Investigations 293

In §293 Wittgenstein considers what it would be if “pain” were a name for a particular kind of inner experience and goes on to show how this picture cannot make sense via his beetle-box example, discussed shortly.
      Suppose that I know what the word “pain” means only from my own case – that is, I know it as a name for a particular sensation that I have. If this is how I know the word, then this must also be how others know the word – that is, Sam knows the meaning of “pain” from his own case, as a name for a particular experience of his, something inward. In order to ascribe “pain” to others, it seems I have to generalize from my own case, something like “When I say I’m in pain I feel this way, so when others say that they are in pain, they feel that way too.” The justification for this generalization is dubious, for I only know one case of application (my own), and cannot infer that others are using it the same way (since I don’t have access to their inner experience). This cannot be the right picture of how I know the word “pain”. We’ll now elaborate.
     Intuitively, it seems that someone can only know what pain is from their own case. Let’s take this intuition seriously and consider the following example. Suppose everyone has a box with something in it called a “beetle”. No one can ever look into anyone else’s box (it is logically impossible), and everyone says he knows what a beetle is only by looking at his own beetle. (We can think of the box as a person’s mind, the beetle as the particular sensation that person has – and the person knows what the beetle is in his own case. In this way, there is analogy to the pain case. There is a sensation of pain [particular beetle] in the “mind” [box], and the public word for the sensation: “pain” [beetle].) In this example, the contents of each person’s box may differ – we can even imagine the contents changing—“beetle” simply designates the box-contents regardless of what is or is not in them.
     In this situation, we cannot say that Sam knows what a beetle is only by looking at his own beetle. Why? Suppose Sam has an orange in his box. You ask Sam “what’s beetle?” He can either say (1) an orange, or (2) whatever is in the box. If (1), we can’t say he knows what a beetle is because for all he knows a pear is in someone else’s box—if “beetle” denotes orange then it shouldn’t denote pear. If (2) then he hasn’t said what a beetle is, for he might as well have said “a beetle is a beetle” or “what is in the box is in the box”. Such an answer is not at all informative, and so not at all meaningful. This echoes §298, where Wittgenstein observes that the fact we’re inclined to say “This is the important thing” – while we focus on our particular inward experience – is sufficient to show how we are inclined to say something which is “not informative”. One cannot know the meaning of “beetle” just from looking at his own beetle.
     Now let’s suppose that these people had a use for the word “beetle”. That is, suppose “beetle” is in fact a meaningful expression. If so, “beetle” couldn’t be a name for a kind of inner experience, for the same reasons stated in the previous paragraph. We cannot name the thing in the box; for suppose someone’s box is empty, “beetle” cannot stand as a name for an orange and as a name for emptiness – we cannot refer to the particular (non)object in any one’s box because it’s contents aren’t part of the language game – whatever it is cannot be shared or expressed, for a private sensation cannot even be given a name that others (or even yourself) can understand. The object in the box is not an object of possible reference, there is no public word for one’s private contents, as we saw in §258. If the word has a use, its use is as something other than a name – it can be publicly understood. If “beetle” has a meaning, it cannot be a name. The idea is that if mental predicates like “pain” are names denoting a kind of object, the object “drops out of consideration as irrelevant” – we can’t actually make sense of our referring to that object. If the word only ever has a public use – is publicly understood – then it cannot ever be used a name for a private object. When I say “I am in pain” I express something we all understand – I do not name a particular inner sensation present to me – this is the sense in which the object “drops out of consideration as irrelevant”.
      §291 buttresses this point. Consider that you might think of a description as a kind of name for an object—“a word-picture of the facts”. On this view, there’s a sense in which the description is idle, it simply depicts a state-of-affairs. But now consider how an engineer might use a description. Drawing a machine, a sort of design, is like a description of what he will build. Recording a measurement is a description that he uses to know where put things or how to put them together. These descriptions have particular uses – they are not “idle”. If we think of words as names for objects, they become idle; if we realize that words have uses (over and above naming objects), we see that words are not mere pictures but rather tools for doing things. The engineer’s description gets its meaning from its use or place in some project – not as a name for his inner imaginings. If we want to grasp the meaning of a word, we must look to its use; if words are merely names for objects (especially for inner qualities), we cannot make sense of how we can use them meaningfully.
      The example in §293 does not show that there is or is not any particular sensation that one stands in relation to. Rather, it demonstrates that the grammar of our language doesn’t allow for this kind of private reference or knowledge of meaning (§304). There is no place in the language for a name for a private sensation, for there is no sense in which we could understand what we are referring to. Insofar as words have uses – and, consequently, meaning – they must be used to talk about something other than private mental contents.
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Investigations 258

In §256, Wittgenstein characterizes a private language as that language which describes my inner experiences and which only I myself can understand. Words of this language cannot be connected with my natural expressions of sensation – if they were, the language could not be private, but is rather public, for anyone might understand my natural expressions and so come to understand my purportedly private language. That is, if a private language is connected with natural expressions, then the expressions of the language are public/observable – its expressions cannot be understood uniquely by me. So if we are to have a private language, it cannot be connected with natural expression – rather, it must work the following way: we have sensations (which are in some sense private) and come to associate names with the sensations and use these names in descriptions (which, presumably, cannot violate the privacy).
In §258, Wittgenstein asks us to consider the following case. I want to keep a diary about the recurrence of a certain sensation or I have. I associate the sign “S” with the sensation, and write this sign in the diary every day on which I have the sensation. This is the only means by which I “express” my experience of the sensation – there are no natural expressions of the sensation, all the outside observer can see is the “S”-writing behavior. I cannot formulate a definition for “S”. Why? Suppose I say, or think, that “`S’ is defined as such-and-such”. If the “such-and-such” is some combination of familiar, public words (in English, let’s say), then my sensation is publicly expressible and cannot be private, contrary to our hypothesis. Or else if the “such-and-such” is some other private sign like “S”, then those signs must also be given some definition, and so on.
Recall that to give an ostensive definition of a thing is to “attach a nametag” to it by gesturing toward the thing and producing an utterance. You might think that “S” could be defined ostensively. Not so. For in what sense can you gesture toward a sensation? It is not as though I could point to the S-sensation in my head (I’d just be pointing at my head!). But you might think that in some sense you can point to your sensation insofar as you “concentrate [your] attention on the sensation [so as to] `point inwardly’”. But this, too, would be a mistake. For we can ask “what is this `ceremony’ of concentrating your attention for?” What does it mean to “concentrate your attention” on this thing rather than that – and what does it actually accomplish? You might think it accomplishes this: by concentrating your attention on the sensation and committing to memory a connection between the sensation and “S”, you bring about the connection between the sensation and “S”.
Committing the connection to memory just means that this process [concentrating the attention] brings it about that I remember the connection correctly in the future. If concentrating your attention makes it the case that you remember the connection correctly in the future, then there must already be some fact of the matter regarding a correct connection between the sensation and “S”. But in the case we are asked to consider, there is no criterion of correctness. I can’t bring it about that I remember the connection correctly in the future unless I have the resources to say that it was correct to apply “S” to the sensation in the first case. There’s a temptation to say that because this is my private sensation and my private language whatever seems correct to me is correct. And so because applying “S” to the sensation seems correct to me, it in fact is. This, however, is not right. To say “whatever seems correct to me is correct” is just to say that “we cannot talk about `correct’”.
A brief elaboration. My “concentration of attention” doesn’t seem like it should change anything about how “S” may be used, nor does it affect the sensation; there is no tangible connection brought about. It cannot be the case that whatever seems right and wrong is in fact what is right and wrong. For if it were, then understanding how to “go on” would just be a matter of conforming to the thought or formula which seems right in your head. But we saw in §154 that understanding how to go on or continue a series is not a matter of having a formula occur in your head and conforming to that. Likewise, what is right or wrong is not so because of some occurrence in your head – like “seeming right”. Suppose I wake up one morning and what seemed right to me yesterday now suddenly seems wrong – has the status of what is right or wrong suddenly changed? Intuitively, we want to say “no”. Because I cannot mentally set my own standard of correctness, then in this situation there can be no “right” or correct use (of “S”).
We can strengthen this point with considerations from §257. If I invent a name for my sensation in my private language, I cannot make myself understood when I use the word. That is, I could never use “S” in a sentence and have someone understand what I mean by it. If I cannot make myself understood to others when I use the sign, then in what sense do I understand “S” when I use it? It seems like I can just stick “S” to whatever sensation I feel like, whenever I feel like—so in what sense could this sign have any meaning to me? Insofar as it a name? Not so, for there is still no criterion of correct usage. A name is used to refer to an object, and I cannot use this name for anything (as no one understands it) – it has no purpose and cannot be used to refer. Should I use “S” to refer to some other thing, no one can tell me I’ve used the sign wrong – if “S” can refer to whatever I like, then there cannot be a fact of the matter as to the correct use of “S”.
In order to give something a name, there must a role existing in the language for that word to occupy. There must be a post at which the word is stationed – a role the world plays. But there is nothing in the grammar of any public language – no station – which fixes the use of the term “S”. So we cannot under the notion of a private language.

