About Two Brain-Pains Posts I Noticed The Other Day

If you have by any chance missed them, over at Brain Pains, Robert Howell has two very interesting posts (here and here) about Categorical Phenomenalism.

Categorical Phenomenalism (CP) is position that physical science can give us information only about dispositional properties of the things – how they behave in different contexts, and conditions, but that it fails to tell us what those things are in themselves. These intristic properties of the thing, which are base of specific dispositions  are named “categorical properties”. Science doesn’t tell us anything about those. CP holds that those categorical properties are also responsible for the phenomenal properties.

As I wrote in the comment there, if one accepts CP, one must go further. Namely, if the knowledge and belief are consequence of the dispositional properties of the matter, and on other side phenomenal experience is there because of the categorical properties, it would be impossible for us to know about those categorical properties. So proponent of CP will have to hold, in my opinion, that also knowledge, and beliefs can’t be properly addressed through account based on dispositional properties (i.e. normal physical properties), but that categorical properties will have to play some important role not just in phenomenal, but also in our believing, knowing, etc…

Any model of the mind will have to show the possibility of this. The possibility not just that we have phenomenal experience, but that we know that we have phenomenal experience. The possibility not just that we exist, but that we know that we exist. The possibility not just to know those things, but to know that we know those things, etc…

Anyway, to my thinking, CP is a shy attempt to get away from physicalism, but fails because 1.it attempts to apply the reductionistic paradigm on the phenomenal and 2.it looks for the ground of the dispositional properties in wrong place. So, it fails because it is too shy (as are other dualistic accounts in general).

Few Explanatory Notes on Grounding the Transcendence

In the previous post – Grounding the Inter-subjective Transcendence, I was explaining the reasons why I think that several different accounts (both idealist and materialist) fail to give ground for intra and inter-subjective transcendence (possibility of same person or multiple persons to think and talk about same thing once or multiple times), and why the only option I see plausible is that it is grounded in the being-in-the-world, or if we take into account the other people – being-along-in-the-world.

Probably to some people this kind of “grounding” might seem weird and might say that this fails to be explanation of the possibility of transcendence of intentional content, because it doesn’t reduce the phenomenon at hand (i.e. intra and inter-subjective transcendence of intentional content) to something more simple, but it grounds it in something that is more complex – namely being-in-the-world.

And this is partly true, and it surely seems weird for a mind that thinks that any proper explanation is reductionist in nature. In such view it is usually taken that what is self-subsistent are objectively existing particles of some kind, with different (also objective) properties that they have. And the explanation of phenomenon, in this view, should be done by showing how it can be (or necessarily will be) based on specific way of interactions of those particles (analyzed on that basic level, or alternatively through some level of abstraction).

On other side this grounding of transcendence of intentional content in the being-in-the-world, is holistic “reductionism”, it takes the phenomenon to be a specific abstraction from the whole, and shows its possibility as such.

In this view, being-in-the-world as term is used to refer to the starting whole, which is neither the objective world (physicalist model), nor the subject (cartesian model), but irreducible being-in-the-world, it is again subject, but a subject IN the world, and not a static subject in a static world, but changing subject in the changing world. World full of things which undergo changes, and other agents which are acting (maybe it is better called becoming-in-the-world for this reason?). Whatever abstraction can be done, is done within this starting whole, and thus being-in-the-world can’t be defined, but only one can just try to point to it – namely… stop for the moment, and there it is, it is the being-in-the-world, or it is that pre-philosophical awareness which philosophy often tends to eliminate, changing it with a more reductionistic model, but which is necessarily the starting point of any thought. The words and notions are learned in this kind of being-in-the-world, and if one just thinks of how we learn things, it is really simple, someone shows a thing to us while our being-along-in-the-world, and because we are in the same world, and because the thing we see is the same thing (no Cartesian duplication, no phenomenal experience set apart from the world)- it is in publicly accessible space, and the ground for transcendence is there, the thing is the same thing for me and for the other. Now, it might seem problematic to take this “naive” view as a ground, but I want to point that the notions are learned in this kind of view, the things we think of are based on this “naive” being-in-the-world. Dismissing this as ground seems to me impossible, analogous to cutting the branch on which we sit. And part of it can be seen in the problems which different moves away from the being-in-the-world (by cutting it to half to subject and phenomenal experience, or by taking the abstraction from it, e.g. atoms and physical forces as self-subsistent and constituting the whole) can cause with possibility to address transcendence of intentional content, but also with impossibility to address what is left out of those abstractions as intentionality in general, what is called consciousness, qualia, and so on.

