This is true, tautological, and not very interesting. But it is not a paradox.
[ul][li]The mouth cannot speak a word it cannot speak[/li][li]The eye cannotsee a sight it cannot see[/li][li]Fractions cannot represent a number that is not a fraction[/ul][/li]If we eliminate teh confusion made possible by variant readings of “conceive”, then teh content of the statement becomes more clear.
No. You are simply making an assertion that the mind’s power of conception is not limitless. A limited mind is omething that quite clearly can be conceived. Therefore, you have not thought of something that cannot be conceived. You have merely asserted that such a thing, if it exists, cannot be conceived.
The rest is all semantic confusion. [/channeling Wittgenstein]
With respect, having read the thread twice, I think the conversation has gone sideways. That is, I think iamnotbatman nailed the fallacy in the OP’s “paradox” back in Post #4. That we can conceive the concept of inconceivability doesn’t mean we can conceive inconceivable things. Frylock may well be right that nothing is literally inconceivable - whatever can exist can be conceived - but that’s not the nub of the paradox. It’s an alternate solution, but I think iamnotbatman’s better “cuts to the chase.” My $0.02’s worth.
This one might be chalked up to a little bit of linguistic trickery.
iamnotbatman insisted that you could not think about the 5th prime unless you knew the concept. Frylock demonstrated it is possible by thinking about the actual 5th prime instance without even knowing the concept.
What needs to be clarified is: when we say think about “the 5th prime” are we referring to the concept of prime numbers and specifically the 5th one, or are we referring to the instance of the 5th prime regardless of concept, or both/either.
This is true for almost everything. When a child thinks about 11, he is also thinking of properties of “11” with which he is familiar: it is one past 10, perhaps it is odd. This collection of concepts grows as we learn, to eventually include that 11 is the fifth prime number. That you or I or Frylock know about its primeness now just means we have already learned it. If someone is confused and think 11 is the fourth prime number, it is still in his collection of “knowledge” which may or may not map directly to reality. Even if these things all map to the same number, it does not make sense for the child to be said to think about concepts he hasn’t learned yet. Yes, he is thinking of the thing with the tag “the fifth prime” only because that points to the same number as the thing he is thinking about.
I am typing this on an old desk, similar to ones that have shown up on Antiques Roadshow. An expert can tell me a lot of things about the desk I don’t yet - perhaps his tags for the desk include the type of wood it is made of, the style, the region and time where it was made. But all this maps to the same desk I’m sitting at. And neither of us can say much about the chemistry of the wood and glue the desk is made of, or the atomic structure of it, Our tag for desk more or less relates to the sane physical object, but it is a fallacy to think we think of it identically beneath that level.
I generally agree with the above, except I do not agree that talking about square circles is really talking about the tag “square circles.” The tag is distinct from the thing it’s a tag of, and talking about one is not the same as talking about the other.
If talk about a square circle were “really” talk about the tag “a square circle” then I’d have to endorse something like “A square circle has two words in it.” But that seems clearly false.
I’m not sure why I should believe that. The following statements are uncontroversial:
My kid believes, de re, that the fifth prime equals his age in four years.
My kid does not believe, de dicto, that the fifth prime equals his age in four years.
My saying my kid can think about the fifth prime relies on the truth of the first statement.
iamnotbatman’s saying my kid can’t think about the fifth prime almost certainly relies on the truth of the second statement.
As far as I can tell, the confusion over the kid/prime thing is directly related to the de re/de dicto distinction. I do not see how you can or why you would think otherwise.
I have no objection to any of the above. The problem is, “thinking about X” doesn’t mean “thinking about the concept ‘X’,” it means “thinking about X itself.”
To think about the fifth prime, no one needs to think about the concept “the fifth prime.” They just need to think about 11.
If iamnotbatman wants to focus on the question of who is able to think about the concept “the fifth prime” that’s fine by me.
I’d need to see further explanation of this. Right now it appears completely unmotivated, since thinking about something is distinct from knowing anything at all.
