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. 
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Intuition, Space, and The Singularity Argument

This post will interpret what Kant means by ‘intuition’ and then explain his singularity argument for space’s being a pure intuition.

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 by means of some other thing (e.g. another representation, conceptual or otherwise).  Rather, if I am intuiting some object K, my thought is immediately directed to the K-ness of K; my mind is directly 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 affect 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.  There is a post before you: you stand in an immediate awareness relation to it: you are intuiting an object, namely my Kant post.

Intuition is to be distinguished from concept.  My concept of K refers to k(s) 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.  Why?  Because in intuition the relation between knowledge and object is direct 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’.

There is always an object of thought — something to which the thought is directed (A19?).  This means that all thought must, directly or indirectly, relate to intuitions (B34).  For objects are given to us only through sensibility, and sensibility alone produces intuitions.  So if a thought could not relate, in some way, to an intuition, then there could be no object of the thought — and a contentless thought is no more a thought than a blank square of glossy paper is a photograph.

An object 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?)

That quality of an appearance which allows its (that is, the appearance or sensations) being ordered in a certain way 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 (or rather, is of 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 and 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.  Why?  If we can only represent one all-embracing space, then our representation of space can only be of one, single thing.  This means that 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 empirical intuition (nor is She an a priori intuition).  Rather, our representation of God is formed from conceptual representations 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 \psi.  The only plausible candidate for \psi 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.

Synthetic A Priori Knowledge

This post discusses what Kant means by ‘synthetic a priori knowledge.’ We will first discuss knowledge, then the a priori, and finally the synthetic.

For Kant, there are two stems of knowledge, viz. sensibility and understanding (B29). Through sensibility, we are presented with ‘objects’ — this can be thought of as perceptual experience. Through understanding, we think, compare, and combine our representations of these objects, and ultimately gain ‘knowledge of objects’ (B1). Understanding, or reason, supplies the rules of thought (B25), and determines how we can relate the items we are presented with in sensibility. Kant, however, acknowledges that all knowledge begins with experience in the sense that our acquaintance with objects gets our cognitive machinery started by affecting our understanding so that we might think or know what we get through sensibility (B1). Sensibility provides you with the ‘raw material’ for knowledge; understanding provides you with the ability to manipulate the raw material. If there is a brown table before me, sensibility provides me with the brownish and tablish features in experience, but understanding allows me to think that ‘there is a brown table before me’ or imagine the brown table being red. So it looks like knowledge is a special kind of relation between one’s representations acquired through sensibility and one’s pure understanding. Understanding endorses some representation(s) as true. Not all our mental representations will be true. But we do know some of them to be true, and the fact we know means we must be able to point to some kind of justification.

There are two ways that knowledge can be justified, viz. a priori or a posteriori. A priori knowledge is ‘any knowledge that is…independent of experience’ (B2). Kant distinguishes this from empirical or a posteriori knowledge, which is dependent on experience (like knowing that most swans are white). By ‘independent of experience,’ Kant means epistemic independence. It is knowledge that never receives its justification from a particular empirical experience, or even from a generalization of particular empirical experiences. An example may help (B2). You see a person digging a big hole beneath their house. A big enough hole will collapse the house. You know before the particular experience of the house collapsing that this person will collapse their house. Your knowledge, nevertheless, is not a priori because knowing that a big hole beneath a house collapses it is knowledge that could only ever be gained through experience. You must have investigated the world before you gained the knowledge that the house would fall. Moreover, Kant must mean epistemic dependence because he recognizes that all knowledge begins with experience (B1) — so the a priori must be independent of experience in some other modality, namely epistemically, not psychologically.

Two criteria for identifying a priori knowledge are (1) that the judgment is necessary and (2) that the judgment carries strict universality (B4). This is tantamount to saying that a priori knowledge brooks no counterexample. It is not possible for a priori knowledge to have been false. Because the a priori is not empirical, a priori judgments/knowledge is generated from the pure understanding or our faculty of knowledge (B5). The knowledge that ‘all bachelors are unmarried men’ is a priori because its justification is absolutely independent of experience. You know the proposition is true in virtue of knowing the meaning of the word ‘bachelor,’ you do not need to empirically investigate the world, checking each bachelor to make sure that he is unmarried. So a priori knowledge is the endorsement of a judgement whose justification does not depend on any empirical investigation.

The analytic/synthetic distinction applies only to judgments or knowledge that admits of a subject/predicate structure, for instance ‘All A’s are B’s’ (B11). In ‘all bachelors are unmarried men,’ the predicate ‘unmarried men’ is (covertly) contained in the concept ‘bachelor,’ making this an analytic judgment. In ‘all bodies have weight,’ the predicate ‘has weight’ is not contained in the concept of ‘body,’ making this a synthetic judgment. So a judgment is analytic if the concept of the predicate is contained within the concept of the subject; if not, then the judgment is synthetic. It is not clear, however, what Kant means by ‘containment.’ He provides some clues, namely that analytic judgments are those which connect subject and predicate through the law of identity, that the rest entirely on the principle of contradiction (Pro. 17) regardless of whether their concepts are empirical, but what is the law or principle operating on?

It cannot be identity of extension. Consider two sets: (1) the set of all creatures with hearts and (2) the set of creatures with livers. These two sets are coextensive. If extensional identity was all Kant had in mind, then the judgment ‘all creatures with hearts have livers’ would be analytic. But recall that all analytic judgments are a priori. We could imagine a counterexample, namely a creature that has a heart and no liver, but then this would contradict the definition of a priori. But Kant does not admit analytic a posteriori judgments, so analytic judgments based on the law of identity are not based on identity of the extensions of the predicate and the concept.

If B is not contained in A in virtue of their extensions, then perhaps B is contained in A in virtue of their intensions. Recall that knowledge is going to consist in some relation between our representations and our understanding. We might think of the intension of ‘creature with a heart’ as something like our completed mental representation of hearted-creatures. The essential features will be the concept of ‘heart’ and concept of ‘creature’ somehow united in our understanding. So the intension of ‘creature with a liver’ will be something else. We’ll have a mental representation that unites the concepts of ‘liver’ and ‘creature’ in understanding. So a proposition like ‘all bachelors are unmarried men’ is analytic (and a priori) in the sense the mental representations of ‘bachelors’ and of ‘unmarried men’ are identical — that is to say the judgment is explicative, the predicate adds no content the cognition of the concept; they are one and the same.

Synthetic propositions are not analytic or explicative. They are ampliative in that the predicate adds content to the cognition of the concept; the predicate extends our knowledge of the concept beyond what is merely ‘thought in’ or ‘contained in’ the concept. Indeed Kant puts it, ‘we are required to add in thought a particular predicate to a given concept’ (Pro. 19). That creatures with hearts have livers extends our knowledge of creatures with hearts.

So synthetic a priori knowledge will amount to the following. It is the endorsement of the truth of a mental representation (like a judgment), where the justification of the endorsement is epistemically independent of experience, and the predicate of the judgment is not intensionally contained within the concept.