Often this being-in-the-world  is reduced by cutting it in half, and putting the subject as some separate self-subsistent essence, and then the other half is often called phenomenal-world. Some imagine this phenomenal world as some kind of representation of the real world, and they call it phenomenal experience, removing the world from it, and moving it to the side of the subject.

Grounding the Inter-Subjective Transcendence

In every intersubjective practice, be it communication, game, or otherwise,  we necessarily accept the possibility of intentional content to show inter-subjective transcendence; possibility for it to transcend not only multiple intentional acts of different quality (or as it is also named – of different psychological type, as e.g. remembering/ imagining/ seeing /wishing and so on), but also the intentional acts of multiple subjects. For it to be transcendental, the content of our intentional acts need to differ from the contingent psychological acts in which it appears (or so to say, not to be defined or constituted by them), and to appear as same content within each of those intentional acts, be those in one subject or in number of subjects.
As I have noted several times (but I think it is worth repeating), denying the possibility of inter-subjective transcendence is impossible, as in the same act when one denies the transcendence, the transcendence is assumed. Namely one can’t deny “possibility of intersubjective-transcendence”, without assuming that the other person is talking about the same thing, when talking about “inter-subjective transcendence”. In similar way one can’t argue against inter-subjective transcendence of ANY intentional content, as by denying the intersubjective transcendence of that particular content, one is assuming the possibility to talk/think of that same content. So whatever is content of intentional acts, is inter and intra-subjectively transcendent. What one can deny though is that there is no inter-subjectively transcendent content (or meaning) of some of the words we use. Though a) this can’t be denied in general, as the denial itself put into words, will have to be inter-subjectively transcendent and b) for any word which is learned and used in society, in lack of inter-subjective content it is hard to see how it would be distinguished from any other such word, i.e. if we say that words W1 and W2 both lack any inter-subjectively transcendent content, it is hard to see in what way those two would be distinguished and used in different ways in communication.

As transcendental, this intentional content can’t be defined through subjective and contingent beliefs about the content, nor by subjective/psychological acts/events. As for the beliefs, the very notion of “beliefs about something”, should be enough to see that there is distinction between beliefs about the thing, and the thing itself.  But also if one takes beliefs as defining the content, it would a) render changing of beliefs about content impossible, and b) it would make it impossible for us to be wrong in our beliefs about the thing. Then, it seems to me, we should not buy into subjective idealism, nor we should buy into some forms of internalism, which would want to reduce intentional content to whatever is happening in the brain (e.g. concepts as some kind of ability/information within the brain). The brain processes are something contingent and individual, and are localized in time, so they can’t be proper ground of intra or inter-subjective transcendence.

One can try to search for the transcendental content in inter-subjective practices. The logic would be that as if the intentional content is supposed to be inter-subjectively transcendent then supposedly the “root” of that content might be in the inter-subjective practices in general, or language in specific. But how can subject get in touch with language or practices in general, if they don’t appear as inter-subjectively transcendental intentional content for him in first place? So to say, the language and practices can’t be held as ground for inter-subjective transcendence, as inter-subjective transcendence is required for those things to appear in first place. The meaning of the word will have to appear as intentional content in order to learn the word.

