“Goodman’s Grue” just doesn’t seem to be a problem at all. It can only seem like a problem if you forget that ‘grue’ is a name given to a somewhat complex sequence of events (relative to a thing just being a color) and start making mistakes when manipulating the symbol. There just isn’t any reason to suppose there is any ‘threat to the whole of science’ in the first place.
I agree, you are essentially saying that if you forget that green and blue are not simply syntactical binary predicates from first order logic – if you remember that they are semantic concepts, then it is clear that the grue problem is not at all a threat to science. But this is no trivial result, it means that there is a part to the application of Bayes, i.e., induction, which requires the acquisition of semantic concepts. If you fed evidence statements into a bayesian program, it would have to have an understanding of the semantic application of terms like green and grue. So you are right: reducing “green” and “grue” to their semantic/physical tests is the key in my proposed solution. Bayes can’t be enough, obviously, since bayes is a syntactical and axiomatic system.
I guessed what seemed bayesian to me about the whole thing was the analogy to bayse’s table problem, which was the main intuition pump I used to solve the problem. I’ll edit the article to reflect this. Thanks
[I]t means that there is a part to the application of Bayes, i.e., induction, which requires the acquisition of semantic concepts.
I think this is incorrect. The actual application of Bayes’ theorem works the same way for each of your theories. What differs is your priors, and that difference sticks around until you have some evidence that’s more likely for one theory than another. If your priors are screwy, then yes, you’ll hold wrong beliefs until you’re given evidence that lets you distinguish between the correct and incorrect beliefs.
I guessed what seemed bayesian to me about the whole thing was the analogy to bayse’s table problem, which was the main intuition pump I used to solve the problem.
I guessed what seemed bayesian to me about the whole thing was the analogy to bayse’s table problem, which was the main intuition pump I used to solve the problem. I’ll edit the article to reflect this. Thanks
The first thing that struck me was the inherently self-contradictory nature of the grue definition. For physical properties to be retroactively alterable seems to contradict fundamental principles of causality and matter.
Am I simply not understanding the topic? Or is my intuitive-conceptualization too influenced by “timeless physics”? (The notion that all moments in time can be stated to ‘exist’).
The most you get with statements about “grue-ness” is that some objects which we observed to be “green” were in fact green but after a specific time (T) all changed to another color. This does not change the fact that they were green in the past.
Science seems perfectly-well suited to handling things that change from one state to another. Radioactive decay, for example. If this is some extra-material transition that occurs… well, I just don’t see how that’s an actually available physical phenomenon. If you change the definition of the term, you are now discussing a new thing.
defenitions point to meanings, but the meaning of a term can only be found by looking at the cognitive machines that use the term, and in that specific contxt as well.
defenitions point to meanings, but the meaning of a term can only be found by looking at the cognitive machines that use the term, and in that specific contxt as well.
… I am not especially aware of there being a functional difference between a “statement of meaning” and the meaning itself when we’re discussing what terms mean.
Anything that is applicable to a definition is applicable to the meaning itself. Any adjustment of the meaning adjusts the defintion. Any adjustment of the definition adjusts the meaning. When you have a direct correlation with bi-directional causality, that is mutual identity.
“mortal” implies that a thing is capable of transitioning from one state to another. This would be more like trying to create a tearm, aled, which those things that have the property of being aled where time=-T are alive but where time=+T are dead...
And yet no events are to have occured at time=T. This is a material contradiction. Even worse; another possible meaning would be that things which are aled where time=-T are alive where time=n; and, simultaneously, things which are aled where time=+T are dead where time=n.
And yet the same group of objects are to have the characteristic of being aled -- yet, again, no events are to have occurred.
This is paradoxical, certainly—but only because the definition contradicts itself. grue and bleen require that A=¬A; a false assertion. (EDIT: Apparently I need to explain that the paradox I mention hereIS NOT the Goodman’s Grue Paradox.)
Contrastingly, those things which are “mortal” are defined as having having a unique time=d, where time=-d they are alive; where time=+d they are dead; and where time=d they transition states.
Can you clarify what prevents a grue/bleen categorizer from saying that when a grue object changes the frequency of light that it reflects (which is something every grue object does at one time or another), that’s an event?
when a grue object changes the frequency of light that it reflects (which is something every grue object does at one time or another)
That’s just it—to be “grue” its color must never change from the color “grue”. “Grue” is a color. Not two colors—just one. If this confuses you—it should. It’s a self-contradicting definition. “Grue” is a violation of the Law of Identity.
I agree that its color never changes from the color grue, nor did I suggest that it did. I’m still curious about the answer to my question (which was about light frequencies, not colors), though.
I am talking about an observer who experiences certain colors in response to certain patterns of light frequencies over time. So, both.
Here’s the thing: “grue” and “bleen” are each only one color. For this to be explicable to your understanding, “grue” would have to have one and only one light frequency for time=n.
The problem of course is that this light frequency is apparently the same as “green” at time=-T, but the same as “blue” at time=+T.
The very definition of “grue” is such that A=¬A.