Information, Mind, and Dretske

This post aims to present the pith of the first three chapters of Fred Dretske’s Naturalizing the Mind, namely the Representational Thesis (RT) and how it accounts for the qualitative, subjective, first-person aspect of mental life; raise some interpretive questions, and some possible responses.

1

The Representational Thesis has two central claims, (1) all mental facts are representational facts and (2) all representational facts are facts about information functions.  The mind being the ‘representational face of the brain.’  So now we ought to get a grip on the meaning of ‘representational fact’ and the meaning of ‘information function.’

Dretske characterizes representation in the following way, a system S: represents a property F, iff S has the function of indicating (providing information about) the F of a certain domain of objects.  S performs its (representational) function by occupying some different states s_1,...s_n corresponding to the determinate value(s) of f_1,...f_n of F.

An initial question: what makes a particular function an information function?

Dretske uses a speedometer as an initial example of representation.  A speedometer S, represents speed F, of a car.  S’s function is to indicate the F of the car.  The representational fact is that S has a speed indicating function, e.g. pointing at ’37’ is supposed to carry the information that the car is going 37mph.  The nonrepresentational fact is that S is connected to the axle by a cable.  The mere (nonrepresentational) fact about the cable connection does not imply that this physical arrangement has a function.  The representational fact is true in virtue of the fact that S is designed to carry that information.

So we may have a partial answer to our initial question.  The representational fact is true in virtue of the fact S is designed.  So design (or perhaps, intentionality?) is characteristic of representation functions.  The mere fact of the physical connection does not imply that S has a function, however, even if it does not have a function, S would still carry the information that the car is moving at (some speed equivalent to) 37mph.  This suggests (a) that the flow of information does not constitute a function, and (b) information and some function (which must in some sense be designed) are both necessary for representation.  What remains unanswered (at this point) is: what separates an information function from a representation function?  Moreover, it is prima facie the case that information is an output of some kind.  You don’t have one bit of information until you flip the coin and it lands ‘heads’ or ‘tails’.  At this point, I see no reason to discriminate between information functions and representation functions — if not addressed, this may become problematic.

2

Dretske emphasizes three ‘pivotal’ distinctions. (1) Natural vs. conventional representations, (2) representational states vs. representational systems, and (3) represented properties vs. represented objects. Conscious experience is a case of natural representation.

So, for instance, I am a representational system in virtue of the fact that I occupy representational states, like seeing the color blue or hearing the crescendo of an opera. There are two categories of representational system, viz. conventional and natural representational systems. Conventional representations are things like language or measured marks on a beaker (amounting to Gricean nonnatural meaning [meaning_{nn}]). Natural representations, however, come in one of two varieties, viz. sensory systems and conceptual systems. Sensory systems are things like experiences, sensations, or feelings. Conceptual systems are things like thoughts, beliefs, or judgments. Dretske implicates that sensory systems are natural to the system or simply part of the system, whereas conceptual systems are acquired by the system. This makes some sense, infants are born with their sense organs functioning (to some degree) while it takes years for them to learn to think, believe, and judge. In a certain sense, these natural representations seem to be varieties/instances of Gricean natural meaning (meaning_n). Dretske holds that the difference between naturally acquired and conventionally assigned functions entails the difference between natural and conventional representation.

Dretske explains the distinction between conventional and natural representations in the following way. Consider the fact that the size of an object is correlated with the temperature of that object. With the right background knowledge, one could look at a paperclip or a flagpole and (maybe with some calculation), calculate the temperature. A thermometer works similarly, the volume of the mercury expands or contracts in accordance to the temperature. Paperclips and flagpoles, however, do not represent temperature; thermometers do represent temperature (in the conventional sense). Paperclips and flagpoles do not represent anything. This is because we have not assigned paperclips or flagpoles the function of indicating the temperature. When an object’s informational or representational function is derived from the intentions of its designers, the resulting representations are conventional. From this we can infer that natural representations, and representational functions, are not derived from something with an intentional character. It’s worth noting that conceptual awareness, like thoughts and beliefs, will be classified as experiences and natural representations on this picture.

This raises the question, however, of how intention and design are related to each other. Dretske wants to maintain that something can be designed to have a certain function, without there being intention anywhere in the picture. After all, kidneys have a function (for we have no problem discerning whether or not they are functioning properly), but we do not think that some entity with intentions (which, I think, are a quality of mental life) designed our kidneys, or humans at all — natural evolutionary processes seem to account for that. It would be nice if Dretske provided a more robust explanation of how there can be any genuine design without an intention behind it. After all, the notion of design seems to imply some kind of vision (which is hoped to come to fruition), some end goal, or else some construction that is, in some sense, deliberate. More explanation here would importantly clarify and elucidate Dretske’s distinction between natural and conventional representation.

After laying out the aforementioned distinctions, Dretske states his working assumption: There naturally acquired functions and, consequently, naturally acquired representations.

This assumption merits some discussion. The idea is that if a function can be naturally acquired, then a representation can be naturally acquired, and, moreover, functions can be naturally acquired. Recall my earlier question about the distinction between information functions and representation functions, for now it seems especially pertinent. Suppose that information functions are equivalent to representation functions. Then there are functions that are naturally acquired which are not information functions. That is, there are functions that amount to brute physical processes, devoid of any semantic/informational/representational component. But it is unclear how this is supposed to entail that there are natural representations or representation functions. Contained in the assumption without any defense, on this interpretation, is the idea that isolated physical processing can give rise to representational functions or representations — these notions are semantic, and there seems no reason to suppose that some collection of purely natural (which is, presumably, physical) processing can catalyze the emergence of something a fundamentally distinct, uniquely semantic character. If someone like me is to be convinced by Dretske’s Representational Thesis, then there must be some defense of this assumption’s implication.

But suppose, instead, that information functions and representation functions are not equivalent. Then we can ask ‘are the (antecedent) natural functions informational, or no?’ If they are not, then I figure a more accurate working assumption would be: there are naturally acquired functions, and so there are naturally acquired information functions, and so there are naturally acquired representation functions. If, however, this is so, then the same question as in the preceding paragraph is raised. Namely, how do we get from the pure physical stuff to the stuff with semantic character? But suppose there can be just informational functions, and it is these which give rise to the representational functions. This interpretation of his working assumption seems more tenable; that there are naturally acquired information functions which give rise to naturally acquired representation functions is a straightforward inference, for they both are essentially semantic in character.

There is a lingering question, however, concerning the status of information functions and how the idea of information should fit into the ontological picture. If this does not resolve itself, then we will have more to discuss. (Especially if it turns out that information is not an output of a function [or input, or relation between input and output], as Dretske implies, for then it is not clear where the information comes from.)

3

So certain things have representational functions and, unsurprisingly, their functions are to produce such-and-such representations.  A representation is a particular (token) state or event.  A token state, i.e. a representation, is representative — that is, has an indicator function — in virtue of two sources.  (1) The token state’s representational status is derived from the system of which it is a state with an indicator function (=function_s).  And (2) The token state’s representational status is derived from the type of state of which it is a token (=function_a).  The former is the systemic function and the latter is an acquired function.  Not all systemic functions are acquired functions.  Experiences — having your senses impinged upon — are identified with functions_s.  Concepts, however, are functions_a.  This is because, for example, when we are born our senses are operational and yet we have no concepts whatsoever.