I agree with this, but ftr iamnotbatman has stated that it’s not his view that you have to be correct about the identity of a thing in order to be thinking about it. This seems to me to be in tension with some other things he’s said, which is why I asked for clarification on two questions about his views, to wit:
A. In order for something to be about X, must it contain information which comes from X?
and
B. In order for something to be about X, must its meaning highly correlate with properties of X?
Going waaaaay back to a post from iamnotbatman which I didn’t originally notice because it was addressed to someone else (and note this is directly relevant to the thread topic):
This appears to be a demonstration of the very claim you’re trying to deny. You’re framing this as an argument against the view that there’s nothing you can’t think about–but the argument you’re giving is actually an argument for that view. Inded, it’s practically the same as the argument I offered.
But where I offer the conclusion “The statement ‘there’s nothing you can’t think about’ is true,” you offer the conclusion “The statement ‘there’s nothing you can’t think about’ is vacuous.” Elsewhere, I think you intend to clarify your term “vacuous” here as meaning “having no informational content.” But I don’t see why you should think it has no informational content. The statement “there is nothing you can’t think about” conveys the (true!) information that there is nothing you can’t think about. Earlier you seemed to think this explication of the information content to be tautological. But it’s not. The following is not a tautology:
“Snow is white” is true if and only if snow is white.
And neither is this:
“There is nothing you can’t think about” conveys the information that there is nothing you can’t think about.
Indeed, the information conveyed helps to distinguish you from a rock. There’s nothing you can’t think about, but there are things a rock can’t think about. And there are things a cat can think about, and there are things a cat can’t think about. None of these are vacuous claims–they each (including the one under debate) convey actionable intelligence about actual objects in the world. (Which is not necessary for information conveyance, but I’d think it’s certainly sufficient.)
I wholeheartedly agree that there isn’t much information content in my statement. But it’s certainly not empty of all information content.
If you’ve thought about the possiblility of things you can’t think about, (and you’ve thought about it under that label, i.e., “de dicto,”) then you’ve ipso facto thought about something you can’t think about.
What’s that argument by induction? If it’s what I suspect, then my post 96 addresses this point. There’s an important distinction to be made between creatures capable of thinking about thinking and negation, and creatures incapable of thinking about these two. Inductions which take the latter as their instances can’t generalize, necessarily, to the former. Such an argument may turn out to be a bad argument from analogy rather than a good argument by induction.
[Note: I am pretty much indisposed this week, and haven’t been able to carefully read through what has been written since my last post, and probably won’t be able to post more than a couple times over the next week. But I will quickly answer Frylock’s questions below. I hope this isn’t counterproductive. I’ll be back to think about this more next week]
It is difficult for me to answer this question due to the fact that I feel you have been unclear on what you believe “X” represents. In some cases from your responses it seems unavoidable that X must represent a set of possibilities you believe to be equivalent, rather than the unique object itself. For example you insist your kid can think about the fifth prime because he can think about the number 11. Well “fifth prime” is informationally distinct from “11”, in that “fifth prime” carries with it not only a label but an idea. The idea of what a prime number is. In this case I would say that X is the “fifth prime”, while you would argue that X is the set {“fifth prime”, “11”, “5+6”, etc}. This is problematic because it subtly re-defines the intention of the term “fifth prime” in the example. There is a reason we use different words: they have different meanings. “11” is just not the same concept as “fifth prime.” So I want it to be clear that when I answer your question, “X” stands for the specific, unique object intended by the label given for X. Now to the answer:
I am not sure what “comes from” means here in all circumstances. In the case of “fifth prime”, no information “comes from the fifth prime.” The information required for something to be about the fifth prime, for example, is the knowledge of what a prime number is, and the prior knowledge that allows for the ability to deduce the fifth prime number.
