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Offlinemorrowasted
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Intuition and Logic: A Social and Philosophical Experiment
    #14115896 - 03/13/11 07:15 PM (12 years, 11 months ago)

Which came first: logic or intuition? Is/Was ‘logic’ simply borne out of our shared and seemingly innate intuitions, or is/was our ‘intuition’ borne out of our habituation to critical thinking strategies that rely on systems of logic that are at least partially learned? In other words: when we describe someone/thing as ‘logical’, is that just a fancy shorthand way of saying that someone/thing makes sufficient use of his/her/its intuition? Or, when we characterize someone/thing as having ‘intuitive’ ability or quality, is that just a fancy shorthand way of saying that someone/thing makes use of its capacity to be logical well enough that it is able to do so sub-cognizantly? Or, could both of these hypothetical situations be true simultaneously? What does your gut tell you?

My attempt at approaching these questions will involve a method that is indisputably learned: a ‘scientific’ survey. The idea is simple: I will present arguments, and you will indicate whether or not you think they are valid or sound by responding to a poll. Because this exercise is intended is to measure your current ability to intuit the validity of arguments, try not to devote more critical thinking resources to checking their validity than you typically would. When the results are in, we can see if there are any examples of invalid arguments that a significant percentage of the sample incorrectly intuited to be valid, and anyone in the sample will then be free to attempt to justify their deliberations (by whatever means; not restricted to formal predicate/propositional/etc. logic).

After a certain period of time, I will close the poll and post the correct answers. (In)Validity of arguments will be demonstrated in Predicate Logic, and a formal counterexample will provided for all invalid arguments. Example:

Argument #1: (1) Any integer larger than zero is positive, and (2) any integer smaller than zero is negative. But, (3) zero is neither larger nor smaller than itself. Consequently, (4) zero is neither positive nor negative.

Is this line of reasoning sound? Is the “argument” valid? Yes or no?




















According to the system of Predicate Logic, this argument is invalid. Here is its Truth-Tree: 



For those of you who don't know what a truth tree is- to put it simply, it's a methodological way of explicating every possible instance of the argument in order to see if there is one among them in which all of the premises are satisfied (true) while the conclusion is not (false). If there is, that instance can be transposed into a counterexample:



Once a counterexample has been produced, the argument is, by the official definition, proven to be invalid.


So, without further adieu, here is your first set of arguments:
When a South Florida home was burgled, the Cuban-American owner reasoned that the theif was also Cuban-American :: "Someone took both the TV set and the St. Lazarus icon. Therefore, the TV and the icon were stolen by a Cuban-American, since only a Cuban-American would take the icon."
Users may choose only one (9 total votes)
Valid
-
3 33%
Invalid
-
6 67%
Philosopher Peter Singer's sentience-boundary is employed by the following argument: "Having the capacity for suffering is a necessary condition for having interests. [Therefore], A mouse has interests because it can suffer."
Users may choose only one (9 total votes)
Valid
-
7 78%
Invalid
-
2 22%
"Animals with good personality aren't filthy. Thus, if a pig had a good personality, it wouldn't be filthy."
Users may choose only one (9 total votes)
Valid
-
6 67%
Invalid
-
3 33%
"My kittens are anatomically identical. If so, then either all of them are males or all of them are females. All calico kittens are female. There is a calico in the litter. Thus, all of my kittens are female."
Users may choose only one (9 total votes)
Valid
-
4 44%
Invalid
-
5 56%
Votes accepted from (03/13/11 07:03 PM) to (03/20/11 07:03 PM)
You must vote before you can view the results of this poll.
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Offlinenanomagnetic
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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: morrowasted]
    #14117300 - 03/13/11 11:45 PM (12 years, 11 months ago)

Fuck. It's been years since my formal logic class. :confused: Maybe if I can dig out my old textbook I'll give this a stab. Tagged for tomorrow

edit:

Well, it's almost tomorrow, Pacific Daylight Time. So close enough? Anyways I'm following you're example and I don't quite follow. I see that your counter example builds from conditions that you found in your logic tree. But i'm not connecting the dots; I'm not seeing where the analysis was internally consistent. I'm not seeing how the analysis is constrained by the argument, I guess.