Should we introduce to the “grue-ites” the notion that objects can change color—then they would be incapable of maintaining their belief in “grue”. Essentially; this entire conversation is predicated upon “grue-ites” existing in a universe without light-frequencies but still possessing color. This is, of course, explicitly contradictory: colors are frequencies of light (as experienced by observers).
1) If the definition of “grue” is such that the light reflected by a “grue” object is the same frequency at all times, and further that the observer’s eyes don’t change and more generally that nothing in the world changes, then I agree with you that “grue” as defined is a contradictory idea, for essentially the reasons you cite.
2) In the real world, “green” is not associated with one and only one light frequency. There are lots of light frequencies that would cause me to experience a sensation I’d label “green”. Indeed, I am seeing several dozen of those frequencies as I write this.
3) In the real world, there is no light frequency associated with “green” and only “green”. There are lots of situations that will cause me to experience an object reflecting a single light frequency as different colors.
In the real world, there is no light frequency associated with “green” and only “green”. There are lots of situations that will cause me to experience an object reflecting a single light frequency as different colors.
For example: change the background color or design an elaborate pattern in a picture. There are some freaky things our brains can do (and can be tricked into doing).
(nods) Or just shine a red light in my eyes for a while, then turn it off.
It’s not even particularly freaky, it’s just that we’re accustomed to treating certain aspects of our perceived environment as primitive atoms of perception when in fact they are the outputs of complicated heuristics that aren’t perfectly calibrated for consistency.
Freaky as in an incredible feat on the behalf of our brain to be able to reconstruct 3d images from subtle clues like relative shading. Giving deceptive input to make it perceive color incorrectly is just a harmless side effect.
There are lots of situations that will cause me to experience an object reflecting a single light frequency as different colors.
Under naively realistic conditions this is a non-issue. If one takes a statistically relevant sampling size of humans at random, and asks them their assessment of the color, they will agree based on its light frequency as the sole understandably relevant qualifier.
Indeed, I am seeing several dozen of those frequencies as I write this.
Frequencies are identified as a spectrum, not as a single point. Furthermore—you can differentiate from one variety to another. But an objecct which is one variety of green (that occupies one specific point) does not become another variety of green without undergoing a transition event.
If the definition of “grue” is such that the light reflected by a “grue” object is the same frequency at all times, and further that the observer’s eyes don’t change and more generally that nothing in the world changes,
There’s a reason why the paradox’s definition completely fails to delve into the physical technicalities of the claim.
This is why I was able to rephrase it with the aled concept.
“Goodman’s Grue” just doesn’t seem to be a problem at all. It can only seem like a problem if you forget that ‘grue’ is a name given to a somewhat complex sequence of events (relative to a thing just being a color) and start making mistakes when manipulating the symbol. There just isn’t any reason to suppose there is any ‘threat to the whole of science’ in the first place.
I agree, you are essentially saying that if you forget that green and blue are not simply syntactical binary predicates from first order logic – if you remember that they are semantic concepts, then it is clear that the grue problem is not at all a threat to science. But this is no trivial result, it means that there is a part to the application of Bayes, i.e., induction, which requires the acquisition of semantic concepts. If you fed evidence statements into a bayesian program, it would have to have an understanding of the semantic application of terms like green and grue. So you are right: reducing “green” and “grue” to their semantic/physical tests is the key in my proposed solution. Bayes can’t be enough, obviously, since bayes is a syntactical and axiomatic system.
I guessed what seemed bayesian to me about the whole thing was the analogy to bayse’s table problem, which was the main intuition pump I used to solve the problem. I’ll edit the article to reflect this. Thanks
I think this is incorrect. The actual application of Bayes’ theorem works the same way for each of your theories. What differs is your priors, and that difference sticks around until you have some evidence that’s more likely for one theory than another. If your priors are screwy, then yes, you’ll hold wrong beliefs until you’re given evidence that lets you distinguish between the correct and incorrect beliefs.
Ahh, that makes sense!
The first thing that struck me was the inherently self-contradictory nature of the grue definition. For physical properties to be retroactively alterable seems to contradict fundamental principles of causality and matter.
Am I simply not understanding the topic? Or is my intuitive-conceptualization too influenced by “timeless physics”? (The notion that all moments in time can be stated to ‘exist’).
The most you get with statements about “grue-ness” is that some objects which we observed to be “green” were in fact green but after a specific time (T) all changed to another color. This does not change the fact that they were green in the past.
Science seems perfectly-well suited to handling things that change from one state to another. Radioactive decay, for example. If this is some extra-material transition that occurs… well, I just don’t see how that’s an actually available physical phenomenon. If you change the definition of the term, you are now discussing a new thing.
you are missing the point. nothing changes color. and no definitions are changed, only meanings.
… but meanings are definitions. You can’t change one without changing the other. The terms are synonyms.
Time-based definitions just mean you use one definition before time T and another definition after time T. I am lost as to what the paradox here is.
defenitions point to meanings, but the meaning of a term can only be found by looking at the cognitive machines that use the term, and in that specific contxt as well.
…
definition:
A statement of the exact meaning of a word, esp. in a dictionary.An exact statement or description of the nature, scope, or meaning of something.meaning:
What is meant by a word, text, concept, or actionDefinitions are meanings. And meanings are definitions.