If the idea that intentional content is created or defined by whatever is there in the subject may be termed “subjective idealism” or “internalist physicalism”, this second view, that the intentional content is created or defined by whatever is there in the practices between subjects, may be termed “inter-subjective idealism” or “inter-subjective physicalism”.

If you agree with me that those two models are not sufficient to give ground of intra and inter-subjectively transcendent content, we need to search for intentional content in some other place.
One other idea is that the content is transcendent, by being connected to objective things in the world – this view might be called externalists physicalism. The intentional content of our thoughts about Venus is then the planet Venus. And really this view seems to provide the needed transcendence. In my numerically different intentional acts, where the intentional content is planet Venus, all of those are about the objectively existing planet Venus. And even when I speak with other people about planet Venus, the intentional content is same for us – being one and the same planet Venus. Further the account can be held to give account for concepts which are not singular (i.e. general notions), by connecting them to refer to the sets of particulars which satisfy given property. What is left for this account then is to explain and explicate the relation which makes certain intentional act to be about certain things/facts in objective reality.

However by this account, we can never know that certain intentional content is inter or intra-subjectively transcendent. The transcendence there is not something to which we have intimate relation, or of which we have intimate knowledge; by this account what we mean by the words, for all that we know might be not intra or inter-subjectively transcendent. When I say tree now, and when I say tree later, for all that I know, I might mean two different things – the knowledge if I mean the same thing by the same word is isolated from me, it is externalized in some kind of relation which is not fully accessible to me. Thus it appears that while I do mean something by my words, I can’t know what I mean by them.

And then, there is the model which I find plausible, where the transcendence is grounded in being-along in the (phenomenal) world, the being-along with other subjects in the same world, which presents a possibility for noticing the same things, be them concrete things, or also presents a possibility for noticing same abstractions – same abstract notions. Both concrete things and abstract notions in this being along in the world are given to us not as something which we create or own, but in publicly accessible world. Because they are in this publicly accessible space, we don’t need to imagine that other people can access them, it is normal that they can, and we need to learn special cases in which they can’t.
On this view, not just that the intentional content transcends the numerically and qualitatively different intentional acts of one or multiple persons, but it appears in every and each of those subjects as such, and knowable as such. Or so to say, the intentional content is present in our intentional acts, not as nothing, but as a concrete idea. In such way a simple identity is made between the idea and the intentional content. And as much the intentional content is something other (e.g. planet Venus), the idea is also something other – i.e. planet Venus.This is not to be taken (as might be common misconception about idealism), that the idea is something subjective, mental, or that because of being idea, the subject holds every and each possible truth about that idea (the things which were already denied). It just means that whatever intentional content is, it is thinkable as something other then the subject or in the case of some notions like “self” as same with the subject.

Hegel, Change and Contradiction

Today I noticed that the entry on Change at the SEP is revised. I had a short glance, and found few things I want to comment on. While talking about the issue if change is consistent notion, the author of the article says:

Hegel was more explicit. In The Science of Logic he said that only insofar as something has contradiction in itself does it move, have impulse or activity. Indeed, movement is existing contradiction itself. “Something moves not because at one moment of time it is here and at another there, but because at one and the same moment it is here and not here.” (Hegel (1812) p. 440).

What I want to say here, is that one should be careful to divide what Hegel says about the moments of movement (namely position and time) from what he says about movement itself. In that particular quote, the contradiction is shown between the moments of movement. That in movement “a thing is at one and the same moment here and not here” is supposed to point that those moments (namely time and position) are not self-subsistent, and that by themselves they necessarily produce contradictions.
Further, as argued in a previous posts about the dialectic method Hegel doesn’t stop at contradictions of notions on certain level. In fact he is taking those contradictions as a kind of negative power – as a need to, by negating this contradiction, get to richer comprehension free of contradictions.