Investigations 201

We should first clarify the meaning of “interpretation”. Suppose I’m traveling from Berkeley to Timbuktu. At some point I no longer know the way, but I see a signpost reading, “Timbuktu → ”. The signpost expresses a rule – that is, the signpost is an expression of a rule, namely a rule regarding how to get to Timbuktu. I see that sign and think, “Ah, I ought to proceed East to Timbuktu.” This thought, which represents what I take the signpost to be expressing, constitutes my “interpretation” of the rule expressed by the signpost. If I had seen the sign and thought “I ought to proceed West to Timbuktu”, that thought would also constitute an interpretation of the expressed rule.
The paradox is: no course of action can be determined by a rule because every course of action can be brought into accord with the rule (87). In what way is every action capable of according with a rule? Consider a teacher expressing a rule (regarding a particular series) to his pupil: “Add two each time.” The pupil proceeds: 2,4,…,998,1000 . We would say that he is following or acting in accord with the rule. But then the pupil proceeds: 1004,1008,… . The teacher sees that the pupil must not understand, though the pupil cannot be made to see that he was not “adding two each time”: he maintains he was following the rule expressed. We might think that the pupil understands the order as “Add 2 up to 1000, 4 up 2000…” and so on; that is, his actions are still governed by his interpretation of the rule expressed. He did not follow the rule (that the teacher expressed) – even for the first 500 terms – but his actions for the first 500 terms were in accord with that rule. And his actions after the 500th term were in accordance with his [the pupil’s] interpretation of the rule “add two each time” (81). In §198, Wittgenstein’s interlocuter says, “…whatever I do can, on some interpretation, be made compatible with the rule.” This is like how the pupil failed to see his own misunderstanding the order – on his interpretation of the sign (expression of a rule) “Add two each time”, his actions were compatible with the rule.
If any action, on some interpretation, is in accord with the rule, then no rule can determine a course of action. For then any course of action is acceptable by some interpretation of the rule, so no particular course of action is determined by the rule. Wittgenstein responds to the paradox, “if every course of action can be [compatible] with the rule, then it can also be [incompatible] with it. And so there would be neither accord nor conflict here.” (87) This is to say that there is no fact of the matter as to whether a course of action is compatible with a rule, because there exist interpretations of the rule which conflict with the action and those which do not.
That is, here is an expression of a rule: “Add two each time”. The pupil’s interpretation may be “ f(x)=x+2 ”. But this, too, is a sign to be interpreted. And based on the pupil’s behavior, we can say that the pupil interprets the expression “ f(x)=x+2 ” as “ ∀ x( x<1000 → f(x)=x+2 ) ∧ ∀ x( x ≥ 1000 → f(x)=x+4 ) ”. But now how are we to say the pupil interprets this sign? Prima facie, it looks like we need a rule which tells us how an expression of any given rule is to be interpreted. But this cannot be possible, for it leads to regress. Why? Because a rule saying how an expression of rule is to be interpreted must itself be expressed and interpreted. We would need a rule which says how to interpret that rule, and so on and so forth, never bottoming out.
Wittgenstein asserts that there is a “way of grasping a rule which is not an interpretation” (87). This must be so, lest we end up with the regress problem. Recall §154, where Wittgenstein argues that understanding should not be thought of as a mental process. To say, “Now I understand the series” is not to say “the formula occurs to me” – where the formula occuring is something like the interpretation of the rule expressed by the series. We say “Now I understand” when we can continue the series correctly. So when we say that “the pupil understands the rule,” we are saying that has the ability to apply it correctly. What does it mean to apply a rule correctly? From §201, this way of grasping a rule is “exhibited in what we call `following the rule’ and `going against it’” in each particular case with its particular circumstances (87). This means that the correct application of a rule does not have to do with an occurrence or given interpretation in one’s head. The deviant pupil did not grasp the rule, but not because his interpretation of the rule differs from ours. Rather, his actions did not conform to what we call “following the rule”. His actions deviated from the actions the “add two each time” order is supposed to provoke in this kind of circumstance (given the effects the teacher was trying to produce, what sign was used, etc.).
There is an inclination to say that every action according to a rule is an interpretation (87) – this is why we concocted elaborate formulas in the deviant pupil’s head to account for his misunderstanding. But this isn’t right, for understanding isn’t “in the head”, so to speak. Actions either follow the rule or go against it – this being judged externally, case by case – but actions themselves are not interpretations (though it seems they can be interpreted). Indeed, Wittgenstein says, “one should speak of interpretation only when one expression of a rule is substituted for another.” (87) That is, an interpretation is an expression of a rule; the substitution of one expression for another constitutes an interpretation of the original expression. An interpretation is not to be confused with a rule, nor is it to be confused with a given action.