Yes, basically. Let me give a few examples, and rate them on how correlated they are with X (using an arbitrary, totally qualitative scale from 0 to 1):
Statement: “I am thinking about the apple in your right hand”
Actual thought:
An apple with color and markings and shape very similar to actual apple, in your right hand: Correlation: 0.99
An apple with color and markings and shape very similar to actual apple, in your left hand: Correlation: 0.90
An apple with color and markings and shape somewhat mis-remembered, in your left hand: Correlation: 0.80
An orange with color and markings and shape somewhat mis-remembered, in your left hand: Correlation: 0.70
A black wheelbarrow, in your left hand: Correlation: 0.20
A unicorn, in China: Correlation: 0.05
A completely random thought: Correlation: 0.00
What, I’m completely indisposed but you don’t see that stopping me.
“X” in the schema is intended to range over all names and descriptions. If you think some should be treated differently than others w.r.t. the question I asked, that’s perfectly fair.
In that case, I was using “the fifth prime” as a description which I took to refer uniquely to the number 11. (Not a set of descriptions of 11 such as “5+6” “fifth prime” etc, but to specifically and just the single thing, the number 11. See subsequent posts about de re/de dicto for a possible diagnosis of where things got confused there.
Me too! And that specific, unique object is the number 11. So, shouldn’t that mean you do agree the kid can think about the fifth prime?
Right, I wasn’t sure what “comes from” means either and if you’d answered in the affirmative I would have wanted to know what you meant. But this appears to me to be a careful answer in the negative, which probably will help me get clearer on your view.
Are you saying that X’s being about Y is a matter of degree?
Is this what you have in mind?
“X is about Y for Z to the extent that Z can use X to discover properties of Y”
As I said in post 94, there’s an important distinction relevant here between creatures that can think about thinking and negation, and creatures that can’t. I do not know whether cats can think about thinking, but I presume they can’t think about negation.
Well, it occurs to me they may be able to think about negation in the same way my kid can think about the fifth prime. No scenario comes to mind, but it seems likely someone could construct one. But as you’ve correctly emphasized, that’s not the kind of “think about” that’s under discussion.
Creatures that can, let’s say, create labels for thinking and negation can create labels for anything. (As argued in post 94.) And having on hand, in the mind, occurently, a label for something, is sufficient for thinking about it. But a cat can’t create a label for negation. So it’s no surprise that there are things cats can’t think about. They’re different from us in this way.
A scenario in the cat/negation case might be something like this: If I train my cat to raise a paw when it sees a dash, and if I only write dashes (after the training) when it is appopriate to do so under an interpretation in which the dash signifies negation, then by thinking about the dash, the cat may be argued to be thinking about negation, though of course there is practically (maybe literally) nothing about negation which the cat can comprehend. It can’t have, in its brain, the concept of negation. But it may nevertheless be able, in special circumstances like those described, to respond systematically to instances of negation. In that sense it’s dash-thoughts are “about negation” in a distal sense. So my post 94 would need to be amended to take this into account–it’s not that cats can’t think about negation, but that they can’t form mental labels which function as part of their own organism to represent the phenomenon of negation. Any mental label the cat has formed in its brain functions as part of the cat’s organism to represent the phenomenon of “I’m about to get food just the second I raise my paw!”
You two have reversed positions between what’s in the hand versus the fifth prime.
In the hand example Frylock argued for the intention, not the object and iamnotbatman argued it must be more than just intention and be based on actual object.
In this case Frylock is arguing that thinking of the instance satisfies the question about having the intention to think about the instance regardless of whether the intention was there or not (Frylock may disagree but I think then it’s due to reading a sentence clearly implying concept X and responding with instance X) - on the other hand iamnotbatman is now arguing for the concept, but to be fair he seems to be arguing that you need a combination of both concept and instance otherwise “think about” has not been achieved.
I think this all sounds about right, with the exception that I don’t think “think about X” ever means “think about the concept ‘X’”–but on the other hand, I guess it’s common enough for people to loosely and unclearly use the former construction to mean the latter so I should be more aware of that. This is understandable since in spoken English “think about X” and “think about ‘X’” sound exactly the same…
But wouldn’t you agree that, setting aside the limits of our language when it comes to describing thought, that having the intention of thinking about X through the pathway of concept A (fifth prime for example), is different and distinct from actually thinking about the instance X without utilizing the pathway involving the concept of A?