At the risk of adumbration, I’ll respond with the following question.  Why should a physical system need a representational function at all, regardless of whether it is function_s or function_a?  And further, at the risk of appearing flippant, what is the ontological status or constitution of a representational system and how, if at all, does it differ from other systems?

Dretske further elaborates on representation and also enumerates the two ways that a representation, e.g. experience, can misrepresent.  That S represents k implies the representational fact that for some F, S represents the F of k.  That Phil represents the blue mug implies the representational fact that for some property, e.g. blueness, Phil represents that blueness of the blue mug.  This is a fact purely about Phil’s representation/representing.  That S represents k, however, also implies a hybrid (a fact part about the representation and part not), namely that k stands in a certain kind of relation, relation C, to S.  This is a hybrid fact because it involves a fact about the object of representation, not merely about the representation, namely that it relates to the representational system in the relevant way.  This brings us to the two ways that an experience, i.e. a representation, can misrepresent.  (1) There can be a genuine object connected to the representational system in the right way, but the system misrepresents the relevant property of the object.  For instance, I am looking at an object, a blue mug, but I see a yellow mug instead.  (2) There can be no object of representation (for instance, a hallucination).  I look at the table and see a blue mug, when there is in fact no mug (nor object with pseudo-blue-mug-like properties).

So what exactly is C?  C is the contextual relation which determines the object of representation for the system, which is to say that C is the relevant external causal or contextual relation which makes the representation of the object veridical (that is, not a misrepresentation).  For instance, the speedometer, whose function is to represent the speed of my car, is hooked up properly to the axle of my car.  That it is hooked up properly is essential to the speedometer’s representation, like the needle pointing to ’37’, being veridical.  To see this, suppose someone severed the cord connecting the speedometer to the axle.  If I had absolute faith in my speedometer, I could be blazing across the countryside at 80mph totally unwittingly, while I’m focused on the speedometer reading ‘0’.  This speedometer is not truthfully representing the speed of my car, and so constitutes a misrepresentation.

It should be noted that things with indicator functions have the function of conveying information about a specific property, not information about the vast array of properties which may be present.  Drestke notes that an instrument can have a pressure indicating function without having a temperature indicating function even when it cannot deliver information about pressure without delivering information about pressure.  The thermometers function is to detect temperature, not pressure.  We can imagine artificially holding pressure constant while increasing the temperature of a room — intuitively, the thermometer will accurately represent the temperature without misrepresenting the pressure, as we haven’t given it made its indicator sensitive to pressure, but rather temperature.

A second example.  Our eyes are sensitive to color, but not other forms of radiation.  We visually represent color without visually representing the rest of the radiation spectrum, even when certain colors may entail facts about other, present radiation.  It’s worth emphasizing that we represent the properties of the objects of experience, not the objects themselves.  I’m on the pier looking out on the lake and see what appear to be two white ducks.  Unbeknownst to me, one of them is a decoy.  This is because the decoy duck is meant to produce some of the same experiences of the duck, like shape and color.  My visual experience of the duck and the decoy are virtually the same, even though the objects are of entirely distinct kinds.  The decoy is designed to have the same color properties of the duck, without actually being a duck.  So our sense modalities are sensitive to certain, specific properties of objects, not the objects themselves.  This also explains the aspectual character of representation.  When I see a tomato, I visually experience the side facing me, an aspect of the the tomato, not the whole thing itself, front, back, inside, and out.

Objections to Verificationism and ‘It-From-Bit’

Schlick’s verificationism is vulnerable to a number of objections.  In light of the similarities between informationism and verificationism, we might wonder whether informationism falls prey to the same sort of objections.  We will now discuss some objections to the given and see if the sort of informationism held by Wheeler can overcome them.

The most immediate objection to Schlick’s verification principle is that the verification principle itself is not logically verifiable.  Fortunately for Wheeler, this will not be a problem for informationism.  Wheeler is not committed to the meaning of his statements relating to some atomic properties of perception.  Meaning is the joint product of all the evidence that is available to those who communicate.  Evidence can be either direct or indirect.  There is no recourse to unanalyzable, non-theoretical features of perception because instead, Wheeler relies on the notions of the kind of question asked and the digital response.  A digital response need not be an atomic response.

Another concern for both verificationism and informationism might be, how can we have third person scientific knowledge if all scientific knowledge is based on 1st person statements?  Fortunately, there is agreement in third person scientific knowledge between scientists.  Supposing that each has a different experience, the fact that they all agree in the way that they communicate suggests that there is a structural similarity between each’s first-person experience.  Scientific knowledge and theory are intimately connected.  And theory is about the structure of relations between those things that feature in our experience.  The description of the structure may (and should) be identical, regardless of the organization of the features of experience for each individual.  And, indeed, this makes a great deal of sense on Wheeler’s picture.  This is because all ‘reality’ for each subject is information-theoretic.  And the information is constituted by the relations between its components, without ever being committed to saying what those components actually are.  Objective, third-person, scientific knowledge is information-theoretic — it strives to capture the formal relations between phenomena, regardless of what the character of the phenomena is to any particular individual.

A larger problem, raised by Plato’s ‘Theaetetus,’ regards the fact that if atomic statements are verifiable by an individual, then those statements will always be true.  And if those statements are always true (and so trivially true) then they can have no descriptive content.  It is as if someone were to say, ‘I’m sensing the thing that I sense over there in the manner that I typically sense it.’  This is completely and totally uninformative.  We will now elaborate on this.  

Prima facie, on Wheeler’s view, knowledge and perception and intimately connected.  Knowledge comes from recording the binary responses of our measurement devices (and interpreting the responses in such-and-such way).  So it seems that ‘man is the measure of all things.’  We grant existential status only to those things which we can measure to be so.  This may be problematic.

Take six dice.  They number more than four by a half.  But compared to twelve dice, the six are fewer by a half.  It is both more and less.  But nothing can become greater or less while remaining equal to itself.  The number of dice is either ‘is greater’ or ‘is less’ depending on the frame of reference that it is considered in.  The veridicality of the ascription of the predicate depends not on the properties of the object under question, but more upon its mode of consideration.  This seems an impoverished notion of knowledge, for it does not seem to give us insight into the actual properties of the object.

Moreover, intuitively, it seems that perception is the union of capacity for sensation and an object of sense.  Perception depends on some connection between an agent with a capacity for certain kinds of sensations and an object with a capacity for producing those kinds of sensations.  But on Wheeler’s picture, it seems like the (‘physical’) object of perception has no (independent) existence until it is united with the subject (for instance, the scientist).  There can be no one, self-existent thing.  Rather, everything is related within the information space.  Each component in the space depends on its existence on the structure of the rest of the components of the information space.  There is a potential infinity of ‘physical’ objects and subjects (which can come together in perception) — each combination of object and subject produces a result which is not the same, but different.  This is because each perception is defined by the unique identities of both the object and the subject.  My capacity for perception, \phi, meets with an object with a capacity to produce certain perceptions in virtue of its identity, \alpha, to produce the unique perception, (\phi + \alpha).  Another agent with capacities for perception, has his own identity \psi.  When he meets \phi, the perception is uniquely defined as the resultant of (\psi + \alpha).  And there can be no justification for the claim that (\phi + \alpha) is identical with (\psi + \alpha).  Consequently, there is no other object I could encounter which should give me the same perception, for another object will correspond to a different agent-patient relation and so the perception must be different.  Nor can any object which affects me in a certain way, if it should meet with some other subject, produce the same perception.  For that perception will be uniquely defined by that other subject and the object.