But, mere pointing to a fact of movement won’t do it (“look, things move!”), as mere pointing doesn’t really solve the apparent contradiction, but is a part of the contradiction (“things move, but by this reasoning they shouldn’t!”).  Or as Hegel says:

…they (i.e. those contradictions) deserve a more thorough consideration than the usual explanation that they are just sophisms; which assertion sticks to empirical perception, following the procedure of Diogenes (a procedure which is so illuminating to ordinary common sense) who, when a dialectician pointed out the contradiction contained in motion, made no effort to reason it out but, by silently walking up and down, is supposed to have referred to the evidence of sight for an answer. Such assertion and refutation is certainly easier to make than to engage in thinking and to hold fast and resolve by thought alone the complexities originating in thought, and not in abstruse thought either, but in the thoughts spontaneously arising in ordinary consciousness.

(For an example of a resolving an apparent contradiction, you can check my previous post on why 1=0.99.., the comments of that post, and also here and here.)

This process of resolving the contradiction, but not through mere empirical pointing to a fact, is what Hegelian dialectics is about:

It is in this dialectic as it is here understood, that is, in the grasping of opposites in their unity or of the positive in the negative, that speculative thought consists.

At other place which makes clear this position of Hegel on contradictions present in the movement on level of abstractions (connected to Zeno’s paradoxes and Aristotle’s solutions of those paradoxes) Hegel says:

The solutions propounded by Aristotle of these dialectical forms merit high praise, and are contained in his genuinely speculative Notions of space, time and motion. To infinite divisibility (which, being imagined as actually carried out, is the same as infinite dividedness, as the atoms) on which is based the most famous of those proofs (i.e. Zeno’s paradoxes), he opposes continuity, which applies equally well to time as to space, so that the infinite, that is, abstract plurality is contained only in principle [an sich], as a possibility, in continuity. What is actual in contrast to abstract plurality as also to abstract continuity, is their concrete forms, space and time themselves, just as these latter are abstract relatively to matter and motion. What is abstract has only an implicit or potential being; it only is as a moment of something real….

So, that is why when in talking about positions and times, for Hegel, one will necessary get to contradictions. It will be because of the “…error of holding such mental fictions, such abstractions, as an infinite number of parts, to be something true and actual”. I wrote also about this situation in my post Time as Abstraction.

Also in the SEP article the author writes…

However, here we can remind ourselves of Hegel’s idealism. Just about everyone agrees that contradictions within ideas are easier to swallow than contradictions in the external world.

I want give a further comment on this one too. It would be understatement to say that Hegel understands that one might seek to resolve the issue of those contradictions by locating notions in our Mind, and then saying that while contradiction will be necessary in the ‘realm of the Mind”, they don’t say anything about the external world (which would be thus left free of any contradictions). That is the Kantian solution, which Hegel contrasts with his own thus:

The Kantian solution, namely, through the so-called transcendental ideality of the world of perception, has no other result than to make the so-called conflict into something subjective, in which of course it remains still the same illusion, that is, is as unresolved, as before. Its genuine solution can only be this: two opposed determinations which belong necessarily to one and the same Notion cannot be valid each on its own in its one-sidedness; on the contrary,they are true only as sublated, only in the unity of their Notion.

How to Extract A Song From YouTube (Or Other Video Sites)

Before talking about the youtube video extraction, here is a quick self-promotional note: If you love good games, you may want to go and check the concept art, screenshots, and development notes for my first iPhone game – Henophobia.

In those few days I was getting a dozens of hits for the Inner Life Of A Cell video, and lot of them were through search phrases like “Inner Life Of A Cell download music”. So, I got interested how one can extract the music from YouTube, and it turns out it is pretty easy… Here is how…
(If you are not interested in the process, but came here looking for the music just go at the bottom of this post, and download the mp3 file.)

