# 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:** 20\ **Page:** 2
**Author:** ![iamnotbatman](https://avatars.discourse-cdn.com/v4/letter/i/858c86/32.png) [@iamnotbatman](https://boards.straightdope.com/u/iamnotbatman)\ **Post date:** [March 9, 2012, 2:13pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/21 "2012-03-09T14:13:38Z")
How do you choose a thing (or a “candidate for a thing”) without thinking about that which you are choosing to not be able to think about? If you do not think about it, then therefore your choice of “thing” is unconstrained, and the statement is vacuous. Perhaps an example will help. I will quote **Frylock** and use the relevant assertion to form the example: > [@Frylock](#): > > Is there anything you can’t think about? No–because for any candidate for a thing that can’t be thought about, it can be thought about by considering it under the label “the candidate for the thing I can’t think about.” Is there anything I can’t think about? No–because while \ can’t be thought about, I can think about thinking about \. But wait, what is \? The statement is vacuous without actually putting forward a candidate for which we may put the assertion to use by “thinking about it by considering it under the label ‘the candidate for the thing I can’t think about’”. What candidate for a thing have we put forward? If we do put forward a candidate, then the statement becomes self-contradictory because we must think about the candidate in order to nominate it as a candidate. If we do not think about it, then the statement is again vacuous because we are talking about our ability to think about something that we have not defined. I mean, try it: “\ can’t be thought about [damn! I thought about it!]” “\ can’t be thought about [wait, what is a square circle?]” “\ can’t be thought about [what is X? A turkey? Ok. Damn, I thought about it!]” This is all about semantics. I’m just pointing out that I don’t think your semantics are great. There just isn’t much information content in Frylock’s statement. It makes more sense to simply say that _we can think about the possibility of things that we can’t think about_. This is distinct from saying _there is nothing we can’t think about_, which I think is a little silly, because of course there are things we can’t think about. We know this by induction. We just can’t point to them. ---
**Author:** ![iamnotbatman](https://avatars.discourse-cdn.com/v4/letter/i/858c86/32.png) [@iamnotbatman](https://boards.straightdope.com/u/iamnotbatman)\ **Post date:** [March 9, 2012, 2:17pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/22 "2012-03-09T14:17:12Z")
> [@Frylock](#): > > Suppose there were something you couldn’t think about. > > Did you suppose it? Well then, you just thought about something you can’t think about. Yes I supposed it. But I did not think about something I can’t think about. I just made the reasonable supposition that there are probably things I can’t think about. I did not point to _some **thing** _ I can’t think about. So no, I did not think about some thing I can’t think about. ---
**Author:** ![The\_Hamster\_King](https://avatars.discourse-cdn.com/v4/letter/t/8edcca/32.png) [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)\ **Post date:** [March 9, 2012, 2:50pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/23 "2012-03-09T14:50:38Z")
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. ---
**Author:** ![Damuri\_Ajashi](https://avatars.discourse-cdn.com/v4/letter/d/898d66/32.png) [@Damuri\_Ajashi](https://boards.straightdope.com/u/Damuri_Ajashi)\ **Post date:** [March 9, 2012, 4:24pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/24 "2012-03-09T16:24:56Z")
> [@Jragon](#): > > I just wrote and submitted a Philosophy paper and managed to discover a logical paradox that will now haunt me forever (that or I’m stressed and being stressed is making me think dumb): > > The mind cannot conceive a scenario it cannot conceive. > > That is, if there is something the mind cannot think of, the mind would not be able to produce a thought **about** thinking about it, because it would first have to produce the thought it can’t think of. However, by making this statement, I am showing that I have thought of something I cannot conceive. > > After all, the definition of “conceive” is “able to be thought of” (first Princess Bride joke gets a punch… or a cookie, can’t decide which). That is, the very concept of inconceivability is, in itself, wrapped up in a meta-recognition that the brain cannot think of something. > > If you acknowledge that the brain can, indeed, conceive of something inconceivable – that it cannot think of something inconceivable, you’ve reached what amounts to a logical absurdity. However, if you deny this property, and say the mind cannot conceive what the mind cannot conceive by definition and tautology, then you must explain exactly **why** inconceivability is not, by its nature, a conscious recognition of something inconceivable. Well I can conceieve of God without having any fucking clue as to his nature. ---
**Author:** ![elucidator](https://avatars.discourse-cdn.com/v4/letter/e/8edcca/32.png) [@elucidator](https://boards.straightdope.com/u/elucidator)\ **Post date:** [March 9, 2012, 4:28pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/25 "2012-03-09T16:28:01Z")
“Inconceivable!” “What is?” “How the hell should I know!?” ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [March 9, 2012, 5:09pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/26 "2012-03-09T17:09:26Z")