Investigations 154

In §154, Wittgenstein claims that understanding should not be thought of as a mental process.
      We asked to consider when we are justified in saying that a pupil understands some system, or to consider when we ourselves are justified in saying, “Ah, now I understand the system”. That is, what is it that goes on in these situations when one is credited with understanding. Consider four pupils each examining the same series of numbers: 1, 5, 11, 19 …. We say that a pupil understands the series if he can correctly produce the next term of the series; for if a pupil did not understand the series, then he would not be able to correctly continue the series. So we say one understands when they can “go on” continuing the series correctly. The question, then, is what does this understanding consist in?
Suppose each pupil can correctly carry on the series, establishing that the fifth term is 29. What is going on in the pupil’s head when he realizes he can correctly continue the series? It seems there are many processes that could have been at work. For instance, it might “occur” to the first pupil that the first four terms can be united under the formula: a_n = n^2 + n - 1 . The formula did not, in contrast, occur to the second pupil. Instead the second pupil notices a progressive series of differences: 4, 6, 8 …, and infers that the next difference is 10 so the fifth term should be 29. For the third pupil, it could be the case that this series is simply as familiar to him as the ordinary series of natural numbers, and from this familiarity can “go on”. The fourth pupil might have some immediate intuition that the fifth term is 29. Regardless of what particular process occurred in each pupil’s head, we will still credit each pupil with having understood, for they can continue to correctly carry on the series. The moral is that there is not one unique “occurrence” in one’s head that constitutes understanding. Understanding cannot consist merely in having the appropriate formula occur to you; for the pupil who notices the differences and yet doesn’t having a formula occur to him is still credited with understanding. Because of this we cannot say that “Now I understand the series” means the same thing as “the formula occurs to me”. To emphasize this point, consider a pupil to whom the appropriate formula does in fact occur. It could still be the case that they misapply the formula, and fail to correctly carry on the series with 29. Consequently we will say that this pupil does not understand the series, even when the correct formula occurs to him. So understanding must be something besides merely having the appropriate formula occur to you.
     If when I say “Now I understand” I have not said “the formula occurs” to me, what then does it mean to say “Now I understand”? You might think that understanding is a (presumably mental) process which somehow occurs behind or along with the occurrence or utterance of the formula. How are we to think of mental processes? Wittgenstein suggests that a pain’s increasing or decreasing, or the listening to a tune or sentence are mental processes. The pain experience or the auditory experience are mental processes insofar as they are particular occurrences “in one’s head”, so to speak. These processes may be interrupted; for instance, I may be in pain and then fall asleep. When I fall asleep, we do not continue to attribute the mental process of being in pain to me. Or if Barry Stroud falls asleep at the opera, his mental process of listening to the tune has been interrupted; we no longer attribute the listening of a tune to him. In a similar way, the occurrence in your head of the appropriate formula is a kind of mental process. You may be representing the appropriate formula, fall asleep, and so cease to be in a state of representing the formula (or of having it occur to you).
      Understanding does not seem to be a mental process in the same sense as the listening to a tune. Sam, grandmaster of chess, we attribute understanding of chess to. When Sam falls asleep, we do not say that his understanding is interrupted. When Sam is asleep we still say he understands chess. Sam doesn’t understand chess merely when the appropriate chess move occurs to him during a game (as when a particular formula may occur to you during a math problem). Sam’s being in a state of sleep does not strip him of his ability to play chess. In this way, Sam’s understanding cannot be identified with the occurrence of some mental process that happens alongside his action.
      So when a pupil thinks “Now I can go on” and utters the correct formula, what can we point to which actually justifies the pupil’s thinking “Now I can go on”? We’ve seen that we cannot point to some unique occurrence in his head, for there were many various occurrences which accompanied each pupil’s ability to go on (e.g. representing the appropriate formula or seeing the sequence of differences). Nor can we point to some mental process, for mental processes can be interrupted in ways that the understanding seemingly cannot. We cannot point to something inside the pupil’s head and say that that’s what the understanding consists in; consequently, we should look at the circumstances of the situation outside of just what is in one’s head. This leads Wittgenstein to suggest that if there is something which justifies the pupil’s thinking “Now I can go on”, it is the particular circumstances which underly the utterance of the formula (or the noticing of the series of differences). There is something about the pupil and the external situation he’s in which determines whether we are justified in saying that he understood. It is not enough for the the formula to occur to the pupil, but the formula must occur to the pupil in the right circumstances, where the pupil reacts in the right way to the given external stimulus (e.g. the series). If the external stimulus had been different but the pupil reacted the same way we would not credit him with understanding. To see that someone has understood, we must look at more than what goes on in their heads, but also what the external stimulus was and what the external reaction on the part of the pupil is. In this way, we see understanding as more of an external process – an ability or a “can-do” – than any particular mental process.

Investigations 32

This post explains §32 of Philosophical Investigations, further explicating the main thrust: that Augustine’s description of how one learns a language presupposes that one already has some kind of language.
      Before examining §32, we should explain ostensive explanation. To give an ostensive explanation or definition of a thing is to “attach a nametag” to it by gesturing toward the thing and producing an utterance (which presumably is the name). For instance, suppose my tutor attempts to provide me with an ostensive explanation or definition of the number two. He points to two black bolts and utters, “this number is called `two’” (18). He does not merely utter “two”, lest he be misconstrued as (a) naming this particular group of bolts “Two”, (b) naming this kind of arrangement of objects “Two”, (c) naming the black color of the bolts “Two”, and so on. By qualifying his explanation with “this number” we specify the role of the word “two” in the language, namely as a counting-word, so that it is not confused with (a), (b), or (c) (18).
             For his ostensive explanation to be successful, however, I must already understand what the word “number” means, or else I will not understand that he meant to define “two” as a counting-word and may miscontrue him in any of the aforementioned ways and I will not come to use the word correctly. If I don’t know the meaning of “number”, then this must be given an ostensive explanation as well; such an explanation will consist, presumably, in other words. And those words would have to be explained via other words, and so on, ad infinitum. The moral is that in order for ostensive explanations to be successful, we must be equipped with some words which we can use to understand the words we are being taught – our minds must already be prepared in a certain way. If we have to resources to understand the role the word plays in language, then we can come to correctly use, and so understand, the word.
      Suppose I am visiting a foreign country. In §32, Wittgenstein observes that I will learn the language of the inhabitants by the ostensive explanations they give me. But we saw that ostensive explanations are given through words, which must be defined in a similar way. He further observes that I will have to guess how to interpret their explanations. If an inhabitant says – in his language – “This number is called two”, but I do not know how the word “number” is used, then I must make a guess as to the meaning of number, if I am to interpret his explanation of “two”. In some cases I may guess correctly and in other cases not. If I guess incorrectly, the inhabitants will take it that I do not understand the meaning “two”.
      The main thrust of §32 is that Augustine describes the manner in which learn our first language as if we were learning a foreign language. That is, in his explanation of the learning of language, he presupposes that we already have a certain “language of thought” or that we can “talk to ourselves” – prior to the learning of any public language (19). Imagine we all in fact have such a language of thought. Then learning our public language (e.g. English) involves something like the following: we learn what English nametags correspond to the words of the language of my thought. This is like the learning of foreign language, where we identify the word of the foreign language with the word we already have command of the use of in our non-foreign language. To have a language of thought is to have a place “prepared” (19) for the learning of language.
      Reconsider my going to a foreign country and recall that I must guess in order to interpret the inhabitants’ ostensive explanations. In order for me to interpret the ostensive explanation of “two”, I must make a guess that “number” (or the inhabitant’s word for it) signifies that “two” is to be a counting-word. In order for me to make this kind of guess, I must already have my own concept of number. This means I must speak some kind of language already; otherwise, I would have no word or sign I could use to represent the concept of number to myself. For me to already be a speaker of a language is for me to have a place prepared for the learning of other words in the foreign language – I am already familiar with the various roles and uses of words. If I did not already have my own language and word for the number concept, I would not be able to guess the interpret the inhabitants’ explanation of “two” as indicating a counting-word. So in order to learn a foreign language through ostensive explanation, I must already have a place in my mind prepared; I must already have some kind of language of thought. And so I am merely connecting the inhabitant’s word with my own way of thinking of things – I am applying a new nametag to an old concept.
   Augustine, in describing the learning of language as a matter of learning what nametags go to what objects, presupposes that we already have some kind of language of thought. In this way, he describes learning language as the same kind of process that goes on when you learn the language of a foreign country via the ostensive explanations of its inhabitants.

Unity of Apperception

This paper will discuss Kant’s argument in section 16 for the unity of consciousness. In particular, it will dissect his claim that the analytic unity of apperception is presupposed by the synthetic unity of apperception. It will also briefly characterize the Humean and Cartesian views of self or the unity of consciousness, in order to bring out views which Kant is striving to avoid.

We’ll first provide a general characterization of both synthetic unity and analytic unity, before discussing them as they relate to apperception.

Synthesis is an activity where the raw material received in sensibility is unified (by certain conceptual rules) into a coherent representation (B130). Synthesis is an act of the understanding which combines the raw sensory input into coherent representations. It takes the spherical-sensation and the orange-sensation and combines them into a representation of an orange. The representation of the orange has synthetic unity in that it unites orangeness and sphericalness in some object under the concept “orange”.

The notion of combination is crucial to understanding synthesis and synthetic unity. Combination is an action by our faculty of understanding, it is not an activity of our faculty of intuition. Nothing in pure intuition is exhibits combination, so combination cannot be tied to sensibility and must be tied to understanding. Combination, then, does not lie in the objects, but is an a priori feature of our understanding (because it is an activity). We cannot represent those properties as combined in some object that we have not previously combined in or through our understanding (B130). In this way, combination is the representation of the synthetic unity of the manifold of intuition. For, a complex representation must unite various properties in one object, and this is just what it is for the faculty of representation to engage in combination-activity. But if combination is the representation of synthetic unity, then we cannot ground the representation of synthetic unity in combination (for that would beg the question). Instead, combination arises by “adding itself to the representation of the manifold”. Kant is not explicit about what this means, but there seems to be only one way, on his picture, that combination can “add itself” to the representation of manifold. Namely, that our representation of manifold of intuition combines sensations (for it is not clear what our representation of the manifold of intuition would be if we did not combine the various sensations into coherent representations), and the very fact that our representations are complex in this way constitutes combination’s “adding itself to the representation of the manifold”.