Step 1 – Downloading the video

  1. If you don’t have Firefox go get it here, and install it.
  2. Install the DownloadHelper extension – using Firefox go to the bottom of that page, and click Install now.
  3. After installing you need to restart Firefox to continue. After the restart you will have a new button on the toolbar, looking like a little person.
  4. Go to the YouTube page from which you want to download the video (in this case here). Note you can use this extension to download flv files from other video sites (like Google Video) too.
  5. The person on the toolbar icon will start to rotate. Click on the arrow beside it, and click on the first choice. The flash file containing the video will start to download. (click Ctrl+J to open the download window if it doesn’t open automatically)
  6. When the download is finished, right click on the downloaded file, and choose “Open Containing Folder”. There you should have the flash (flv) file. Copy it to the Desktop.

    (Alternatively you can try YouTube downloader site.
    Just paste the address of the YouTube video there, and click “Get Download URL”.
    When you do that, you will be given an URL from which to d/l the file.
    When I tried this, the file was downloaded, but I had to rename the file, and give it flv extension.
    But once you do that, you should be OK)

Step 2 – Extracting the music

  1. Download the AoA Audio Extractor 1.1 (it is free)
  2. Install it, and start it.
  3. Once the program starts, click the “Add Files” button, and choose the flv file you copied to the Desktop.
  4. Change some of the options if you want, choose where to export the mp3 file, and press the big orange Start button.
  5. If everything is OK, the extraction will start, and you will get mp3 file in the folder you chose.

Step 3 – The Music

    And here is the result – the music from the Inner Life Of A Cell video.

UPDATE:Tim in the comments points to the Vixy service, which does (I didn’t try) the transformation automatically and let you download the result. If you are not interested in having control over some details of the transformation, just go to Vixy, paste there the YouTube address, and choose MP3 transformation. BTW, I don’t know if it works with other video sites.

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Lifeless Laws

Physical laws present to us, (or would present to us in ideal case), the necessary relation (necessary for any measured system in this world) between different values we measure on a system.
Number is ratio, and measurement is applying of such ratio to certain quality of the system by comparing to the quality which is taken as unit. In such way through measurement, we abstract number from the physical system.
Time is merely one of those values which are measured.

Can we say then that physical laws are not the thing that give life to universe? They just say that for any system in the universe, the values will fall into certain relation.

Hegel on Atomism

At present, students of nature who are anxious to avoid metaphysics turn a favorable ear to Atomism. But it is not possible to escape metaphysics and cease to trace nature back to terms of thought, by throwing ourselves into the arms of Atomism. The atom, in fact, is itself a thought; and hence the theory which holds matter to consist of atoms is a metaphysical theory.

Newton gave physics an express warning to beware of metaphysics, it is true, but to his honor be it said, he did not by any means obey his own warning. The only mere physicists are the animals: they alone do not think: while man is a thinking being and a born metaphysician. The real question is not whether we shall apply metaphysics, but whether our metaphysics are of the right kind: in other words, whether we are not, instead of the concrete logical Idea, adopting one-sided forms of thought, rigidly fixed by understanding, and making these the basis of our theoretical as well as our practical work. It is on this ground that one objects to the Atomic philosophy.

Encyclopedia of Philosophical Sciences – VII. Being § 98, Attraction and Repulsion

Familiar Faces, Gestalts and A Priori Truths

We easily recognize a familiar face in a group of people.
We recognize her face in a moment, without analyzing the details of the face. In fact, if someone has asked us to describe features of that face, or to answer questions about it while not looking at it, there is a good chance that most of us would fail to do so. I’m thinking here about features like color of the eyes, the form of the lips, the length of nose and so on.

I would say that as far as we can answer such question or provide descriptions, it is because either we can bring that familiar face from the memory before our “inner eye”, or because we had explicitly attended to that feature in the past (we might have had intentionally focused on it, or it attracted our attention).