> [@iamnotbatman](#): > > Yes I supposed it. But I did not think about something I can’t think about. I just made the reasonable supposition that there are probably things I can’t think about. I did not point to _some **thing** _ I can’t think about. So no, I did not think about some thing I can’t think about. But you don’t have to point to a thing in order to think about it. I’m thinking about the next child concieved on the planet. I can’t point to it–indeed, it doesn’t even exist. But there I am thinking about it. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [March 9, 2012, 5:10pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/27 "2012-03-09T17:10:31Z")
> [@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. Yes, this is a good way to put what I’m saying. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 9, 2012, 5:17pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/28 "2012-03-09T17:17:58Z")
> [@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. Then I suppose random numbers are inconceivable? (Being incompressible…) Of course, they are, in a sense, since human beings can’t create true randomness. But thinking about random numbers – indeed, proving theorems about them, determining their properties and so on – poses no problem at all. ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [March 9, 2012, 5:18pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/29 "2012-03-09T17:18:13Z")
> [@The\_Hamster\_King](#): > > Understanding is data compression. That’s one idea; I think it was a computer scientist that first came up with it (Gregory Chaitin). It’s hardly a consensus view. Personally I think understanding as _prediction_ works better. I have some form of understanding if I can make valid predictions or inferences about a system / entity. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 9, 2012, 5:40pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/30 "2012-03-09T17:40:53Z")
> [@Mijin](#): > > That’s one idea; I think it was a computer scientist that first came up with it (Gregory Chaitin). It’s hardly a consensus view. Leibniz got there before him, which Chaitin readily acknowledges: he likes to cite the ‘inkblot-story’, in which Leibniz muses when a pattern of ink blots on a page can be supposed to follow a law; the answer he arrives at is that they do precisely if there is a function than generates this pattern, such that the function is ‘smaller’ than just the pattern itself. In other words, it is lawful if it is non-random, and if it is lawful, knowing that law surely constitutes understanding that pattern; but the law is precisely a compression of the set of data points, so in this sense, understanding is indeed data compression. ---
**Author:** ![epolo](https://avatars.discourse-cdn.com/v4/letter/e/b487fb/32.png) [@epolo](https://boards.straightdope.com/u/epolo)\ **Post date:** [March 9, 2012, 6:01pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/31 "2012-03-09T18:01:07Z")
Since “thought” is really just the language you speak to yourself, isn’t this really a question about the formal completeness of language? Grabbed this quote [here](http://itre.cis.upenn.edu/~myl/languagelog/archives/000131.html): > [@](#): > > The American linguist Edward Sapir wrote in 1924: > > The outstanding fact about any language is its formal completeness … To put this … in somewhat different words, we may say that a language is so constructed that no matter what any speaker of it may desire to communicate … the language is prepared to do his work … The world of linguistic forms, held within the framework of a given language, is a complete system of reference … ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [March 9, 2012, 6:27pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/32 "2012-03-09T18:27:40Z")
Sounds like Donald Rumsfeld’s “unknown unknowns.” ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 9, 2012, 6:41pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/33 "2012-03-09T18:41:42Z")
> [@epolo](#): > > Since “thought” is really just the language you speak to yourself, isn’t this really a question about the formal completeness of language? > Grabbed this quote [here](http://itre.cis.upenn.edu/~myl/languagelog/archives/000131.html): I’d phrase it in terms of computational universality: the human mind is computationally universal, i.e. it can compute everything that can be computed (by some formalized notion of computability, such as furnished by Turing machines) (at least in the limit of infinite time and resources, i.e. with enough note paper), and the universe is (to all appearances), too, so anything the universe can come up with, a human mind can, too, at least in principle. ---
**Author:** ![The\_Other\_Waldo\_Pepper](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_other_waldo_pepper/32/12370_2.png) [@The\_Other\_Waldo\_Pepper](https://boards.straightdope.com/u/The_Other_Waldo_Pepper)\ **Post date:** [March 9, 2012, 7:03pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/34 "2012-03-09T19:03:01Z")
Or consider the sentence _“I can’t refer to things I can’t refer to.”_ Forget conceiving of them; can I refer to them? Didn’t I, just then? _“I can’t talk about things I can’t talk about.”_ Am I talking about them? ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 9, 2012, 7:15pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/35 "2012-03-09T19:15:15Z")