Analysis is the opposite of synthesis. The “dissolution of combination” is analysis. That is, we can only break a representation into its elemental components if that representation was complex, combining various properties to be teased apart. Because analysis breaks down complex representations into their components, analysis presupposes synthesis1 – for in order to have a complex representation, synthesis must be possible, “you cannot dissolve what has not been combined” (B130). A group of objects have analytic unity if, when broken down into their components, they all share some property P. For instance, trees, shrubs, ferns, and watermelon are analytically united under the concept/property “green”. They “belong together” in virtue of their greenness – we break each representation down and see that they share this common element.

We’ll now explain Kant’s argument for the unity of consciousness.

The most significant claim of the passage is that the analytic unity of apperception is presupposed by the synthetic unity of apperception (apperception is self-consciousness). We’ll later see how this allows Kant to establish his conclusion regarding the unity of apperception, but we must first explain how he justifies this claim and what it amounts to. Establishing this claim relies on a crucial premise: that it is possible to attach “I think” to any one of my representations.

If I am representing a keyboard on the desk, I can attach “I think” to it and produce the representation “I think that there is a keyboard on the desk”. “I think” is a special representation with three major components. (1) The “I” indicates that whatever representation “I think” is attached to I am conscious of as mine. (2) I am ascribing a certain representation to myself. (3) The representation (e.g. of the object, say, a pear), is somehow related to me. So we have a power to think of ourselves and ascribe things to ourselves, and this cries for explanation. We will explain this further after we explicate the justification of this initial claim.

Suppose I had a representation that I could not attach “I think” to. Then I am representing something which I can have no thought of representing, for I can never think to myself that I am representing it. If I can have no thought about this representation, then this representation is “nothing to [me]” (B132). That is, it is meaningless and has no content. But all my representations are contentful, so I must be able to attach “I think” to all my representations. This possibility of attachment is the condition under which any representation can be said to be mine (B133).2  If it were not, then there would be representations (of mine) that I could not attach “I think” to, that is, I have representations that I cannot be aware of representing or thinking that I represent them (B133). And it’s not clear how we are supposed to make sense of this – that is, your having representations that “do not belong to you”, that you cannot be aware of. Consequently, I must be able to attach “I think” to all my representations.

If I see, or have a representation of a pear, I can attach “I think” to the representation such that I represent, “I think that there is a pear”. If I represent a counterexample to the modal invariance lemma, I can also represent “I think that there is a counterexample to the modal invariance lemma”. (That is, we can attach “I think” to representations in the intuitions of both space and time.) All my representations bear a necessary relation to that special representation of mine (me being the relevant subject), the “I think” (insofar as I must be able to attach “I think” to them, regardless of whether or not I actually do [B132]). Because I can attach “I think” to all my representations, all my representations I can ascribe to myself, and so all my representations share the property of “being mine”. It is important to note, however, that the “I think” representation is a concept belonging to the understanding and not the sensibility (for you will never perceive your “I” or “think” concept from any appearance in sensibility); moreover it is an activity and not a passive occurence. Again, we’ll need some account of what kind of concept this is and whence it comes, since it cannot be gotten through experience (this suggests that it will be a priori, as we will later show).

Having established this crucial premise, that it is possible to attach “I think” to any one of my representations – that is, that all my representations necessarily conform to the condition that I can attach “I think” to them, the condition “under which alone they can stand together in one universal self-consciousness” lest we have representations which do not belong to us – Kant can now argue for the claim that the analytic unity of apperception is presupposed by the synthetic unity of apperception.

Recall our earlier characterization of analytic unity, where objects are united under some property they share. Recall, too, that all my representations are such that I can attach “I think” to them. Then all my representations have analytic unity. That is all my representations can be united under the “I think that such-and-such” concept. This is crucially different from our examples of trees and watermelons being analytically united under green, for greenness is a sensible property which is importantly different from the property of being mine. There is no sensation of “being mine” that I could point to which accompanies my representations. It’s not as though all my purported representations come with an identifying red tag that I use to discriminate between those representations that are not mine. “Being mine” is not a property of objects which is represented by some feature. But each representation of has the property of having “I think” or “is mine” attached to it – even though this is not sensible. But it is this property that all my representations share, and consequently it is this property which gives apperception its analytic unity – all my representations belong together in virtue of being mine. In this sense, they have analytic unity. This is to be regarded as the analytic unity of apperception. How is the analytic unity of apperception possible, and whence comes the “I think”? The subsequent portion of Kant’s argument offers some insight.

Apperception contains a synthesis of representations (B133): whenever “I think” is attached to my representation the result, “I think that R” is synthetic, bringing together “I think” and R (and R’s relation to me [in virtue of the “I” in “I think”]). For self-awareness or apperception requires not just that we think R, but that we be able to think that we think R, or else we would have no use for the “I” in “I think”. But to be able to think that we think that R, Kant argues, we must be conscious of our representations’ being synthesized. Why? Suppose I am not consciouus of my synthesizing of representations. My experience of empirical reality, varied as it is, will never present me with some relation to my identity as a subject. (For, as we showed earlier, there no “red tag” present in outer sense representing yourself as a subject of diverse representations.) But we do have a concept of our identity as a subject, and since we just saw this cannot be obtained on the supposition that we are not conscious of the process of synthesizing representations, it must have something to do with our being conscious of the process of synthesizing representation.

But how do we bring about this relation to our identity as a subject? It comes out of our conjoining or combining representations as we do and, moreover, by being (able to be) conscious of this process of combination.

This entails that I can only represent to myself the identity of my consciousness in these representations insofar as I am able to unite the manifold of representation under one consciousness. That is, the former – the analytic unity of apperception – is only possible in virtue of the latter – the synthetic unity of apperception, the ability to attach the “I think”.

Having established that the analytic unity of apperception is only possible by the synthetic unity of apperception, Kant claims that the synthetic unity of apperception (with regard to the manifold of intuition) is generated a priori and, consequently, serves as the ground of the identity of apperception – that is, the ground of the identity of a persisting self. Why is the synthetic unity of apperception qua the manifold of intuition a priori? (1) It must precede a priori all determinate thought, and (2) combination is not a thing which lies in objects themselves. In order to have a determinate thought, the thought that such-and-such is so, I must have a “such-and-such” and an “is so”. That is, I need a representation synthesizing an object and a property (or properties within some object) before I can have a thought which unites a property with an object. In this way, the synthetic unity of the manifold is a necessary condition on having any determinate thoughts. This suggests that combination is a necessary condition on thought. If combination is a necessary condition on thought, then it cannot be a feature of objects themselves and must be an activity of our minds. Thus, synthetic unity (of apperception) is a priori. And because the analytic unity of apperception is possible only because of the synthetic unity of apperception – that is, analytic unity of apperception is grounded in the a priori synthetic unity of apperception – the analytic unity of apperception is, too, a priori. So the unity (both synthetic and analytic) of apperception is a priori. And the unity of apperception is the identity of the enduring subject.

At this point, it will be useful to consider two alternative accounts of the self in order to bring out the salient features of Kant’s view of apperception as well as clearly show what Kant is not saying. First, we’ll characterize the Humean view and demonstrate Kant’s issues with that. Then we’ll characterize the Cartesian view, and explain how Kant would reply.

The Humean view is that one has awareness of self through a sensible intuition. The “self” one is aware of, however, is not a persisting self, but rather a mere collection of distinct representations. When you look internally, the only self that is present is whatever current state-of-affairs is being represented. A new representation (one that, say, occurs an instant later) is a new, distinct representation. Consequently it relates to a new, distinct subject. There is no persisting self; rather, there is a continuum of different selves relating to the continuum of representations experienced. Every thought of the form “I think that such-and-such is so-and-so” must have a different subject as the referent of “I”.

