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Is X Y because it is X, or is X X because it is Y?
X is Y because it is X
X is X because it is Y
...wtf?
waffles!
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BDR
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>_> Sorry if I hurt your brains; I'm trying to write a short response on the Euthypro and so be sure I get how the logic goes..
01-28-2007 at 10:27 PM
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Chaco
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I picked the second option - of course X can't be Y because it's X, because we just said it was Y. But X can be X because it's Y because Y can be a quality describing X, and "X can be X" is merely self-referential redundancy.

...Also, I like waffles, but I didn't want to pick that option.

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01-28-2007 at 10:44 PM
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Alneyan
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BDR wrote:
Sorry if I hurt your brains[...]

I certainly wish I had a spare one. Your question just went a couple parsecs over my head. So, if someone knows *what* the question is about, I wouldn't mind a slightly clearer formulation.
01-28-2007 at 11:01 PM
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zex20913
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I think it's just an exercise in totally abstract logic. No context, just a statement. I read it as Y->(X=X), which is always true, because X=X, and the consequent must be false for a false statement.

Though I do indeed like waffles.

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01-28-2007 at 11:08 PM
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BDR
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Background on the Euthypro commencing...

Socrates was headed off to the trial where he was going to be indicted for the crime of impiety (as well as the slightly more famous charge of 'corrupting the youth') and runs into a guy named Euthypro who claims that his knowledge of piety allowed him to be sure that charging his father for murder (the guy was a servant who killed another servant, but who was then left outside with no food or water while the father went to some oracles to figure out what to do; when they came back the guy was dead) was the right thing to do. Socrates asks Euthypro to tell him what piety is then (so he can rebut the charges laid against himself), and Euthypro comes up with the idea that piety is what the gods love. Socrates asks him whether piety is pious because it's loved by the gods or if it's loved by the gods because it's pious (Euth answers the latter), and then asks whether that which the gods love is god-loved because it's loved by the gods or if it's loved by the gods because it's god-loved (this time, it's the former). Socrates then tells him that the pious can't be the same thing as that which the gods love, and explains the logic.

EDIT: But yeah, the poll as stated shouldn't really need any context (only bit that exists is what inspired the question anyway). Oh yeah, and the plural (brains) was meant not because there is some reader with multiple brains out there but because there are multiple readers (who then, according to the laws of this universe, should have just as many brains).

[Last edited by BDR at 01-28-2007 11:22 PM]
01-28-2007 at 11:18 PM
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eytanz
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zex20913 wrote:
I think it's just an exercise in totally abstract logic. No context, just a statement. I read it as Y->(X=X), which is always true, because X=X, and the consequent must be false for a false statement.

Though I do indeed like waffles.

y -> (x=x) is not a valid formula since y is not a proposition.

I understood the two options to be:

is(x,y) -> is(x,x)

and

is(x,x) -> is(x,y)

But the rest of your logic holds - is(x,x) is a tautology so the first statement is always true, but is(x,y) is a contingent truth so the second statement can be false.

Note that "because" is a poor translation for material implication, however, since it implies causality.

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01-28-2007 at 11:57 PM
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BDR
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eytanz wrote:
But the rest of your logic holds - is(x,x) is a tautology so the first statement is always true, but is(x,y) is a contingent truth so the second statement can be false.

I'm not terribly sure of that (or at least that this logic can be extended to other cases); consider the example "Is a box tall because it is a box?" A box can be tall, but not just because it's a box.

For those who'd like an example of the latter statement, one could be "Are the righteous righteous because they are virtuous?"
01-30-2007 at 01:16 AM
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zex20913
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The example here should be "Is a box a box because it is tall?" A box is a box, regardless if it is tall or not.

Basically, there's not enough here to make logical statements that work.

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01-30-2007 at 02:22 AM
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eytanz
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(note- this is a response to BDR)

That was what I was saying in the end of my post - the logic only works if you translate "because" as the logical operator "->". But that's a poor translation, because the word "because" implies that there is a relationship between the two statements, and the material implication "->" does not.

So, if I say (in English) "This box is tall because it is a box" that sounds weird. But if I write the logical statement "This box is a box -> it is tall" then that is always true.

"Are the righteous righteous because they are virtuous?" is a particularly bad example, because X and Y in this case are related - it's difficult to be righteous without being virtuous. So while the question needs to be answered affirmatively, it does not allow conjecturing to the general case.

Compare:

"Are the circles circles because they are round?"

and

"Are the circles circles because they are triangular?"

The sentences have exactly the same form as the sentence you gave, but the first must obviously be answered "yes" while the second must be answered "no".



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[Last edited by eytanz at 01-30-2007 02:30 AM]
01-30-2007 at 02:29 AM
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Banjooie
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AH, but it doesn't.

Circles are circles because they are *perfectly* round, 360 degrees, and have exactly one side.