> [@Jragon](#): > > The mind cannot conceive a scenario it cannot conceive. I think you might have created an unapparent tautology by using homonyms. I’m going to give the word “conceive” two of its most common definitions. ( **red** dictates an _a priori_ sense, and **blue** an _a posteriori_ sense): **The mind cannot conceive [imagine] a scenario it cannot conceive [understand/know].** This is untrue, as given above: I can imagine what it’s like to give childbirth, but I’ll never really know or understand the _actual_ feelings involved, given I’m male. Females can imagine to a greater degree, but cannot ever come to full understanding and knowledge of giving birth, until she actually does. Now, let’s reverse the definitions: **The mind cannot conceive [understand/know] a scenario it cannot conceive [imagine]** Again, this is untrue. We can understand the particulars of a hypercube, and what it would mean if we extrapolated space into 4 or more dimensions. We can even understand an infinite universe, that is eternal. Blind people can understand color, and parallax, but to really _imagine_ it, however, is something entirely more difficult, frustrating, or downright impossible. To keep the definition of conceive the same within the same sentence, then it goes without saying, in either case. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 9, 2012, 7:27pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/36 "2012-03-09T19:27:02Z")
> [@The\_Other\_Waldo\_Pepper](#): > > Or consider the sentence _“I can’t refer to things I can’t refer to.”_ Forget conceiving of them; can I refer to them? Didn’t I, just then? > > _“I can’t talk about things I can’t talk about.”_ Am I talking about them? Not really. In a meta way, I suppose, but this looks sort of like a [Type/Token](http://en.wikipedia.org/wiki/Token-type_distinction) distinction problem. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 9, 2012, 7:29pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/37 "2012-03-09T19:29:12Z")
> [@Bryan\_Ekers](#): > > Sounds like Donald Rumsfeld’s “unknown unknowns.” Or even Sir Arthur Eddington’s, “something unknown is doing we don’t know what.” ---
**Author:** ![epolo](https://avatars.discourse-cdn.com/v4/letter/e/b487fb/32.png) [@epolo](https://boards.straightdope.com/u/epolo)\ **Post date:** [March 9, 2012, 7:31pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/38 "2012-03-09T19:31:57Z")
> [@Half\_Man\_Half\_Wit](#): > > I’d phrase it in terms of computational universality: the human mind is computationally universal, i.e. it can compute everything that can be computed (by some formalized notion of computability, such as furnished by Turing machines) (at least in the limit of infinite time and resources, i.e. with enough note paper), and the universe is (to all appearances), too, so anything the universe can come up with, a human mind can, too, at least in principle. I was trying to think of something along those lines but then I was thinking that natural language is more like [formal language](http://en.wikipedia.org/wiki/Formal_language) than like programming language. But maybe you’re on to something with the notion that the mind is Turing equivalent to the universe. Not sure how you would prove it, though. Could you come at the problem from this direction: What is the set of concepts that cannot be described in language? The set itself can be described, so it’s not self-referential. But it can’t have any well-ordering; otherwise, we could describe the “least element of the set of concepts that cannot be described in language”, which would be paradoxical. I think that implies that the set is either null or infinite. I don’t know how we would go about trying to prove that it’s the former rather than the latter. Related thought: Do all real numbers have a name? ---
**Author:** ![The\_Other\_Waldo\_Pepper](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_other_waldo_pepper/32/12370_2.png) [@The\_Other\_Waldo\_Pepper](https://boards.straightdope.com/u/The_Other_Waldo_Pepper)\ **Post date:** [March 9, 2012, 7:32pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/39 "2012-03-09T19:32:16Z")
> [@cmyk](#): > > Not really. In a meta way, I suppose Well, see, that’s sort of my point: it seems to me the OP can conceive of things, _‘in a meta way,’_ that he can’t conceive of in, uh, a non-meta way – and that he’s doing so when conceiving of things (in a meta way) that he can’t conceive of. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 9, 2012, 7:34pm UTC](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243/40 "2012-03-09T19:34:22Z")
> [@The\_Other\_Waldo\_Pepper](#): > > Well, see, that’s sort of my point: it seems to me the OP can conceive of things, _‘in a meta way,’_ that he can’t conceive of in, uh, a non-meta way – and that he’s doing so when conceiving of things (in a meta way) that he can’t conceive of. Right. But sentences like, “I can’t talk about the things I can’t talk about” is basically being implicit about stuff you can’t be explicit about. [Previous page](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243.md?page=1) [Next page](https://boards.straightdope.com/t/help-me-untangle-this-logical-paradox-involving-mental-conception/615243.md?page=3)