather have a state related to "action potentials". I am told that these do not resemble the computer science model of binary information storage, but I've not yet learned enough about it to understand properly. 2) As near as anyone can tell, the brain actually functions from a constantly cascading series of operations; any apparent "state" is actually more of a cycle of operations in the brain. As such, the standard computer science conception of a computer doesn't map very well onto the brains of humans; the ideas of state, information, and processing may be very different in our heads than in your desktop computer. Some people (like Penrose) believe that the human brain is the only possible form that an intelligent brain can have; I doubt this. Others have varying beliefs about the structure of human intelligence. If you're looking for something to read, there's a book by Daniel Dennett called "Consciousness Explained" in which he details the things he believes are required to have a conscious entity. Its ISBN is 0316180661 if you're interested, but briefly speaking he believes that intelligent creatures are made up of immense arrays of interacting parts that develop associations between sensations and occurrences. I don't know how helpful I've been. Do you have any more specific questions?
River Wind Interesting research - thanks for sharing it. (You've got me trying it now). I wonder if the fact that you can't hold more than 3 or 4 items in your awareness (without using some algorithm) relates to the fact that some types of people have no higher numbers than this. E.g the Hottentot people had no number higher than three (anything higher was 'many'). BigBluehead I should have made my question more clear. I'm not concerned so much with how the brain works, rather with how our rational reasoning works. I was asking whether all our rational calculations, (as opposed to our direct experiences or intuitions), are Boolean in structure, or are there other ways of thinking and proving. I suppose I could rephrase it as - are all rational arguments and proofs Boolean in their logical structure? Thanks for the Dennet reference but I find 'Consciousness Explained' to be nonsensical and am more of a Chalmers fan.
Ah... I have a personal opinion on this one, but this is a problem that has troubled the mind of the philosopher for thousands of years. My personal belief is that reasoning (beyond the very basic inductive form) is a TECHNOLOGY. It's something that humans developed in the same way that they developed clothing and violins and crop rotation. It's a technique that we apply because it gets us better results. Boolean logic, which has strong ties to set theory, is a way of thinking about things. It assigns truth values to atomic statements and formulas composed of atomic statements and connectives. With respect to your original question, I would say that although our thoughts can be expressed in Boolean algebra, it is not necessarily sufficient to describe them. Even if it was, that doesn't mean that our thought processes are fundamentally based in Boolean logic. I seem to recall that there was a statement from DeMorgan that couldn't be stated in first-order logic: "All horses are animals, therefore the head of a horse is the head of an animal." This statement can be expressed as a formula of the predicate calculus, but in general our natural languages (English, French, Chinese &c.) cannot be entirely represented by logical constructions. There is an entire field, the Philosophy of Language, which tries to address this problem. If our artificial languages fail to model our natural languages completely, then they probably also fail to model our thought processes completely. But that's just a theory.
There have been studies in which monkeys have refused a reward for some action when a monkey next to then got a better reward for the same action. That seems to imply that some form of boolean logic is in use to determine a course of action in a non-human. This would throw doubt on logic being invented (though it could be that the rules of boolean logic could be a human invention to describe how the brain natively functions). "I won't take this cucumber because that monkey got a grape for the same work. I want a grape" in other words: "My work=his work, therefore my reward should=his reward. This reward != that reward therefore, it suggests that my work!=his work. This isn't the case (as my work does=his work), so this whole exersize is crap, I refuse to participate anymore." http://www.newscientist.com/news/news.jsp?id=ns99994179
River-wind - that's not Boolean logic. What you're describing in the monkey thought process is not something you can express in Boolean logic. To rephrase what you said, here's the monkey thought: (I'm going to have to invent an "equivalent value" symbol here, because = in boolean algebra is identity, not equivalent. I'll use Q to indicate equivalence.) P1 (mywork)Q(hiswork) P2 ((mywork)Q(hiswork) -> (myreward)Q(hisreward)) P3 ~((myreward)Q(hisreward)) So: 1. (myreward)Q(hisreward) (P1, P2, MP) 2. ~((myreward)Q(hisreward)) (P3, R) 1 and 2 are opposites so this system is inconsistent. Therefore abandon this system as unfair. If we pursue a derivation of these premises we can get the conclusion, but there's a problem. There's no Boolean representation for problem domains, so we can't represent the idea of exiting this problem domain to look for a more consistent one. The fact that this thought process can be (partly) expressed in a sort of mathematical notation doesn't mean that that is how it works, and it doesn't mean that the notation is sufficient to describe all circumstances. Also, as I described before, the "equals" in Boolean algebra is the "equals" of identity, not equivalence. That means that under normal circumstances (mywork)=(hiswork) would NEVER be true because (mywork) is a different thing from (hiswork). Already we are abusing Boolean logic. Consider the following series of thoughts. 1. I can sell an apple pie for two dollars. 2. Making an apple pie takes ten apples. 3. Jane sells apples for ten cents each. 4. So, normally I make a one dollar profit per pie. 5. If I can get them cheaper, my profit will be larger. 6. Jane doesn't know how much I sell the pie for. 7. So, she doesn't know exactly how much the apples are worth (to me) even though I do. 8. I will tell her that her apples look crummy today, and try to buy them for only eight cents each. 9. Then I will make one dollar and twenty cents per pie instead. 10. Then I will get more money, which is good. This will be very difficult to express as in Boolean logic, because of the following progression: Every apple I buy is worth exactly (twenty cents minus the purchase price) to me. Jane believes that they are only worth (ten cents) to me. I will lie to Jane and tell her that they are only worth (eight cents) to me, because she does not know that I know exactly how much they are worth. I will be lying because I will say that the apples are worth less, when in fact they are worth the same because I will still sell the pie for the same price. Things like this are easy to describe in natural language, even fairly accurately, but difficult to describe in logical notation. Also, when you translate anything to a system where there is no implicit concept of motivation, it's difficult to bring motivation in as a term.
BigBlueHead Great post. I can see the complications. Is there any general way of describing the sort of calculations humans do? (Leaving aside motivation etc.) For instance do we always use a syllogism type model to reach conclusions, or are there all sorts of models? Do you have any good references, I haven't found any but I don't know quite what I'm looking for. This news about monkeys seems to have caused a surprising stir. Did the experts really used to believe that monkeys weren't this intelligent?
Many people still believe that animals and humans are fundamentally different. (Something to do with Descartes, I think.) As such, for an animal to display qualities that we are supposed to have reserved as exclusively human is usually cause for people to either rethink their idea of animals, or believe that the action the animal took isn't really what we thought it looked like. To learn about syllogisms and the broader form of them, the Propositional Calculus, there are probably many good primers that you can google for. I'll see if I can find one. This is a pretty standard series of lecture slides for the propositional calculus. http://www.thoralf.uwaterloo.ca/htdocs/FALL00/SLIDES/chap2.pdf It is a little confusing because it is (at least intended to be) a rigorously defined system. This was the system of logical notation originally developed by Aristotle, so I understand, although it's obviously changed a bit in the last ~2000 years. This system STRONGLY resembles Boolean logic, so if you're already familiar with stuff like circuitry design/Boolean algebra then it shouldn't be too bad. Good luck!
Thanks. But I don't want to follow up how each of these work in any detail. I'm just trying to establish if there's any agreement as to what general system best models human deductive thinking.
In that respect I can only offer the anti-Empirican proof, which is that it's impossible to prove that nothing is true. Whether this is correct is not known.