When I perceive something, I must be the percipient of something.  For there could be no such thing as perception without some thing being perceived.  In the words of Socrates, ‘nothing can become sweet which is sweet to no one.’  So on Wheeler’s view we can only be bound to one another.  The existence of all things depend on their relation to something else — no thing can be absolute.

Moreover, if this is so, then all my perceptions must be true to me.  And if this is so, then how could I ever fail to know that which I perceive?  For if truth is found only in perceptual experience (or sensation), and no man can know another’s feelings better than he, then each is to himself the sole judge — and everything that he judges must be true.  There is no need for us to consult each other, for each is the God of his own perception and consequently determines what is true of his own reality.

Three points are crucial here.  (1) That there be some intersubjective agreement on matters of fact, (2) Wheeler does not mean to deny that there is some object of our perception, and (3) if we take the primacy of information spaces seriously, then that ‘there can be no one, self-existent thing’ is not as counterintuitive as you may suppose.

With regard to 1, while each individual may be the final arbiter of the character of his own perceptual experience, this only entails that his (honest) reports about the character of his experience be true — not that his (honest) reports with respect to his inferences from his perceptual experience be true.  I say, ‘such-and-such looks green to me,’ and this may be true, regardless of whether or not the object I am referring to actually is green.  But if I say, ‘such-and-such is green,’ then I am not reporting my experience, but rather reporting a fact inferred from my perceptual experience.  It is often the case that such inferences are false.  It does not matter that no identity can be drawn between (\phi + \alpha) and (\psi + \alpha); what does matter is that \phi‘s report and \psi‘s report be in agreement, not that they be identical.

With regard to 2, Wheeler, unlike Schlick, does not straightforwardly dismiss the notions of an internal or external world.  Rather, to confirm an object of reality, we just need some empirical justification, direct or indirect.  That there are objects of our perception is not denied.  What is denied is that they really are ‘physical,’ for the word ‘physical’ is itself a theoretical term.  It does not matter that perception requires the union of a subject and an object, for Wheeler allows there to be independent objects.  (He is just reluctant to make a definitive claim to their ontological status.)

With regard to 3, we must first consider Wheeler’s views on space and time.  Wheeler claims that there is no space, nor no time.  He cites both Leibniz, ‘…time and space are not things, but orders of things…,’ and Einstein, ‘Time and space are modes by which we think, and not conditions in which we live.’  He goes on to describe Einstein’s notion of spacetime, saying that on this theory, predicted fluctuations grow so great at distances on the order of the Planck length, that ‘they put into question the connectivity of space and deprive the very concepts of ”before” and ”after” of all meaning.’  So for Wheeler, spatial and temporal concepts are modes of thought, not features of reality.  This sort of view is lent support by the establishment of nonlocality and absolute simultaneity in quantum mechanics.  Split a pion to produce an electron and a positron.  The outcome of the measurement of the electron collapses the associated positron (into the opposite value), regardless of the distance between the two particles — the effect is absolute simultaneity, and that causes need not operate locally.  Absolute simultaneity entails that local realism is false, and if local realism is false then realism about special relativity is false, too (space and time are not part of reality).  Now recall how an information space is constructed.  There are difference relations between information states embedded in an information space, and the relations can be transmitted down some causal pathway.  You might think that there has to be some self-existing thing, that there must be some loop like this: physics gives rise to observer-participancy, observer-participancy gives rise to information, and information gives rise to ‘physics.’  So first, there is something that exists, which causes there to be observers, and only then can the information relation be constituted, wherein we can then access ‘physical’ knowledge.  This line of reasoning presupposes that time is a feature of reality and not a mode of thought.  There is something thought to ‘exist before’ which at some time later gives rise to observer-participants.  But if time is not a feature of reality, and reality is just an information space, then we cannot make sense of a real temporal relation between physical processes giving rise to observers.  Here’s one way to think about it.  All ‘reality’ is at once instantiated — objects, subjects, and relations, all.  You, as a subject instantiated someplace is the information-space of reality, perceive time to give order to your perceptual interactions with objects in the information space.  Objects do not precede you in time, they are instantiated alongside you in the information space and are experienced in a certain order.  As such, there is no need to talk about some unobserved/unobservable feature of reality prior to observation which gives rise to observers.

So it seems like informationism does, in fact, overcome the objections to verificationism that we’ve been discussing.  This looks promising for Chalmers.  However, there is a larger, more powerful objection to this kind of view which is clearly articulated by Sellars, and we will discuss next.

Informationism and Verificationism – A Comparison

Wheeler’s informationism should remind us of Schlick’s verificationism and the old school of logical positivism.  Schlick shares with Wheeler this sort of hardline empiricism.  This section will explore the similarities and differences between the two.  As a first order of business, we should briefly explain Schlick’s verificationism.  (Note that this explanation can also be found in the above Schlick link.)

The main thrust of verificationism is this.  A statement is meaningful only insofar as it is logically verifiable.  Any statement that is not logically verifiable is not meaningful.  The only statements that are logically verifiable or knowable are those which reduce to some description of the given.  The given is the domain of all that is knowable; it is roughly your perceptual experience at some particular point in time.  The given should not be confused with the terms ‘the internal world’ and ‘the external world,’ both of which are meaningless for the verificationist.  This is because propositions like ‘there is an external world,’ will turn out to be not logically verifiable.1 All difference in the given is detectable.  Because the given is what is presented to you in perceptual experience, there can be nothing in the domain of the given that is undetectable.

Features in the given are describable with atomic words or atomic sentences.  Atomic words, like green, pain, and so on, can only be known by ‘pointing’ to some feature of our perceptual experience.  They cannot be understood in terms of other words.2  I point or otherwise gesture to a grassy knoll and say ‘that green.’  The word’s meaning is established by the agreement of the reactions of others, e.g. that other react by observing, ‘green.’  That is, the use of the word occupies the same relational-role in the given}as it is experienced by each of us.  For the verificationist, the question of whether the phenomenal quality of his green-experience is identical to the phenomenal quality of my experience, is meaningless.  This is because that fact is not logically verifiable.

Atomic sentences are composed of atomic words.  All complex propositions, like ‘there is a deer by the bush,’ are made of atomic sentences, like ‘there is a brown spot with such-and-such features by that green spot arranged in so-and-so way.’  So complex propositions are reducible to (some sequence of) atomic words, whose meaning directly describes the given.  To see this, suppose that a proposition’s meaning is something over and above its determining some state of affairs in our perceptual experience.  If this additional meaning is expressible, then it would be a (complex) proposition (and so nothing over and above an atomic description of some feature of our perceptual experience).  But if the meaning is not expressible, then it cannot mean anything, for that which expresses nothing means nothing.  So the truth or falsity of a proposition must correspond to a difference in the given in order to be meaningful.

