# Help me untangle this logical paradox involving mental conception **URL:** \ **Category:** Great Debates\ **Created:** [March 9, 2012, 8:12am UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243 "2012-03-09T08:12:35Z")\ **Posts on this page:** 7\ **Page:** 7
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [March 12, 2012, 7:44pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/121 "2012-03-12T19:44:42Z")
> [@Frylock](#): > > Yes, I think so. Do you think this has an implication for the whether it’s true that there’s anything a normal human being can’t think about? Not at all. It only relates to the discussion between you and iamnotbatman. I think there is a difference between the capability to conceive of something from a brain/structural perspective and the “what information is available” perspective. But I’m not convinced one way or another that having an internal placeholder for something rises to the level of thinking about something. If there is a concept such that the best we can do is mechanically create a placeholder for that concept despite having no capability to actually consider that concept, then it seems we aren’t thinking about it quite yet. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [March 12, 2012, 8:09pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/122 "2012-03-12T20:09:42Z")
> [@Frylock](#): > > 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. It would be more accurate to say “the tag square circle has two words in it.” Given that, what does talking about square circles mean? In one sense we are talking about something that does not exist, and which can’t be conceived of, but we can always talk about characteristics of such things. We can say both “a square circle has four sides” and “a square circle has one side.” So we can make two statements which are mutually contradictory. Perhaps these things describe the concept of a square circle, though not the non-existent square circle. ---
**Author:** ![Dr.Colossus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.colossus/32/9423_2.png) [@Dr.Colossus](https://boards.straightdope.com/u/Dr.Colossus)\ **Post date:** [March 13, 2012, 8:25am UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/123 "2012-03-13T08:25:32Z")
> [@The\_Hamster\_King](#): > > Understanding is data compression. > > So when I think about a ball I’m not thinking about a ball in its totality. I’m not thinking about every single feature of a real ball – every atom, every vibration, every electron orbital. I’m thinking about a small collection of properties that will roughly approximate the behavior of a real ball. > > What this means is that NOTHING is inconceivable. Some things will be better approximated in our thoughts than others – our understanding of some things will be less lossy. But there is always some level of crudeness of representation we can dial back to that will make thinking about a thing computationally tractable. also, the approximation can be off but you’re still conceiving of something. (right?) a child hears you talk of John Candy and thinks “oh yeah he’s that guy who played Rosanne’s husband on _Rosanne_.” the child has confused two corpulent actors with similar names–so their approximation is a little wonky but the ballpark is right. so if that counts, does that mean nothing is inconceivable…? is it just that some things are beyond our capacity to clearly grasp (and thus result in very loose or even flawed approximations…?) is the term ‘inconceivable’ just another loose approximation of “pretty hard to get your head around?” or does it only apply to patently impossible blivits and penrose stairs and illuminated darknesses and honest politicians? is conceivability circumstantial to the individual? i can’t really discuss QT much because i cannot discuss, do, or even start to understand the theoretical math involved. my friend, Brainy Smurf, is awesome at math and can do some light reading the field. conceivability of the same ideas between the two of us is quiet disparate. ---
**Author:** ![iamnotbatman](https://avatars.discourse-cdn.com/v4/letter/i/858c86/32.png) [@iamnotbatman](https://boards.straightdope.com/u/iamnotbatman)\ **Post date:** [March 14, 2012, 2:56pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/124 "2012-03-14T14:56:00Z")
> [@RaftPeople](#): > > But I’m not convinced one way or another that having an internal placeholder for something rises to the level of thinking about something. If there is a concept such that the best we can do is mechanically create a placeholder for that concept despite having no capability to actually consider that concept, then it seems we aren’t thinking about it quite yet. This is a more forgiving way of expressing my essential opposition to Frylock’s thesis. But as I’ve tried to point out before, it’s just a question of definitions. I don’t at all think a good definition of “to think about” requieres nothing more than having this internal placeholder. Basically what I’ve attempted to describe about information content comes down to the fact that a placeholder by itself has zero meaning. It is a “dummy index.” It’s just a symbol. ---