There are many round things that are not circles. For instance, ovals.
01-30-2007 at 04:17 AM
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eytanz
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Banjooie - that's a totally stupid nitpick - so my example of a special case wasn't that great. That just proves my point, which was "X is X because it is Y" is not a universally true form.

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01-30-2007 at 04:23 AM
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zex20913
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Banjooie wrote:
AH, but it doesn't.

Circles are circles because they are *perfectly* round, 360 degrees, and have exactly one side.

There are many round things that are not circles. For instance, ovals.

Circles have 2 sides. An inside and an outside. Ask any topologist.

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01-30-2007 at 04:26 AM
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Maurog
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Hmm...
((X==X)->(X==Y))      // X is Y because it is X
((X==Y)->(X==X))      // X is X because it is Y
                      // a->b means (b || !a)
((X==Y) || !(X==X))   // X is Y because it is X
((X==X) || !(X==Y))   // X is X because it is Y

((X==Y) || false)     // X is Y because it is X
(true   || !(X==Y))   // X is X because it is Y

(X==Y)                // X is Y because it is X
(true)                // X is X because it is Y 

I have to conclude that X is X because it is Y...


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01-30-2007 at 07:19 AM
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English is the same as Propositional Logic because it is English?
or
English is English because it is the same as Propositional Logic?
01-30-2007 at 07:27 AM
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Banjooie wrote:
AH, but it doesn't.

Circles are circles because they are *perfectly* round, 360 degrees, and have exactly one side.

There are many round things that are not circles. For instance, ovals.

Well, if we're going to nitpick, what is a perfectly round object that has more than one side?

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01-30-2007 at 09:49 AM
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A hollow sphere, why do you ask?
01-30-2007 at 10:11 AM
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A circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, called the centre.

The way I define "side", a circle has infinite number of sides. How do you define "side"?

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01-30-2007 at 10:32 AM
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Rereading my posts above I see that I've been a bit confusing since I've been shifting assumptions between them without being explicit about it. So just to summarize all my points:

A - *If* we translate "X because Y" as "Y -> X" *then* "X is X because it is Y" is always true.

B - "Y -> X" is a reductive translation of "X because Y" and should be avoided.

C - Under a less reductive translation, "X is X because it is Y" is not always true.

D - Regardless of how we translate "because", "X is Y because it is X" is not universally true.

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01-30-2007 at 01:03 PM
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Mattcrampy wrote:
Banjooie wrote:
AH, but it doesn't.

Circles are circles because they are *perfectly* round, 360 degrees, and have exactly one side.

There are many round things that are not circles. For instance, ovals.

Well, if we're going to nitpick, what is a perfectly round object that has more than one side?

The Death Star. It has an inside and a dark side. (An outside too.)

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01-30-2007 at 01:11 PM
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The word "because" has this cause-effect meaning to it, which has no intrinsic meaning in logic (you could define one, but if two people went into different rooms to define "X causes Y" they'd almost certainly come back with different definitions). So if we're trying to be logical, I'd interpret "X is Y because it is Z" as "X is a Z, the set of Z's is a subset of the set of Y's, therefore X is a Y."

In that case, you can re-formulate this stuff according to basic set-theory/first-order logic, i.e., are all God-loved things loved by the Gods? Yes? Then piety is loved by the Gods because it is God-loved. Are all things loved by the Gods God-loved? Etc.

By the way, being a topologist, I thought I'd mention that a circle only has an inside and an outside when thought of as embedded in a 2-dimensional space. Put a circle into 3-dimensional (or higher) space and it doesn't divide it up any more. View it as a space on its own with no ambient space and it doesn't have an inside or an outside (and I suppose could be considered a 1-sided figure then). Of course, to a topologist, a square and a triangle are both circles :)

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01-30-2007 at 03:07 PM
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MartianInvader wrote:
The word "because" has this cause-effect meaning to it, which has no intrinsic meaning in logic (you could define one, but if two people went into different rooms to define "X causes Y" they'd almost certainly come back with different definitions).

Well, being a semanticist, I'd like to think this is the interesting part.

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01-30-2007 at 03:20 PM
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zex20913
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MartianInvader wrote:
By the way, being a topologist, I thought I'd mention that a circle only has an inside and an outside when thought of as embedded in a 2-dimensional space. Put a circle into 3-dimensional (or higher) space and it doesn't divide it up any more. View it as a space on its own with no ambient space and it doesn't have an inside or an outside (and I suppose could be considered a 1-sided figure then). Of course, to a topologist, a square and a triangle are both circles :)

And as a mathematician, this is the interesting part to me. :)

I totally forgot about higher dimensions. Good catch.

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01-30-2007 at 04:34 PM
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i didn't undersatand a word so i simply put
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02-03-2007 at 04:56 PM
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By far, Waffles seem to be the most popular snack of mathematicians! Rofl! Is a Rofl a Waffle because it Rofls? Or does a Rofl Rofl because it eats waffles?

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02-10-2007 at 04:10 AM
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