It follows from this that the meaning of a proposition is identical with its verification in the given.  The meaning of ‘there is a deer by the bush’ is just whether or not there is a familiar arrangement of brown situated by another familiar arrangement of green, and perhaps some audible rustle — for these are the features of our perceptual experience which verify and are associated with the presence of a deer.  So if we cannot conceive of some verification in the given of the fact, then the fact means nothing.  So, a proposition is meaningful only insofar as it is logically verifiable.  A meaningful statement says that under certain conditions, certain data appear.3

Here are the similarities between Wheeler and Schlick.  Prima facie, both seem to share the verification principle — that is, the only statements that are meaningful are those which are logically verifiable.  For both Schlick and Wheeler, if something is meaningful, it must correspond to some empirical indication of fact.  Consequently, both Schlick and Wheeler grant existential status only to those things that have some possible effect on our perceptual experience — for something to exist, it must be meaningful.

They also share a sort of ‘atomism’ about reality.  For Schlick, meaning comes from the atomic features of our perceptual experience.  For Wheeler, meaning comes from the binary answer to a question.  But these binary answers are a lot like the ‘atoms’ of Schlick, as for both reality bottoms out at something that is impenetrable to further investigation or analysis.  The ‘atoms’ of Wheeler are fundamental digital questions/answers, while the atoms for Schlick are atomic words that directly ‘point to’ features of perceptual experience.  They differ in how and when they ‘bottom out,’ but they agree on ‘bottoming out’ somewhere upon which the entirety of our discourse gets its meaning.

Both the ‘it-from-bit’ doctrine and verificationism, at heart, are deeply antimetaphysical views.  For Wheeler, physical objects have the status of ‘theory’ because they are the result of an interpretation of a binary item in our perceptual experience.  Because reality is theoretical, we ought not make metaphysical claims about it and, moreover, at any rate, such claims will be meaningless.  Likewise Schlick, in explaining the given, emphasizes his avoidance of any commitment to an internal or external world — for such concepts are meaningless.  Metaphysical statements are not verifiable, and so not meaningful; whence the antimetaphysicalism.  But if we take physical objects to be objects in the external world, then Schlick will see physical objects as the same sort of ‘convenient’ myth as Wheeler and Quine (for, for Schlick, there is no external world — any talk of the [objects of] the external world can only be taken as heuristic).

The differences between Wheeler and Schlick primarily revolve around (1) space and time, and (2) meaning.  For Schlick, space and time will be features of the given, their reality easily ‘verified’ by the mere fact of the given at all.  In contrast, Wheeler sees space and time as modes of thought, not part of reality.  If space and time are modes of thought, then there must be something that we are thinking about.  This seems to imply that there is something external to us or mind-independent that our thoughts try to ‘reach out and grasp,’ or represent — but this kind of talk is forbidden on Schlick’s account.

For Wheeler, meaning is the joint product of all the evidence available to communicators.  For Schlick, meaning is identical with method of verification in the given.  Prima facie, these views are rather similar.  But for Schlick, all meaningful statements must be reducible to some concatenation of atomic words, directly referring to the immediately apprehensible features of the given.  Wheeler doesn’t explicitly commit himself to such reductionism (to atomic words).  Rather, evidence is more broadly construed so that we can actually talk about theoretical entities without talking about only our phenomenal experience. For Wheeler, to say that there is a forcefield is to infer a theoretical fact about reality from a set of registrations on some device.  Schlick, in contrast, maintains that just to say that there is a forcefield is to say that such-and-such a device registers so-and-so in a particular way — and does not ascribe reality to the forcefield itself.  The differences in their respective accounts of meaning will be important going forward.


  1. The truth or falsity of the reality of the external world has no impact on your perceptual experience.  If we are all in the internal world and this should be some fantastic dream, there is no empirical matter of fact you could ever come across which would verify that you are in an internal or an external world. 
  2. For such a description of pain can only amount to something like, ‘pain hurts,’ ‘pain is the opposite of pleasure,’ or ‘pain is what makes you recoil.’  The first is a tautology, the second is almost as trivial, the third overbroad and not necessary, and none of them convey any nontrivial knowledge about what pain actually is to the person who has never experienced it. 
  3. For such a statement to be verified re vera, is for there to be consistent agreement in the reactions of a sufficient number of persons to a given stimulus — an agreement that under certain conditions, certain data appear.  (In this way, hallucinations and illusions will not be verifiable.) 

It from Bit, Information as Fundamental

The main problem that leads Wheeler to propose his ‘it-from-bit’ doctrine is the mysterious nature of the fifth axiom of quantum mechanics, viz. the collapse postulate, which we will discuss later.  ‘It-from-bit’ is an antimetaphysical thesis.  The motivation for holding an antimetaphysical thesis is that it provides a clearer notion of truth and a definite, methodical path to getting there.

Wheeler’s central distinction is between ‘its’ and ‘bits.’  An it is a thing (that is, something that we ascribe existence to).  This class includes particles, forcefields, the spacetime ‘continuum,’ and your mother’s rosebush.  A ‘bit,’ is an apparatus-elicited answer to a yes-or-no question (that is, a binary choice); e.g. the counter registers a click in a specified second, indicated ‘yes’ for ‘photon.’1   Every ‘it’ derives its function, meaning, and existence from ‘bits.’  The reality of every ‘it’ is derived and established from the affirmative answer to a binary/digital question.  I establish the reality of my coffee mug by asking ‘is there a coffee mug on the table?’, looking to it and registering the familiar shape of the cup and handle, and the characteristic deep blue color, in my visual experience (resulting in an affirmative answer), and then I can say, ‘there is a coffee mug on the table.’

Wheeler says that ‘It from bit symbolizes the idea that every item of the physical world has at [very] deep bottom…an immaterial source and explanation;…reality arises in the last analysis from the pose of yes-no questions and the registering of equipment evoked response.’  This amounts to: all things physical are information-theoretic in origin — that is, information is in some sense ‘prior to’ the physical world.  We can break most things down and explain them in terms of their component parts — and take those component parts and do the same.  But eventually we will bottom out somewhere (binary).  Suppose we reach the most fundamental physical particle — some physical point — call it \omega.  At that point, the only question we can ask is the brute question, ‘is an \omega there?’ as we cannot explain it in terms of other things (or anything else more fundamental).  If we can measure its presence, and in the affirmative, then that is the brute bottom of our explanation of \omega.  But the reality of \omega comes from being able to measure its presence.  The information precedes the ascription of existence to the physical object.