Kant rejects the Humean view because it does not account for unity of thought. All my representations I ascribe to a single thing, which can consider all of them (the representations), judge and think about them accordingly. This speaks to a certain “unity of thought” present in us. There is a stronger sense in which we must account for the unity of thought, however. The perception of an ice cube melting follows a necessary temporal sequences in which it gets smaller and forms a puddle, regardless of however else your mind may relate to it. Whereas the perception of various faces of a cube as you move around it follow no necessary temporal sequence. The former perception, insofar as it has a necessary sequence of perceptions, highlights the unity of consciousness. That is, these representations are necessarily united in consciousness in a certain way – and this is what cannot be accounted for on the Humean view. The Humean picture, wherein “I” always takes a new subject as its referent, cannot account for this unity of thought, because there is no unity of subject. Consequently there is no reason that perceptions should follow this kind of necessary temporal sequence. Kant, however, in arguing for the unity of apperception provides a successful account of the unity of thought for there is a persistent self who bears all the representations.

The Cartesian view maintains that one has awareness of a self through an intuition of a self as a persisting entity bearing representations. I have a nonsensory intuition of a single thing which bears the representations, and call this thing “self”.

Kant rejects the Cartesian account because it relies on a nonsensory intuition. On Kant’s picture, all intuitions are sensible. If there is an intuition of a single thing which bears all the representations, then there is some sensation corresponding to that single thing. But as we explained earlier, there is no sensation or “tag” in our experience which delineates my representations from those which are not mine. If there is some nonsensory thing which bears all the representations, then, it cannot be an intuition. This would suggest some sort of conceptual insight. But if this is so, then the concept must be a priori (for we saw how it could not be obtained through experience). Fortunately, Kant furnishes some argument for this, as we saw when explaining how the synthetic unity of apperception is a priori.

To recapitulate, Kant argues for the unity of apperception in the following way. We can attach “I think” to any representation. All my representations have analytic unity because they all belong to me. All my representations have synthetic unity because I can attach “I think” to any of them. The former is true in virtue of the latter. And the latter is grounded in something a priori. Because the unity of apperception, both analytic and synthetic, is a priori, we can know that we have a persistent self or identity.


  1. This foreshadows the rational behind Kant’s argument, shortly to be discussed. 
  2. This is to say that if a representation is mine, then it is necessary that I be able to attach “I think” to it. 

Kant and Things in Themselves

This post aims to explain Kant’s argument that things in themselves cannot be spatial in B66 (provided below, which we’ll call “P”). It will then evaluate the success of this argument against the neglected alternative view and, more specifically, the restriction view, which holds that all objects of outer sense must have the property of being spatial.

If there did not exist in you a power of a priori intuition; and if that subjective condition were not also at the same time, as regards its form, the universal a priori condition under which alone the object of this outer intuition is itself possible; if the object (the triangle) were something in itself, apart from any relation to you, the subject, how could you say that what necessarily exist in you as subjective conditions for the construction of a triangle, must of necessity belong to the triangle itself? You could not then add anything new (the figure) to your concepts (of three lines) as something which must necessarily be met with in the object, since this object is [on that view] given antecedently to your knowledge, and not by means of it. If, therefore, space (and the same is true of time) were not merely a form of your intuition, containing conditions a priori, under which alone things can be outer objects to you, and without which subjective conditions outer objects are in themselves nothing, you could not in regard to outer objects determine anything whatsoever in an a priori and synthetic manner.

P essentially boils down to a modus tollens argument. Kant establishes the conditional (C): if space were something more than “merely” a form of sensibility, then we could not have synthetic a priori knowledge (B66). He then relies on earlier arguments to make the claim that we do in fact have synthetic a priori knowledge. By modus tollens this entails that space cannot be more than a form of sensibility, and so it cannot be a feature of things in themselves.

Now we’ll break up the argument presented in P. Kant asks us to suppose two things. (A) That we do not have a “power” of a priori intuition, that is, suppose there is no a priori intuition we could use to produce universal and necessary facts (e.g. about geometry) before experience. And, (B) that space is “merely” a universal a priori condition under which alone the object of outer sense is itself possible (B66). With these two suppositions in mind, consider a triangle as a thing in itself – that is, as something apart from any relation it may bear to you (or any other subject). Kant asks, rhetorically, “how could you say that what necessarily exists in you as subjective conditions for the construction of a triangle, must of necessity belong to the triangle itself?” (B66). Because a priori intuition is the subjective condition for geometric construction, what we establish about triangles through a priori intuition are facts about triangles with respect to us (because a priori intuition is subjective). But to know a fact about an object in itself is to know something about that object independent of its relation to any subject (of experience). But it seems we can only know of objects insofar as they are related to us.

An elaboration. What can be established as synthetic a priori (e.g. about triangles) – necessary and universal propositions – only delimits the character of empirical reality. What is empirically real are appearances (of objects), not objects in themselves. In other words, our synthetic a priori knowledge of triangles is of how triangles must appear to us through our sense modalities. But if we consider a triangle apart from its relation to us, to sense, then we are considering the triangle over and above its “mere” appearance. Having necessary and universal knowledge of how triangles appear to you does not entail necessary universal knowledge about triangles in themselves. For the knowledge you can establish about triangles is only true insofar as the triangle is related to you. And what may be true of the appearance is not necessarily true of the object in itself. Consequently, in considering the triangle as a thing in itself, you cannot make necessary and universal claims about it, nothing about it can be established in a synthetic a priori way.

Kant elaborates somewhat. For you might think you can use your concept of three (non-parallel) lines to establish what “must necessarily be met with in the object” (B66), that is, considering a triangle in itself and your concept of three lines gives a necessary feature of other triangles (in themselves). But this is not so. For, (1) relations of concepts only yield analytic knowledge, so we must rely on an intuition. And, (2) if the triangle in itself is given to you (as an intuition) and you relate it to your concept of three-lines, then you establish that that triangle has three sides. But this does not establish any new knowledge because the three-lined-ness is already given to you along with the object. Your understanding has no work to do, for the concepts are already embodied in the “intuition” of the triangle in itself – there is no knowledge to “synthesize” in the relevant sense. So your knowledge of triangles-in-themselves cannot extend beyond your intuition of some triangle in itself. Even if you succeeded in discovering something “new”, this would only be a fact about the triangle you are considering, and not all triangles in themselves – that is, it would be an empirical rather than a priori fact. You cannot know that this object (e.g. this triangle) has that property (e.g. three-sided-ness) until you’ve encountered the object in experience. So if the object itself is given to you, rather than just the appearance, you cannot have synthetic a priori knowledge of that object (or its kind).

This partly addresses why we ostensibly can’t talk about things in themselves. When I have an intuition of (the appearance) of a triangle, I can say that that object, whatever else it may be, has the property such that it produces triangular representations in me. But can we say that the object in itself is triangular? No. Consider a world devoid of subjects to whom objects appear. If there are no particular appearances, then there are no particular properties you can apply to any object in itself. We cannot say that an object in itself has a particular property, because we don’t know what kinds of appearances it will produce. An object that I represent as a triangle is not triangular, rather it has the property of producing triangular representations in me – the latter does not entail the former. Without a subject to be affected, objects will not have properties, because the knowable properties of objects always trace back to their appearances in some mind.

So if we suppose (A) and (B), that is, that space is also a feature of things in themselves, then we cannot have synthetic a priori knowedge. This establishes (C). And because we know we have synthetic a priori knowledge (e.g. geometry), by modus tollens we must reject the antecedent of (C). Consequently, space can be nothing over and above one of our forms of sensibility.

For Kant’s argument in P to be effective, we need to have good reason to accept (C) and to accept that geometry is, in fact, synthetic a priori, provided that each step in P is valid. Do we?