**Author:** ![iamnotbatman](https://avatars.discourse-cdn.com/v4/letter/i/858c86/32.png) [@iamnotbatman](https://boards.straightdope.com/u/iamnotbatman)\ **Post date:** [March 14, 2012, 3:58pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/125 "2012-03-14T15:58:27Z")
> [@Frylock](#): > > 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? To me, the specific, unique phrase “fifth prime” (as opposed to “11” or “5+6” etc) means “the fifth natural number greater than 1 that has no positive divisors other than 1 and itself,” as distinct from “the eleventh natural number,” or “the summation of the numbers ‘5’ and ‘6’.” The de re referent may be the number 11, but the phrase itself carries information that is distinct from the symbol ‘11.’ To “think about the fifth prime” is distinct from “to think about the number 11” which is in turn distinct from “to think about the symbol ‘11’” (one cannot think about the number eleven if they do not know what ‘number’ is; in that case they are thinking of the symbol ‘11’ rather than the ‘number’ 11). For all of the above confusion, perhaps the thought experiment would be better to have been “I think about prime numbers,” rather than “I think about the fifth prime.” I don’t know how one can think about “prime numbers” without knowing the definition of “prime” and “numbers.” > [@Frylock](#): > > 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” > > ? Yes, it is a matter of degree, until the specification of Y becomes unambiguous. This is possible despite X’s description of Y sometimes being approximate, as I’ve described previously. I think it is most reasonable to define “X thinks about Y” to be unambiguous, ie referring to cases in which X can unambiguously specify Y (in principle, but for example if asked). In cases where X can only partially constrain Y, I think it is reasonable to discuss the matter of degree. But none of this is a complication for the examples I’ve brought up, where I think the “degree” is very near, if not precisely, zero. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [March 14, 2012, 4:54pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/126 "2012-03-14T16:54:26Z")
> [@iamnotbatman](#): > > This is a more forgiving way of expressing my essential opposition to Frylock’s thesis. But as I’ve tried to point out before, it’s just a question of definitions. I don’t at all think a good definition of “to think about” requieres nothing more than having this internal placeholder. Basically what I’ve attempted to describe about information content comes down to the fact that a placeholder by itself has zero meaning. It is a “dummy index.” It’s just a symbol. I think a lot of learning would be impossible without such dummy indexes. However, I can get on board with the idea that there’s an “aboutness” relation that’s a matter of degree. My more liberal and binary “aboutness” relation, I think, can be expressed in terms of your continuum of aboutness degrees, in that I would have counted any index as being “about” (in my sense) an X, even if the degree to which it’s “about” X (in your sense) is very near (or even at) zero, so long as the index nevertheless functions as part of a process which itself functions to use that index ultimately to get an even better hook into X (i.e. to become “about” X to an even greater degree.) This invites questions about what “functions” are and so on. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [March 17, 2012, 7:16pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/127 "2012-03-17T19:16:16Z")
> [@Frylock](#): > > I think a lot of learning would be impossible without such dummy indexes. However, I can get on board with the idea that there’s an “aboutness” relation that’s a matter of degree. > > My more liberal and binary “aboutness” relation, I think, can be expressed in terms of your continuum of aboutness degrees, in that I would have counted any index as being “about” (in my sense) an X, even if the degree to which it’s “about” X (in your sense) is very near (or even at) zero, so long as the index nevertheless functions as part of a process which itself functions to use that index ultimately to get an even better hook into X (i.e. to become “about” X to an even greater degree.) This invites questions about what “functions” are and so on. I thought I posted something about this, but can’t find it. There are many unknowns which could be considered members of an eclectic series. The knowledge of a label, even though empty of information can be the start of a process in determining the contents that should be associated with that label. However, in the end, there are those two generic tags, “Thing I know” and “Things I don’t know”. The latter is always, by definition, content free. [Previous page](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243.md?page=6)