Wheeler shows how this comes out in a number of ways.  Take a putative physical object, like a forcefield.  We measure the strength of a forcefield by using a device which measures shifts in interference patterns by representing the number of ‘fringes’ in the pattern.  But all the fringes can possibly stand for is a statistical pattern of yes-no registrations.  Or consider how we determine the existence of a photon.  We ask a question like, ‘did a counter register a click during a specified second?’  If so, we say, ‘a photon did it,’ thus ascribing existence to the putative physical object on the basis of binary information.  Blackholes furnish a particularly interesting example.  Consider the following discovery by Bekenstein.  The surface area of the horizon of a blackhole measures the entropy of the blackhole.  Thorne and Zurek explain that, in performing an operation on the value of the surface area we get N, the number of binary digits (‘bits’) required to specify in all detail the constituents of the blackhole.  Entropy is a measure of lost information.  No outside observer can determine which of the 2^N configurations of bits compose the blackhole.  So the size of a blackhole (an ‘it’) is defined by the number of ‘bits’ lost within it.  Finally, a more ordinary example.  You wish to determine whether or not your tea is too hot to drink.  If you taste it and burn your mouth then ‘yes’ it is too hot to drink.  If you taste it and do not burn your mouth, then ‘no’ it is not too hot to drink.  In this way, the evaluation of a putatively physical property like temperature is reduced to a binary choice, and so the information precedes the ascription of the property.

What this means is that physics can be cast in terms of information.  Wheeler calls (physical) reality a ‘theory.’  We can make each physical item a (metaphysically neutral) element (in some arbitrary state — either 0 or 1) in an information space, and characterize the relations (and their similarities and differences) between elements without ever being committed to a metaphysical claim about what those elements actually are.  Physics does not require a commitment to physicalist metaphysics.

For Wheeler, the notions of ‘meaning’ and ‘existence’ are intertwined.  Meaning is ‘the joint product of all the evidence that is available to those who communicate.’  So for something to be meaningful it must be (1) communicable and (2) empirical.  Let’s explain 1 first.  It’s plausible to say that anything expressible is communicable (and vice versa). If something that is meaningful were not expressible, then it could not mean anything, for that which expresses nothing clearly means nothing.  So for something to be meaningful it is necessary that it be expressible. Now let’s explain 2.  Something that is meaningful must make an empirical difference — that is, there must be some item in possible perceptual experience, which is logically possible to access, that corresponds to the thing’s truth-value.  This notion of meaning is not as impoverished as you might expect, for there is quite a bit of evidence available to communicators.  Even with regard to the past, an intrepid crew of investigators, armed with the right equipment, will be able to establish that such-and-such happened so-and-so long ago in the past, based on some chain or network of physical evidence.  Their findings will contribute to the establishment of that past event’s meaning.  Here’s how this importantly ties into existence.  If a \phi is not meaningful, then it is meaningless to assert something like, ‘\phi exists.’  (Attach any other predicate you choose, and it will nevertheless presuppose the existence of \phi.)  For suppose I do assert that ‘\phi exists.’  That entails there must be some possible item in my perceptual experience which ‘verifies,’ so to speak, the existence of \phi.  If there isn’t anything that I could see, or smell, or taste, or hear as some result of \phi‘s existence, then it means nothing to say that \phi exists.  What would it mean to ascribe existence to something which could never impinge upon our perceptual experience?  Its existence or lackthereof will never affect the truth-value of any proposition of this world.  So if something is not meaningful, any assertion of its existence is meaningless; therefore we can only grant existential status to those things which are meaningful.

Chalmers’ observes that this sits nicely with the idea of Shannon information.  In Shannon information, where there is information, there are information states embedded in an information space — where an information space is a structure of (difference) relations between its components.  Differences may be transmitted down some causal pathway.  Notice how this sits nicely with how Wheeler thinks that past events are meaningful.  Consider the infamous tree that fell in the forest with no one to hear it.  Nevertheless, its fall will leave some kind of evidence (like a depression in the ground, scattered needles, etc…) which some investigators may happen to stumble across (and so make the fall meaningful).  On this picture, the tree in the forest, prior to its fall, is an information state (to be defined in terms of its relations to other trees, perhaps).  The information space evolves, differences are transmitted, and some information relates to the tree in such a way that it falls (its fall constituting continuous differences down a causal pathway).  When the information corresponding to the falling tree is related to the ground, there are changed information states corresponding to the depression it leaves and the needles which scatter.  The information is finally communicated when our intrepid explorers see the depression and so receive the information of the tree having fallen.

Physical ‘its’ must come from ‘bits,’ which are discrete, for there is no continuum in physics.  There is no continuum in physics because there can be no continuum in mathematics.   Of the number continuum, Weyl says ‘belief in this transcendental world taxes the strength of our faith hardly less than the doctrines of the early Father of the Church.’  Likewise there can be no continuum of/for physical objects; they must be discrete.  Quine articles this point quite well, ‘Just as the introduction of the irrational numbers… is a convenient myth [which] simplifies the laws of arithmetic… so physical objects are postulated entities which round out and simplify our account of the flux of existence…  The conceptual scheme of physical objects is a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.’  (1) That physics is discrete in this way means that it must yield to digital questions and consequently physics will be information-theoretic.  (2) I think that the phrase, ‘conceptual scheme of physical objects’ is particularly telling.  We interpret empirical evidence through a particular theory or conceptual lens — to call an object ‘physical’ is just to conceptualize a feature of our perceptual experience in a certain way.  We reserve the word ‘physical’ just for those meaningful, empirical items in our perceptual experience.

So on Wheeler’s account, ‘reality’ has the status of theory.  Reality is constructed out of the kinds of questions we ask about the world, and the ways in which we interpret those binary answers.  To press the point, consider how we measure the spin-properties of electrons.  Suppose I have an electron.  I cannot ascribe either ‘black’ or ‘white’ or both (or neither) until I shoot the electron through a color-box.  If the color-box does its job right, the outcome of the measurement will be with ‘black’ or ‘white’ (each with exactly 1/2 probability).  But my choice to measure color disrupts the electron’s hardness value — that is, I can never predicate a definite hardness property and a definitely color property to the same electron at the same time.  The moral is that the choice of question (e.g. what is the hardness? vs. what is the color?) and the choice of when the question is actually asked play (some [but not the whole]) part in deciding what we can justifiably assert about reality or ‘the World.’  So to say that reality is a theory isn’t as unintuitive as it may first appear.

So if information is primary to physical objects — and, indeed, the status of physical objects is merely theoretical — then it seems like something which must be fundamental is perceptual experience.  This is the notion which led Chalmers to suggest something like Wheeler information as the fundamental constituent of reality.  Our conscious perception of ‘the World,’ or of things underlies all other empirical (and even metaphysical) knowledge.  Without it, reality wouldn’t even speakable.  So on this picture, physics has a distinct theoretical quality, whereas perceptual experience is non-theoretical and most fundamental.


  1. Here’s the reason why I put scarequotes around ”photon.”  We ascribe existence to the thing we think caused the counter to register a click.  But a photon is a theoretical entity (you can never actually see a photon — only its causal influence).  If we conducted the experiment within a different theoretical/conceptual framework, we may attribute the registering of a click to some other theoretical entity. 