You might think that we could still achieve synthetic a priori knowledge even if space was a feature of things in themselves. Suppose something like Newtonian space obtains of things in themselves, where space is an independently existing containter. You might think we could still obtain synthetic a priori knowledge. We could know that triangles have three sides by relating it to our concept of three lines (via some construction). Because all objects are in space, and my construction presumably occurs in space, what is true of my construction on that kind of thing will be true of others of that kind of thing insofar as they conform to certain spatial axioms. Because the Newtonian space is all-encompassing, whatever I construct in it should be equivalent to however I construct things in a priori intuition, because all possible objects of experience (that is, spatial objects), will be in this Newtonian space and determined by it – there are rules that objects universally and necessarily conform to. Because this process should be equivalent to construction in a priori intuition, the knowledge we obtain should be synthetic a priori in the same way. So, prima facie, it seems that considering space also as a feature of things in themselves does not threaten synthetic a priori knowledge. This would be reason to doubt (C).

On second glance, however, we see that any construction involving Newtonian space cannot be synthetic a priori. This is because any fact that I prove about how triangles are in Newtonian space is, in absence of a ceteris parabus clause, ineluctably a contingent fact. For if space is independent of my form of sensibility, then I cannot with “apodeictic certainty” know that space remains a certain way. For instance, I cannot know that space does not fluctuate between Euclidean and non-Euclidean manifestations. Nor can I know that it is Euclid’s axioms, in particular, that describe features of space, as opposed to some other set of similar but nonidentical axioms. So, I cannot know that some geometric fact I prove must be the case, for I cannot know that space remains constant; so whatever fact I prove may be subject to change – it is contingent on space’s being a certain way. So this knowledge is neither universal nor necessary and so cannot be a priori.

What would a ceteris parabus clause look like? It would be a stipulation that it is necessarily the case that space is a certain, constant way – Euclidean, say. If this is so, then we know that our constructions in Newtonian space are universal and necessary, and so a priori. Kant, however, will not allow this stipulation. We could not know that space, independently of us, is a certain way a priori. We have no grounds beyond experience for saying that space is necessarily this way rather than that, if we do not have a power of a priori cognition.

The important aspect of P is that a priori intuition (of space and time) constitutes necessary and invarient features of experience. If we are to have universal and necessary knowledge, it must trace back to a priori intuition, for there is no other universal and necessary feature of anything to which we could appeal in pursuit of synthetic a priori knowledge. This is why whatever can be known a priori cannot be a feature of a thing in itself, for if it were, then it would become empirical rather than a priori knowledge and lose its necessity. Suppose space were not a form of our sensibility. Then we would have no grounds whatsoever to assert that things in themselves are necessarily spatial or even just spatial. (It’s not even clear a subject could know what that would mean.)

P relies on accepting that geometry is synthetic a priori. But this, too, could be questioned. We saw that if space is also a feature of objects in themselves, that we do not have synthetic a priori knowledge. While Kant says that this shows space cannot be a feature of objects in themselves, someone else might think that instead we ought to reject geometry as being synthetic a priori. Maybe it is a contingent fact that space is such as it is, and that it has in fact remained constant. That would account for why geometric propositions seem universal and necessary, even if they are ultimately contingent and so not synthetic a priori. If this is so and Kant cannot establish the falsity of (C)’s consequent, then he has not successfully argued that space is nothing over and above the form of sensibility. To establish that geometry is synthetic a priori Kant needs to ground it in something constant, something universal and necessary. For Kant, this is the a priori intuition of space. But in P, Kant argues that because we have synthetic a priori knowledge, that space must be only a form of sensibility. We are grounding space as “merely” a form of sensibility in the fact that geometry is synthetic a priori. There is a sense in which each of these claims seems dependent on the other. If so, this could be problematic, but in the interests of space we’ll leave that to the commentators.

The restriction view is the thesis that for X to have the form of sensibility F, is just to say if X is to know an object through intuition, that object necessarily has the F property (e.g. spatiality). Kant’s argument in P shows that this is not so. Even if the object is known through intuition, so has the F property, we cannot know that the object is F as a matter of necessity, because this is empirical, and so contingent, knowledge. So P constitutes a successful reply to the restriction view.

It is less clear, however, whether the argument in P is a successful reply to the neglected alternative more generally. Namely the thesis that space, in addition to being a form of sensibility, is also a feature of things in themselves. Presumably, it is a contingent fact that humans have the form of sensibility that they do. And it is contingent that external space is the way that it is. But granting this, you might still think that there is a necessary connection between humans and the external space they are embedded in. We cannot say that objects are necessarily spatial, but rather that because they are contingently spatial, and we have space as a form of sensibility, there is a sort of necessary connection between humans and the world. Kant’s argument in P does not seem to rule out this possibility.

Part 2: Intuition, Space, and Singularity Argument

You can see a discussion of pure intuition, more generally, here.

Intuition is an immediate relation between a mode of knowledge and an object, to which all
thought is directed (A19). By ‘immediate’ we mean that intuitions do not relate to their
objects by means of some other thing (e.g. another representation, conceptual or otherwise). Rather, if I am intuiting some object K, my mind is directly, immediately aware of K. We intuit an object only insofar as the object is ‘given to us’; an object cannot be given to us unless our mind is affected in the right way (A19). We are given objects via sensibility (B34). This means only sensibility can give rise to intuitions, for an intuition is a direct relation to an object and objects are only given through sensibility. You stand in an immediate awareness relation to the post before you: you are intuiting an object, namely my Kant post.
Intuition is to be distinguished from concept. Concepts refer to objects indirectly – that
is, ‘mediately by means of a feature which several things may have in common’ (B377).
Call it the generality criterion. My concept of an elf refers to Galadriel (and Legolas and
Haldir) by means of feature(s) they share, e.g. pointy ears or forest-frolicking, (and not by
my representation of the totality of elves). So I can indirectly refer to Galadriel and Haldir
by considering and representing the concept of pointy eared forest-frolickers.

This means that intuitions must be singular representations, in the sense that they always
present a particular, single object, for in intuition the relation between knowledge and object is unmediated. If your relation were indirect, then you would be representing features that a set of objects share, not that particular object as it appears to your sense organs (and so this could not be called a singular representation). Your intuition of an object is brought about from a particular object affecting your sense organs, consequently it must be a representation of that object producing those sensations – that is to say, it must be a singular representation. Call this criterion for intuition ‘the singularity criterion’.

An object’s affecting our faculty of representation is a sensation (B34). An intuition is
empirical iff relates to an object of sensation. The (undetermined) object of an empirical
intuition is an appearance (B34). So in experience there is an appearance which affects my
sense faculties, producing sensations of, e.g. browness, bitterness, warmth. (A cup of coffee? It depends on how the sensations are arranged.) The ordering/organization/arrangement of the sensations of the appearance is the form of appearance (B34). Sensation is not the form/arrangement/ordering of sensation – to say that sensations are ordered is not to say that sensations are an ordering or arrangement. Because the form of appearance is divorced from the sensation of the appearance, the form of appearances must given to us a priori. For objects affect our sense-faculties and are given through sensibility, giving rise to sensation, but sensations are not orderings – only effects of objects on our mind. So the ordering cannot come from experience of objects – it cannot be a posteriori – and so it must be a priori, in the mind (B34).

A pure or a priori intuition is an intuition-sans-sensation. Consequently, pure intuitions
are present even in the absence of all appearances. That is, a pure intuition contains nothing but the form of sensibility. The form of sensibility is a feature of our minds which determines the manner in which we necessarily must represent things. It gives rise to two pure intuitions, (1) the representation of space and (2) the representation of time. We say representation of space/time because pure intuitions, as containing nothing but the form of sensibility, are mind-dependent – not mind-independent features of the world.

We’re now in a position to explain Kant’s singularity argument for space’s being a pure
intuition, as opposed to a general concept (e.g. a general concept of the particular spatial
relations of things). Recall that intuitions are singular representations: they are not representations of features which a set of objects might share; they are always representations of singular/particular objects. Kant’s aim is to show that space is a particular representation which contains nothing but the form of sensibility.