When we see a person’s face, we don’t see it as an aggregate of multiple features, but we see it and later recognize it as a whole, as a gestalt. But while we can remember and recognize things as a whole without learning about specific features, still in any case when the face is before us, it is there as analyzable. When we look at it, the features are there – open to our possibility to focus on them, open to our skills for analysis which may be “triggered” either spontaneously or by some kind of reflex (e.g. when something attracts our attention).
And in those cases we can attend to different things, we can attend to one eye, or to the other eye, or to both eyes at once, we can attend to something which we previously didn’t notice – for example we can attend to a small part of the curve of the left eye, or to the relative brightness of a specific place vs. another, or to the number of speckles on the right cheek, etc…
But while we attend to one of the things, our consciousness is not limited to it. As when at the start the gestalt was there as gestalt presenting the possibility for wealth of different abstractions; now when we attend to a specific abstraction (feature), it is there as an abstraction – as a part of the whole which is still there to return to.

So, let me now turn from familiar faces and gestalts to a priori truths.
In a previous post I was wondering if some tests in developmental psychology might be taken as a hint that the infants believe that 1+1=2 based on intuition. While it might be taken as a hint, as it was pointed in the comments by Pete and Curtis those experimental results hardly show anything decisive – one can explain the results in different ways which wouldn’t include any mention of intuitive truths.
But let me look at the issue in the context of the previous discussion…
When we have in front of us two things, we can see them as a gestalt, as “two things”, something which we can see and recognize. But the same gestalt, which we can name as “two”, is also analyzable – it is implicit in that gestalt that I can attend to the one or to the other of those two things. And while attending to one of them, as in the case with the face, the other one is not disappearing – it is still there. And I can spontaneously change the way I attend to the whole, I can focus on the other one. So, in that whole of two things, I can switch my attention, look at the both things as a whole (two), or I can attend to each of them separately.
In this way, we are presented with the a situation, in which the same gestalt is analyzable either as one two, or as two ones. And that goes for any gestalt which I can imagine – as long the gestalt is two, it will present possibility for attending to two separate ones (among which we can switch the attention).
This a priori relation of possibilities is there, be it if what we characterize as two is in front of us, or if as in the case with the experiment done with the kids mentioned in the other post, one or both of the things are tracked (as hidden behind the screen), or even if we have imaginary gestalt.
This is, I think, what is behind our intuitive understanding of what we express by 1+1=2. The equation shouldn’t be taken as identifying two separate sides, namely a)1+1 and b)2 , but as expressing that the whole, if it is characterized as two, can be also characterized as one and another one. The identity is in the whole, and the equality is expressing the necessity that in every possible world the whole which is 2, is also 1+1 and vice versa.

And at the end, let me finish with a doubt I have…
While I’m pretty convinced that I have grasp of the a priori truth of the equation that 1+1=2 (meaning what has been just described), I’m not very sure what to say about the issue if the truth of 1+1=2 is analytical.
On one side, it seems to me that the potential to analyze the whole into separate things (i.e. to focus on the one and the other) is what is required for something to be named as two, but on other side having on mind the case with the face, I’m thinking that a whole might be recognized as two even without explicitly or implicitly being aware of those possibilities.

Aggregator Page Changes

The aggregator page is now tracking 109 114 117 blogs, and it used to get crowded with posts sometimes. Because of that I did two changes:

  1. Posts which come from same blog are now grouped, so they take less space.
  2. I added possibility for grouping blogs, and posts from blogs belonging to certain group are now grouped and shown in separate column.

Also you will notice that at the bottom of the page there is link to the aggregation archives for previous days.

I plan in future also to add tracking of the comments for those blogs that offer comment feeds, but can’t give concrete dates.
I don’t have information about how much (if at all) the aggregator is used, but if you use it, and have some requirements or ideas please leave a comment here.
I’m also interested about your opinion about some other groups that would be useful (currently there is just a Mind&Cog.Sci group, which might be little artificial), recommendations for other blogs to track on that page, etc…

UPDATE (Dec.09):
A little more tweaking…

  1. I solved also the problems with reading a few of the blogs which were using namespaces in their HTML (probably result of copying the content from MS Word to the blog). This leaves a problem with reading Show-Me the Argument which is of some other nature. Fixed this issue too – the site returns results if the code presents itself as a browser.
  2. Also added the names of the authors to the posts.