I'm not even sure if that's necessary -- still gotta find that text book.

In any case, for now I'll just do the poll on intuition. Come back to the formal logic actually-tomorrow. It's good practice anyways. :strokebeard3:

second edit :yawn:

Well they all sound valid without thinking about them too much. I'm not sure what that says about my intuition. I mean, if I think outside the arguments I can come up with counter-examples that would make the arguments wrong, but I can't instinctively think of anything that makes them invalid.

Weird.

And now I will dream strange dreams :lol:

Edited by nanomagnetic (03/14/11 12:21 AM)

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: nanomagnetic]
    #14118425 - 03/14/11 08:32 AM (12 years, 11 months ago)

The counterexample is simply: (1) Any integer larger than zero is positive [T], and (2) any integer smaller than zero is negative [T]. But, (3) zero is neither larger nor smaller than itself [T]. Consequently, (4) zero is neither positive nor negative. [F]

The conclusion is false, because it is possible, as the truth-tree demonstrates, to have a instance where zero is both positive and negative (while still satisfying all of the premises).

You should avoid using any external resources or formal knowledge (inasmuch as you possibly can) to respond to the polls... that kind of defeats the purpose.

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InvisibleDieCommie

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: morrowasted]
    #14118446 - 03/14/11 08:38 AM (12 years, 11 months ago)

I dont get it.  Could you explain branch 3 to 5 on your truth tree?  And why is it the same as branch 11?

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: DieCommie]
    #14118497 - 03/14/11 08:59 AM (12 years, 11 months ago)

Quote:

DieCommie said:
I dont get it.  Could you explain branch 3 to 5 on your truth tree?  And why is it the same as branch 11?



Technically that isn't "branch 3", it's just a number indicating that it was the third formula that was used in the tree-building process. But I'll refer to it as branch 3 for the sake of this post.

Branch 3 indicates, "Pe or Ne". You will notice the two arrows desceding from branch 3 point at two new branches that are respectively headed by Pe and Ne. In the branch (and all sub-branches) below Pe, you will find every possible permutation of the truth values of Ne, Le, Se (assuming Pe). On the right branch, you will find every permutation of Le, Se, and Pe (assuming Ne). In this way, every possible instance of the argument is iterated.

Simply put, at Branch 3, you are saying, "What happens if Zero is positive, and what happens if zero is negative?" which you answer by subsequently asking, "If Zero is positive, then zero must either be positive or must not be larger than itself. What happens in either case?" (branches 5-7). This is again answered by asking, "If zero is positive, and zero is not larger than itself, then it must either be negative, or it must not be smaller than itself." This is of course a very confusing question, and you'd never ask such a thing in real life, but precision is apparently a vital characteristic of logic, so there it is. The other branches, then, represent other series of questions. Thus, the truth tree is a shorthand way of evaluating every series of considerations about the possible outcomes of any line of reasoning.

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InvisibleDieCommie

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: morrowasted]
    #14118515 - 03/14/11 09:06 AM (12 years, 11 months ago)

Im not convinced.  It looks like you are just redefining zero to come to a crazy conclusion that you would never be able to come to if you used the traditional definition of zero.  Any branch that asks what if zero is positive or negative must be terminated because zero cannot be positive or negative.  Otherwise, you are not talking about zero.

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: DieCommie]
    #14118554 - 03/14/11 09:19 AM (12 years, 11 months ago)

Quote:

DieCommie said:
Im not convinced.  It looks like you are just redefining zero to come to a crazy conclusion that you would never be able to come to if you used the traditional definition of zero.  Any branch that asks what if zero is positive or negative must be terminated because zero cannot be positive or negative.  Otherwise, you are not talking about zero.



Your argument, then, is

(1) If the concept being discussed can be either positive or negative, then it cannot be zero.
(2) |:. Therefore, either zero cannot be positive or negative, or zero is not subject of our discussion.