Kant’s first premise is that ‘we can represent to ourselves only one space’. By ‘space’
here, Kant has in mind the representation of the single all-embracing space. That is, the
space in which all our intuitions of outer sense take place or are seemingly represented. (If
Kant did not mean the ‘all-embracing space’ then this first premise would not make sense
because we represent particular objects in particular spatial locations and arrangements, and so there would in fact be multiple spaces we represent, contrary to his opening premise.)

Because we can represent to ourselves only one space, the representation of space must
be an intuition. For it is a representation of a particular thing. Representations of particular
things are always intuitions, by the singularity criterion. Our representation of space is not a conceptual representation of general features of space that all spaces or spatial things share, rather it is the particular manifold upon which my sensations of particular objects take place (B34).

Prima facie, this looks like a misapplication of the singularity criterion. Consider our
representation of God (a maximally perfect being). God is certainly not an intuition. Rather,
our representation of God is formed from conceptual representations of finitely and relatively perfect beings (presumably we relate these conceptual representations in such a way as to form a concept bearing maximal perfection as a feature. In a similar way, you might think that our representation of all-embracing space is formed from the conceptual representation of a finite space (or spaces). That is, the concept of our all-embracing space is formed from considering and representing the aggregate of all objects falling under the general concept of space, in order create a sort of infinite ‘all-embracing’ space (B40).

But the subsequent portion of the singularity argument aims to overcome this objection.
A part of space cannot be prior to the singular, all-embracing space. Therefore, parts of
space are not constituents composing the all-embracing space, but rather we can only think of parts of space as being in the all-embracing space (A25). Consequently, we cannot build a general concept of space out of the concept of a space. Why is the all-embracing space prior to a part of space? For Kant, space is ‘essentially one’ (A25). All things in space
(parts of space, empirical intuitions, etc…) depend on placing ‘limitations’ on space. To
bring this out, consider your representation of a particular region of space. In representing
this, you must also represent it as having bounds. In representing it as having bounds,
you represent it as being surrounded by something. The only plausible candidate for this
something is the all-embracing space. Therefore, the representation of all-embracing space is necessary for any particular representations within its manifold. This entails that the intuition of all-embracing space is a condition on our representing particular spaces (and things in them).

So space must be an a priori intuition, for two reasons. (1) Our representation of all-
embracing space is singular, so it must be an intuition. (2) Our representation of space is
the condition on our having empirical intuitions, but the representation of space itself does
not depend on any particular mind-independent objects and as such cannot be empirical.
Therefore, it is a priori.

Mereological Universalism

This post will explain Van Cleve’s argument against the “commonsense” restricted composition view regarding the conditions under which a set of objects compose a whole. We will then evaluate Van Cleve’s argument, concluding that we have good reason to revise commonsense.

The commonsense, or restriction composition, view takes a middle road between asserting that “no objects ever form wholes” and asserting that “all objects always form wholes”. That is, objects sometimes compose objects, but not always. So there must be some rule or restriction which determines when objects compose wholes. To say that there is some rule of restriction is to say that a set of objects compose a whole iff those objects all stand in the right kind of relation (R) to each other. Van Cleve considers two candidates for this rule, R. (a) A set of objects compose a whole if they occupy a continuous region of space (i.e. are in contact or connected by a series of contact relations). For example, the pieces of wood compose a chair (a whole) if the pieces are connected to each other in the right way and not broken apart. (b) A set of objects compose a whole if they are “dynamically interconnected”. For example, the front end of my car is dynamically interconnected with the back bumper, insofar as wherever the front end of my car goes, the back bumper follows.

Van Cleve argues that any account which tries to create a rule of restriction to delineate parts and wholes (the “commonsense” view) ineluctably fails. Now we’ll explain Van Cleve’s general argument against restricted composition views. His conclusion is that if we must use some rule of restriction to ascertain R, then that rule must give rise to objectionable arbitrariness or objectionable vagueness.

Suppose that there are some collections of objects which compose wholes (like the collection of particles that compose the Sun) and that there are some collections of objects which do not (e.g. my left shoelace and a bust of Alexander the Great do not form a whole). If so, then there are cases where composition occurs via forming a continuous region of space (again, like the particles which compose the Sun). But consider these regions: they’ll all be adjacent to or connected with objects that purportedly do not constitute wholes. For, something is either a whole or is not – the only objects that the set of all continuous wholes could come into contact with [besides each other] are those objects which do not compose wholes.

But there doesn’t seem to be a distinct “cut-off point” that delineates the continuous compositional objects from those objects that are not wholes. There is no boundary that we can point to and say that the objects to left make a whole, but the objects to the right do not. Consider the black-white spectrum. Black transitions to grey, grey transitions to white, but there is no unique point where you can say, “here, this is the point where it is no longer black but grey”. While, you can tell which end is the black end and which the white, you couldn’t define the point at which black becomes grey.

It is always determinate whether a collection of objects forms a whole. That is, statements of the form “these objects make that whole object” are always strictly true or false. If this were not so, then mereological assertions would be objectionally vague. For what could it mean to say “these objects kinda sorta, or perhaps maybe, constitute that thing”? They either sum up to that thing or do not.

If there is always a fact of the matter as to whether some objects compose a whole, but there does not exist a definite cut-off point between those which compose wholes and those which don’t, then either any collection of objects compose some whole, or no collection of objects composes some whole. That is, there is no “middle road”. How does this follow? If there exists no definite cut-off point between all the many and various objects, then R holds between all those objects or R holds between none of them. If the former, then any collection of those objects are related by R and form a whole. If the latter, then any collection of those objects are not related by R and do not form a whole. If R held between some of the objects, but not all, then there must be a definite cut-off point, but we showed that there is not.

Why does this constitute a revision of commonsense? Because in addition to the atoms, cells, and neurons that compose you as a whole object, there are also whole objects that are composed of the collection of pennies on my desk and the moon. For as we showed, any collection of objects must form some whole. While it may sound counterintuitive to admit an object composed the pennies on my desk and moon, it is not actually so. We are not saying that there exists a material object that, for example, we could hold which is composed of the pennies and the moon. Rather, both the pennies and the moon exist, and taking them together as a system or whole of some kind can be done just as legitimately as taking the cells and neurons together and considering that system or whole they compose (namely, you).

We might wonder whether Van Cleve’s mereological universalism commits us to an explosion of reality, that is, an unnecessary proliferation of the real existences like in Aristotelian mereology. In Aristotelian mereology, Fred the spherical snowball is one object, but when Fred is flattened, he becomes a new object, because the form of his composition has changed – this view adds an indefinite number of entities to the world, without good reason. What, on Van Cleve’s picture, limits the number of entities in the world? Van Cleve subscribes to two “plausible” philosophical principles, (1) two or more things cannot be in the same place at the same time and (2) there cannot be a difference of entities without a difference in content. For Van Cleve, the content of Fred (the matter composing him), and the content of Fred after he’s flattened, are the same, for the material constituents being considered as a whole are all the same – in this way, there is only one Fred, not an indefinite number of Fred’s depending on form. We consider the matter composing the whole without considering the form or the arrangement of the matter – for there is an indefinite number of arbitrary arrangments we could ascribe to any material collection, so consequently if form were taken into consideration we would end up with an explosion of reality.

Van Cleve’s argument concludes that any collection of objects forms a whole or no collections of objects form a whole. If you hold the latter view, then you’ll think that there are fundamental entities whose existence is real, and then ordinary entities like tables whose existence is nominal – that is, when I say “a table exists” I am really saying that “these particles are arranged in a table-like fashion”. But this is not the revision of commonsense that Van Cleve is proposing. For suppose there are no simple entities, we can indefinitely break particles into smaller and smaller pieces. Then tables, and everything else, are in fact nominal entities, for they are always composed of something more fundamental which we just use linguistic shorthand for. For all entities to be nominal is absurd, because then all entities are fictionalized.