Semiotics and System Development

This post will concern the development of systems, assuming the earlier supposed ‘systems theory’ ontology. In particular it will focus on the ‘canonical development trajectory’ (CDT) and show this fact, with an ontological plurality of systems, suggests emergent dualism, and a systems-theoretic way of thinking about the development of consciousness experience.

Assume the definition of Nature previously provided. A system undergoes development, and this development can be modeled as part of Nature. Development is a process from vague beginnings toward more and more specified particulars. Each stage of development will be a ‘refinement’ of the earlier stages, via having acquired more information in its process. For example, consider how a stream may develop from a glacier or mountainous lake. As the stream descends, its path down the mountain (its development) will progress in a way supervenient on the totality (of the development) of the preceding stages (this is how the system becomes increasingly specified as it accumulates more and more information at each stage [e.g. about the ruts and ridges which further specify the trajectory of the stream]).

Few developmental tendencies are universal; one such is the ‘canonical development trajectory.’ In CDT, each stage is defined by some thermodynamic and/or some informational change. Consider the universe at its inception and assume that it is thermodynamically isolated. As the universe expands, it becomes increasingly disequilibrated. This is to say that the universe’s constituents slowly clump into vague, amorphous masses; in these masses, continued disequilibration sharpens them into having more definite forms. Through continued disequilibration these forms develop into organizations. And so on, as the universe moves further from thermodynamic equilibrium.1 So the general pattern of development looks like this: [vague \rightarrow [more definite \rightarrow [more ‘mechanistic’]]]. This pattern of development occurs at different rates for different kinds of systems (e.g. chemical, biological).

Note that things like striving and haste make work less energy efficient, and that entropy production is the way that a disequilibrated region can foster or restore (some of) the universe’s thermodynamic equilibrium. This observation leads us to an Aristotelian conception of cause qua the development of a system. Consider a developing system S — what is it that causes it to develop in the way that it does? (1) The components of the system must have a susceptibility to being changed. That is, the ontological status of the substrate of the component must be the kind of thing that can undergo some kind of change. E.g. the bronze of Aristotle’s bronze statue is the kind of material that is susceptible to being carved into a statue. This is the material cause. (2) The system must have initial and boundary conditions, organized in a definite and particular way, constraining its development. The ruts and ridges of the mountain set the conditions for the development of the water (for instance, the water will flow down a rut and cannot balance on a ridge). This will be the formal cause. (3) There is some inciting ‘force,’ ‘push,’ or ‘action’ that initiates the process. Perhaps the dam (holding the water) gives way, initiating the water’s developmental flow down the mountain. This is efficient cause. (4) There is some thing that it ‘strives’ to develop into as it gains more information. This ‘striving’ will be attributable to the Second Law of Thermodynamics. The water flowing down the mountain is trying to ‘dissipate’ its energy (and increase the entropy of the universe, pushing it toward equilibrium). Put plainly it is the answer to ‘why’ the water flows down the mountain the way it does. All ‘work’ is undertaken to move the universe toward increased equilibrium (and entropy). This will be the final cause.

Each level in development represents a different ontological (or integrative) level: [physical dynamics $latex \rightarrow$ [chemistry \rightarrow [biology \rightarrow [neuropsychology (and so on)]]]] This is contrary to the ‘unity of the sciences’ perspective, which maintains that lower levels give rise to and subsume higher levels — that each higher level is supposed to be entirely supervenient on the lower level(s). But the ‘unity of the sciences’ thesis doesn’t seem to match with reality (or how we take things to be). For, prima facie, it seems that each higher level integrates and harnesses all the lower levels under its own local rules. That is, they synthesize all the lower levels in order to promote the final cause of the higher level from one moment to the next. To see this, consider a person (a biological system). Individual action comes from a person instantiating neural firings, which defines and restricts the space of biological (re)actions; the organization of the biology sets the criterion for what chemical/molecular actions can be, and so on. The highest integrative level determines the space of action for the lower levels. We say that levels are ontologically separate in that they are ‘integrative.’

In the course of development, there are two (interrelated) principles we must keep in mind, viz. total novelty denial and the principle of continuity. The former asserts that nothing ‘totally new’ appears in the course of development. The latter asserts that all emergent features at higher integrative levels would have been ‘vaguely and episodically’ present (primitively) in the lower levels. This entails that any present configuration at a high level implies that which gave rise to them (either ontologically-materially or conceptually). It’s worth noting that total novelty denial does not deny that something ‘apparently novel’ may emerge, only that it is not actually novel. If that sounds confusing, here is an example. You might think that the development of some new species or of a unique poem seems ‘new.’ But it is not ‘new’ re vera. The development of each is just a restriction on what was possible before its (that is, the species’ or poem’s) emergence. Salthe asks us to consider language. We ‘chose’ the English language and can express infinitely many things with it; however, English cannot express the ‘larger moods’ expressible in French (which may have been expressible in a common, ancestral language). So something ‘apparently’ novel can emerge in the long run,2 but in actuality it is just a restriction on the previous stage(s) of development.

And now we can reach the crux of the matter. Consider the proposed developmental pattern: [physical dynamics \rightarrow [molecular connectivities \rightarrow [biological activities \rightarrow [individual action \rightarrow [sociopolitical projects \rightarrow [culture]]]]]. Notice that as the development of this system proceeds, causation is less susceptible to material reduction (in the sense that, at higher and higher integrative levels, it becomes progressively more difficult to describe the actions at those levels in terms of the more basic systems it out of which it arose). For when we reach culture, we have not a material form (assuming we ever thought we had one) of evolution, but a purely informational form of evolution. For culture is a product of information, of written history and literature, of the behavioral customs and norms between people of the same society, the thought behind certain practices, and so on. Culture is a highly-integrative level, and is in no sense straightforwardly material. By total novelty denial and the principle of continuity, culture logically implies constituents which give rise to it. But the constituents of culture are purely information, not matter. This, then, is resistant to material reduction, for the constituents that it implies are informational, not material. That development moves toward this suggests something like semiotics being the ‘ultimate framework’ of reality, as opposed to matter. Semiotics amounts to information through isomorphisms in ‘signs.’ And this seems consistent with our earlier developed ‘systems theory’ ontology — the (onto)logical priority of systems. If what constitutes a system are (1) ‘objects’ and (2) relations between them, then a semiotic framework seems intuitive. For each ‘object’ can be taken as a token or sign, and the signs will be related in a certain way. Two discrete systems are isomorphic if we can establish some \meaningful} mapping between them.3  If the concept of a system is the most prior, then the domain of semiotics seems to follow almost immediately after.


  1. The continued development of increasingly complicated systems will, then, be dependent on the continuation of the universe’s expansion. 
  2. Here’s lookin’ at you, consciousness. 
  3. A robust account of this can be found in Godel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter. 

The Priority of the System

The concept of a system is going to be logically prior to any other concept. This has both scientific and metaphysical ramifications. This paper seeks to explain systems’ priority and touch on the consequences thereof.

Suppose that physicalism is true. Reality consists just in matter and motion, governed by physical laws, and that reality is nothing over and above this. The physicalist thesis logically entails that all reality is a physical system.