A ⊃ B & B ⊃ A ⊨ A = BI remain lost as to where the paradox is supposed to be.
The quotes you give suggest definitions are statements of meaning, not meanings.
… I am not especially aware of there being a functional difference between a “statement of meaning” and the meaning itself when we’re discussing what terms mean.
Anything that is applicable to a definition is applicable to the meaning itself. Any adjustment of the meaning adjusts the defintion. Any adjustment of the definition adjusts the meaning. When you have a direct correlation with bi-directional causality, that is mutual identity.
Have you read the cluster structure of thing space? Or the exponential concept space article? I recommend them.
Yes I have read them, and they are not relevant to the topic of mutual identity between ‘definition’ and ‘meaning*’.
*: s/magic/meaning/. Thanks, Swype!Would you similarly say that “mortal” is a term with a self-contradictory definition?
“mortal” implies that a thing is capable of transitioning from one state to another. This would be more like trying to create a tearm,
aled, which those things that have the property of beingaledwhere time=-T are alive but where time=+T are dead...And yet no events are to have occured at time=T. This is a material contradiction. Even worse; another possible meaning would be that things which are
aledwhere time=-T are alive where time=n; and, simultaneously, things which arealedwhere time=+T are dead where time=n.And yet the same group of objects are to have the characteristic of being
aled-- yet, again, no events are to have occurred.This is paradoxical, certainly—but only because the definition contradicts itself.
grueandbleenrequire thatA=¬A; a false assertion. (EDIT: Apparently I need to explain that the paradox I mention here IS NOT the Goodman’s Grue Paradox.)Contrastingly, those things which are “mortal” are defined as having having a unique time=d, where time=-d they are alive; where time=+d they are dead; and where time=d they transition states.
Can you clarify what prevents a grue/bleen categorizer from saying that when a grue object changes the frequency of light that it reflects (which is something every grue object does at one time or another), that’s an event?
That’s just it—to be “grue” its color must never change from the color “grue”. “Grue” is a color. Not two colors—just one. If this confuses you—it should. It’s a self-contradicting definition. “Grue” is a violation of the Law of Identity.
I agree that its color never changes from the color grue, nor did I suggest that it did. I’m still curious about the answer to my question (which was about light frequencies, not colors), though.
Please pick one: are we discussing “grue/bleen categorizors” or are we discussing “light frequencies”? Because the topics are mutually exclusive.
I am talking about an observer who experiences certain colors in response to certain patterns of light frequencies over time. So, both.
If that’s a contradiction in terms, then I’m likely too confused to contribute usefully to further discussion.
Here’s the thing: “grue” and “bleen” are each only one color. For this to be explicable to your understanding, “grue” would have to have one and only one light frequency for time=n.
The problem of course is that this light frequency is apparently the same as “green” at time=-T, but the same as “blue” at time=+T.
The very definition of “grue” is such that
A=¬A.Should we introduce to the “grue-ites” the notion that objects can change color—then they would be incapable of maintaining their belief in “grue”. Essentially; this entire conversation is predicated upon “grue-ites” existing in a universe without light-frequencies but still possessing color. This is, of course, explicitly contradictory: colors are frequencies of light (as experienced by observers).
Three things.
1) If the definition of “grue” is such that the light reflected by a “grue” object is the same frequency at all times, and further that the observer’s eyes don’t change and more generally that nothing in the world changes, then I agree with you that “grue” as defined is a contradictory idea, for essentially the reasons you cite.
2) In the real world, “green” is not associated with one and only one light frequency. There are lots of light frequencies that would cause me to experience a sensation I’d label “green”. Indeed, I am seeing several dozen of those frequencies as I write this.
3) In the real world, there is no light frequency associated with “green” and only “green”. There are lots of situations that will cause me to experience an object reflecting a single light frequency as different colors.
For example: change the background color or design an elaborate pattern in a picture. There are some freaky things our brains can do (and can be tricked into doing).
(nods) Or just shine a red light in my eyes for a while, then turn it off.
It’s not even particularly freaky, it’s just that we’re accustomed to treating certain aspects of our perceived environment as primitive atoms of perception when in fact they are the outputs of complicated heuristics that aren’t perfectly calibrated for consistency.
Freaky as in an incredible feat on the behalf of our brain to be able to reconstruct 3d images from subtle clues like relative shading. Giving deceptive input to make it perceive color incorrectly is just a harmless side effect.
Ah. Yes.
As optimizing systems go, we leave a lot to be desired, but for self-organizing soup we’re pretty impressive.
Under naively realistic conditions this is a non-issue. If one takes a statistically relevant sampling size of humans at random, and asks them their assessment of the color, they will agree based on its light frequency as the sole understandably relevant qualifier.
Frequencies are identified as a spectrum, not as a single point. Furthermore—you can differentiate from one variety to another. But an objecct which is one variety of green (that occupies one specific point) does not become another variety of green without undergoing a transition event.
There’s a reason why the paradox’s definition completely fails to delve into the physical technicalities of the claim.
This is why I was able to rephrase it with the
aledconcept.Err… no? Sometimes they are identified as a spectrum and sometimes as a single point.