  1. Under the list of blogs sorted by days of (in)activity, you will now find also a link to a separate page with Technorati stats for blogs tracked. Not very useful, but I was interested how easy is to work with Tehcnorati API.


  1. The aggregator page should be updated now every two hours. (Is that often enough?)
  2. Also change in formating – I moved the blog title before first post title as Jeff G. suggested in the comments, so now if there are more posts from same blog it makes more sense.

Inner Life of A Cell

UPDATE: If you got here looking for the song of this video, or how to download the video, check this post.

This is so cool (and weird), I had to link to it:

The Inner Life of a Cell, an eight-minute animation created in NewTek LightWave 3D and Adobe After Effects for Harvard biology students… The animation illustrates unseen molecular mechanisms and the ones they trigger, specifically how white blood cells sense and respond to their surroundings and external stimuli….Nuclei, proteins and lipids move with bug-like authority, slithering, gliding and twisting through 3D space.

For better video quality and more info visit this page.

Is 1+1=2 Intuited?

Over at Brain Hammer, Pete Mandik as a part of his post Abusing the Being-Knowing Distinction proposed that a following principle can be valuable in attacking claims of intuited metaphysical truths:

It is intuited that P. Philosophical theory T explains P. But philosophical theory T is inconsistent with the fact that P is intuited. Too bad for T!

In the comments of the post I wondered if the following example would fall also under that principle:

  1. It is intuited that 1+1=2
  2. Russell and Whitehead gave theory of why 1+1=2 in Principia Mathematica
  3. If 1+1=2 was true *because* of the logic in Principia, nobody could’ve possibly intuit its truth.

Pete raised the issue if 1+1=2 is intuited at all. I said I believe it is intuited, and Pete said that he believes that it is learned.
As I don’t want to abuse the comment-space over at Brain Hammer for discussing a question which is just marginally connected to the central topic of the post, I will put my thoughts on it here.

The question of what is a belief, and the issue of when we can say that one beliefs something is surely problematical.
When we say that a person P believes that X, we don’t e.g. expect that P continuously contemplates on the truth of X. Probably we will require only that in certain cases, in the right conditions, his belief that P to be actualized somehow, affecting what the person says, what the person does and so on. Based on that we can talk abut dispositional vs. occurrent belief. If that is so, then we can say that the person doesn’t have actually to claim that 1+1=2, in order to count as believing as 1+1=2. But if the person doesn’t claim that 1+1=2 (or sincerely report that he believes that 1+1=2), how do we get to know that person believes that 1+1=2?
One behavioral sign besides actually P claiming X, might be that P is surprised if he/she observes a situation in which X is shown false. While of course, this behavioral act doesn’t have to mean that P believes that X (generalizing beliefs to dispositions to act would fall into some kind of behaviorism), it is clear that it can be taken as a good indicator.

The question if this kind of behavior can be found in human infants has been tested by experiments. Wynn K.(1990)1 did experiments where he presented the following sequence to four and half month olds.


After this, two outcomes were presented, which are marked in the following picture as a)possible outcome and b)impossible outcome, and the time infants kept looking at the outcome was measured in each case.


In psychology, the sufficiently longer time in those cases is taken to represent a surprise. And that’s what Wynn got for the impossible outcome. The infants looked longer at it.

While I’m not very  knowledgeable about the field of developmental psychology, it seems to me that if those results are true and if the interpretation of the results is right, it isn’t very unreasonable to talk about infants having belief that 1+1=2. However because this is shown for very early pre-linguistic age, it makes it problematic to speak of a learned theory.

1Wynn, K. (1992) Addition and subtraction by human infants. Nature, 358: 749-750, reference taken from Lakoff&Nunez (2000) Where mathematics comes from p.16-17