Your argument is probably valid. You have made an error of reasoning, however. You are assuming that the premises of an argument must have some kind of objectively factual basis; thus, any premise that is not factually and objectively True will render an invalid argument. The problem with this line of reasoning is that facts are, in fact, illusory. Truth is relative; all is perception. The success of argumentation, therefore, depends on the capacity of its participants to presume the truth of certain assertions. Thus, the first step towards constructing a good argument is to be very picky about what you assert in your premises, so that they will be as close to what people call "common-sense" as possible.

Note that not all (or necessarily any) of the arguments in post #1 are intended to be good arguments, they are simply arguments that have structures similar to those commonly used by average people in their day-to-day lives.

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InvisibleDieCommie

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: morrowasted]
    #14118565 - 03/14/11 09:24 AM (12 years, 11 months ago)

Quote:

You are assuming that the premises of an argument must have some kind of objectively factual basis




If that were not the case, then why did you pick 'zero' which has well defined properties rather than just using a variable place holder like 'A'?  By using zero you are either inherently assuming all of its properties or you are secretly redefining it to prove a shocking conclusion.

(also note that the properties of zero dont depend on truth or perception, they are defined to be what they are.)

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: DieCommie]
    #14118594 - 03/14/11 09:38 AM (12 years, 11 months ago)

I understand that zero is, by official definition, neither positive nor negative. My point is that my post is not intended to demonstrate that it is. The argument is just an example. The content of the argument is 100% irrelevant to its validity. Here is a reformulation of the exact same argument using completely different content:

(1)Anyone who [l]oves shrooms is [p]robably cool. (2) Anyone who hates [s]hrooms is probably [n]ot cool. (3) [E]than does not love or hate shrooms. (4) |:. Therefore, Ethan is probably neither cool nor uncool.

If the argument containing words about the number zero is valid, then so is the preceding argument. It doesn't matter whether or not they are True- truth is user-defined. Logic is about taking all of the truths you already know and trying to find a way to represent them all without being inconsistent.

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InvisibleDieCommie

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: morrowasted] * 1
    #14118599 - 03/14/11 09:42 AM (12 years, 11 months ago)

Yea, I have taken logic classes before.  In the first week they always 'shock' you by giving a valid argument along the lines of;

P1: If you are a human, then the sky is green.
P2: You are a human.
C1: The sky is green.

Then the students do a collective "What?, but the sky isnt green!" :kingtard:

Beyond that initial shock value, I see no reason to use non-conventional definitions.

edit- that is, if you want to talk about zero - then use the definition of zero and talk about it.  If you want to talk about the structure of logic, then use variable placeholders.  Otherwise, you are just going to confound the two.

Edited by DieCommie (03/14/11 10:17 AM)

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Re: Intuition and Logic: A Social and Philosophical Experiment [Re: DieCommie]
    #14124456 - 03/15/11 10:31 AM (12 years, 11 months ago)

Okay, I understand what you are saying. Yes, part of the point of the thread is that fuzzy logic can be employed to trick people into becoming persuaded of things they otherwise wouldn't have. People can construct very consistent and structurally valid arguments that are nevertheless irrelevant because they still involve redefining the connotations of words from whatever conceptualization of them the listener has to whatever conceptualization of them that the persuader wants them to have.

Many people do not have de facto knowledge of the precise properties of zero. Many people would probably say that zero is indivisible, for example. Thus, it is conceivable that someone could be convinced that zero is, in fact, both positive and negative, based on this argument.

When it comes down to it, though, it is still true that your conception of zero as being neither positive nor negative is not one that you arrived at as a result of your own critical thinking, but rather one that you adopted because you were told to do so. There was a time, however, when the idea of zero did not even exist- much less have properties like being positive or negative. The officially established definition of zero, however, which asserts that zero is neither positive nor negative, was arrived at through the practice of logic. The argument in my post, thus, is not intended to be a demonstration that logical thinking strategies necessarily result in the conclusion that zero is positive or negative. The content of the argument, as I said, is irrelevant to validity (by the technical/official definition of validity). If you think the technical/official definition is irrelevant or meaningless, then keep in mind that your own response (that my argument is invalid because it asserts an abuse of zero's definition) also necessitates the inclusion of a technical definition- that of "zero".

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