Van Cleve relies on the premise that it is always determinate whether a collection of objects forms a whole. You might try to reject this along the following lines. If I have a pile of 500 grains of sand, and continue to add one grain at a time, at what point does the pile become a heap? It is not clear whether this collection of objects forms that heap of sand. Or consider the black-white spectrum: it is not clear where black becomes grey. Doesn’t this mean that it is not determinate whether a collection of objects forms a whole? And, if so, then there doesn’t need to be a distinct cut-off point delineanating wholes and Van Cleve is not entitled to his conclusion.

This reply confuses semantic vagueness with metaphysical vagueness. Whether the grains of sand are a heap or pile is semantic vagueness – there is nothing vague about the physical grains or their collection. All those grains of sand form the total of those grains of sand – whether we choose to call it a pile or a heap has no effect on any of the actual properties of the collection of sand. Disagreement in whether it is a pile or heap is disagreement in language, in what we choose to call a heap – but everyone sees the same collection of sand, the same whole. The same applies to the black-white spectrum. When black becomes grey is going to be a semantic judgment made by a variety of people. But the shade is still whatever shade that it is, and together they still form the spectrum that they do. Nothing about the spectrum itself is indeterminate or vague – only our judgments thereof.

The Identity of Indiscernibles

This post distinguishes between substantivalism and relationalism, and how the principle of the identity of indiscernibles threatens substantivalism. Then we’ll evaluate the principle, showing under what conditions it is plausible.

We will assume Leibniz’s view of relationalism. Broadly, this is the view that there are no substances such as space and time. Rather space and time are real only insofar as they are basic relations and properties between material objects – they do not exist independently of material objects. Facts about space and time are derived from material bodies, and without material bodies or events, there simply are no facts about space, time, or their relations. So, what makes it the case that the basketball is five feet away from the hoop is nothing over and the fact that there is a basketball and a hoop that are such-and-such apart.

Substantivalism is the denial of relationalism: space and time are substances which exist independently of any material objects. Consequently the substantivalist can imagine an empty universe, or an empty space/time container, where only facts about space and time obtain. So, what makes it the case that the basketball is five feet from the hoop is that the basketball occupies one region of space and the hoop occupies another, and those two regions are some equivalent of five feet apart. This way we can explain spatial relations without taking them as basic in the sense that relationalism does.

To explain the problem of a Leibniz shifted world, we need to explain the principle of the identity of indiscernibles. This principle states that if any two objects are indiscernible, then those two objects are identical. Two objects are indiscernible if they share all their properties and there does not exist a property belonging to one which does not belong to other (or vice versa) by which you could tell them apart. Jackson and Geoffrey are discernible in that one wears glasses and the other doesn’t. So Jackson and Geoffrey are not identical. Mark Twain and Samuel Clemens, however, are indiscernible. You’ll find they have an identical genetic structure, both occupy the actual world, and both are named both “Mark Twain” and “Samuel Clemens”.

Substantivalism holds absolute time as an ordered set of instants, and the universe must have come into existence in (an arbitrary) one of these instants. These two facts entail that there could be a possible world which would have come into existence at different instant, but otherwise contains all and exactly the same events as our actual world with all the spatial and temporal relations between material bodies being the same. This is one example of a Leibniz shifted world, a world which is identical to ours, except differing in some “absolute” property (e.g. time of instantiation, where that entire world is drifting to the “left” at 5m/s).

Because their relative spatial and temporal relations are identical, the only way they could possibly differ is in an absolute spatial or absolute temporal property. But their arbitrary absolute differences are weak grounds for discernibility. Why should “God” choose to instantiate one world at one time and another identical world at another? Intuitively, there is no reason that God should choose to instantiate two identical worlds at two arbitrary points in time, with some particular duration of absolute time between them. In the spirit of parsimony, the worlds are indiscernible, and so, by the principle of the identity of indiscernibles, they must be identical. But their identity contradicts the claim that there could be a relatively identical world to ours that comes into existence at some other instant of absolute time. If you subscribe to absolute space or time, then your only option is to abandon the principle of identity of indiscernibles.

But is problematic, for this entails the possibility of Leibniz shifted worlds, and this entails an unnacceptable proliferation of relatively identical possible worlds – indeed, we could have an infinite set of these, each differing only in, say, absolute time instantiation. Prima facie, we have better reason to maintain the principle of identity of indiscernibles than to admit the possibility of this proliferation.

The substantivalist might reply by rejecting the principle of indiscernibles. It is logically possible that the universe should have contained nothing but two exactly similar spheres. Every quality and relational characteristic of one holds also of the other, in virtue of the symmetric relations between the two spheres. You might think that the one sphere has the property of being not the other sphere. But this property is also true of the other sphere.

If we introduced an observer, he might name one sphere “A”, and the other sphere “B”. Then A has the property of being -B, a property which B cannot have, so they are discernible and not identical. But there are two considerations here. The first is that by naming them different things, an observer is merely stipulating that they have the property of being different, which is uninformative. The second is that this difference in property is dependent on there being a “namer” in the universe, so this purported difference in property is really more a feature of how observers apply names than a feature of genuine property difference between the two spheres.

It is tempting to think that the spheres differ in virtue of the fact that one is located in a place that the other is not. But their spatial relations are identical, so the only way we could point to this difference in property is if we say that A occupies location R and B occupies location S. But this move can only be made if we admit that regions of space are independently existing things, not merely a consequence of brute spatial relations between objects. So the relationalist would have to concede absolute space to the substantivalist.

If we introduce an asymmetric observer, however, one sphere will be on the “right” and the other on the “left”. Then the spheres would have different properties. So it is logically possible that the spheres have different properties. The substantivalist admits this, but holds it is in virtue of newly acquired relational characteristics. But the relationalist might argue modal properties are real properties.

Here’s how that argument might run. The substantivalist holds that A and B have the same properties. The spheres are equivalent in that they both satisfy all the same propositions. Each sphere must bear a reflexive relation to itself and a symmetric relation to the other. But the substantivalist admits that if there were an asymmetric observer, then the two spheres might have different properties. But we can say something stronger. For an asymmetric observer must be an observer which is closer to the center of one sphere than the center of another, and so it is necessary that the spheres would have different properties (qua to the observer).

So the substantivalist has admitted that it is possible that it is necessary that A and B are not equivalent. This, together with A and B being symmetric, entail that it is not the case that A and B are equivalent, by the axiom of symmetry.1 But if A and B are not equivalent, then they cannot be identical, contrary to the substantivalist’s supposition.

But the substantivalist might reply as follows. In instantiating the asymmetric observer, the spheres are no longer symmetrical in all their spatial properties. Using the axiom of symmetry, then, is not valid.

At this point, it’s hard to see who is right. Because the relationalist might think that it is possible that there is an asymmetric observer before we move to instantiate one. And from that observer’s perspective, it would be necessary that the two spheres are distinguishable in virtue of a spatial-relational property. So before we have disrupted the purported symmetry, there is already a difference in (modal) properties between the two spheres.

The tension here is that discernibility seems to essentially involve the idea of some observer doing the discerning, whereas identity is an objectively necessary condition for this being this, regardless of observation. Two things are indiscernible iff it is logically impossible for an observer to tell them apart. The asymmetrical observer can discern between the spheres (so it is logically possible). But when left out, it is logically impossible to discern between them, so the relationalist cannot explain why they are not identical. (There’s a certain antimony here.)

The notion of a point of view is required for discernibility to be logically possible, if the two spheres are not in fact one and the same. I am not sure what resources the relationalist has to be able to make sense of “point-of-viewness” – without positing an observer – in this situation. But if he can make sense of this, then he will have a means of discerning between the two spheres and so can explain why they are not identical. But if he cannot, then we really can conceive of two spheres which are indistinguishable but not identical. That would falsify the principle of the identity of indiscernibles, and so defang Leibniz shifted worlds.

1 Axiom of symmetry: <>[]p → p