But to even talk about a ‘physical system’ or conceive of one, we must first have the concept of a system. For now, we can think of a system as (1) composed of components, (2) composed of relations between those components, and (3) the relations between the components perform some kind of function. To think of any thing requires first the thought of a system. Even to think of a thing in isolation is to think of a system. For suppose I consider a system amounting to nothing more than a thermodynamically isolated rock. To think of a thermodynamically isolated rock, I must also think of the pieces of rock which constitute it (exactly what constitutes a rock) — and that’s going to be some relation of things. The constituents of the rock relate to each other in such a way as to function as the identity of a discrete (if isolated) object. Or consider the following. Systems are prior to even the most general and abstract scientific discipline, logic. For to even do logic requires that one have some set of sentence letters and some set of axioms. The sentence letters amount to components and the axioms define the possible relations. Often, the relations between the sentence letters function to output (or be capable of outputting) some truth-value. Logic requires the instantiation of a system.

At the inception of any new science, there is some new realm of objects that are to be investigated. These objects are components and the relations between these objects (and their functional outputs) are to be investigated. New sciences require the instantiation of new systems.

Here’s an important point about modeling that reveals something crucial about systems. For a model of any system (take, e.g., a physical system) to be a good model, it need only depend on the model’s formal characteristics. We can create a cybernetic model of an organism. A cybernetic model simulates all the behaviors (of an organism) regardless of its material constitution (and its ontological status) — all that is important to the model is the preservation of the formal relations between components, but what those components actually are is irrelevant to the functioning (of the model).1  What this suggests is that material constitution of a system is irrelevant to that system’s functioning. An organism with a biological-material structure can perform the same functions equally as well as a cybernetic mechanism — the material constitution differs, but the functioning does not. So our understanding of a system must be independent of our understanding of its material constitution. That is, the whole (the system) is a sum of logical relations or connections between objects of any ontological constitution.2  If the ontological constitution of the object is irrelevant to the system, then we may consider systems as composed of mechanical stuff, or material stuff, or mental stuff without changing the behavior of the system. In cybernetics, when we try to simulate an organism, we must always make use of strictly formal concepts or tools like feedback, information, or control. And these concepts are what actually must figure in at the level of the simulated organism’s functioning, too. In this way, a model depends only on the formal concepts and not on the physical substrate. Systems theory uses these formal tools and is more general — and this generality heralds its ontological priority.

Now consider a system S composed of subsystems S_1, S_2, and so on. In this situation, we can study the structure of just one of the subsystems (say, S_1). To S_1 we take some established science and use it to study the relations and mathematical functions that govern S_1. Then we go on to S_2 and do the same thing (using, perhaps, some different established science). And then onto S_n, and so on. After studying each subsystem, we can consider all the relevant relations and mathematical functions which hold between S_{1...z}. For example suppose we consider the system of a person (something with both mental and physical attributes). We can study the structure the body system and, independently, we can study the structure of mental life (the mental system/perceptual experience). Having done this, we can try to map features of the mental structure to features of the physical structure (aiming to achieve some sort of isomorphism) in order to understand their relevant similarities and differences and how they both importantly figure in to the overall constitution of the person. Note, however, that the person is not going to be reducible to the mental or physical subsystems (or both), because the presence of both (working in tandem [in some way]) is going to be what makes the person the system such as he is. This highlights how we can cut up and divide a system in whatever way is most fruitful to investigation, give each subsystem the scientific treatment it deserves, and then look at the relations between each of those (in a sort of general systems theory).

That systems are divisible and relatable in this way is refreshingly antimetaphysical. We do not need to be committed to metaphysical theses which maintain that all reality is a physical system. Such theses are, at any rate, impotent. For if you are given the world, knock your head against it, and say, ‘Ouch! How physical,’ then you are simply appending a label, ‘physical,’ to the world and haven’t yet said anything about it. For a physicalist thesis to have any teeth, there must be nonphysical things that do not (or maybe could not) actually exist in the world. To say that all reality is physical is to say nothing; it is tantamount to saying that all reality is just reality. (Moreover, the physicalist who claims he can not even conceive of anything non-physical renders his physicalist inert. He is not saying that all things bottom out at the physical, he is simply saying that all reality is physical. This is nothing more than an uninformative new label for ‘reality.’) Here’s another way to bring this out. Physical laws can be cast in terms of ‘information.’ We can talking about how different states give rise to different effects without ever specifying the ontological status whatever is actually in that state.3  All that matters is the position of the object in the information space.

One advantage of a ‘systems theory’ view is that it is a better ontological fit with our ways of thinking about science and scientific objectivity. Because of the reducibility problems earlier mentioned, the ‘unity of the sciences’ thesis seems not only ad hoc, but forced. Different researchers operate in different domains — it is not as though physicists are out to discover the truths of neurophysiology, but rather the motions of bodies. When we are not dogmatically trying to reduce one science to another, we tend to treat each science as more or less independent from the others. This is why a ‘systems theory’ approach sits nicely with our contemporary scientific, intellectual climate.

And a parting thought. Reality or ‘the World’ is what is mediated to us in perceptual experience. All we are directly acquainted with are the aspects of our perceptual experience. Schlick, a logical positivist and verificationist, was distinctly antimetaphysical in a similar sense. He referred to ‘the given’ as what is (possible to) present to us in perceptual experience, and claimed that ‘the given’ is the domain of all that is knowable.4  I do not think of ‘the given’ in as narrow and impoverished a way as Schlick; I will, however, admit that reality or ‘the World’ is only present to us insofar as what information we can (possibly) acquire or know about reality must be contained in our perceptual experience (or else be some kind of a priori knowledge). ‘Nature’ should be thought of as distinct from ‘the World.’ Call Nature what is not what we can be presented with in perceptual experience, but is rather our scientific construct for scientifically examining the world, and it must be mediated through language. Nature is what happens when we talk about the world, try to contain and grasp it in our language (and its corresponding concepts). Consequently, statements about Nature are going to be theory-laden. Laden with whose theory? Observation about nature will be couched in the preexisting theoretical structure of whoever the observer is. Berkeley and Newton’s conceptions of Nature are radically different, but they both ‘reach out and touch’ the same reality or ‘the World.’

When the physicalist says that reality is a physical system he is not making a claim about ‘the World.’ Rather, he is making a claim about Nature, that all empirical science is ultimately about fundamental physical particles. This has a certain intuitive appeal. But (1) reductionism is often not successful (as indicated earlier) and (2) this really just amounts to saying that we can only conceive of the objects of perceptual experience as made of material constituents (but again this just nerfs the meaning of ‘material’).


  1. This has been used to argue that psychobiological entities must be considered as nothing over and above mechanical things/processes. 
  2. Take ontological constitution to be the ontological status of the component. As an example, you might think that the ontological constitution of your body is material, whereas the ontological constitution of your perceptual experience is mental
  3. This is meant to emphasize the point about cybernetics. And also foreshadow discussion to come. 
  4. Presumably mathematical truths are either abstracted from ‘the given’ or else ‘the given’ actually refers to all that is empirically knowable. 

The Liar Paradox and the Measurement Problem

Just a quick observation.  I think that a telling analogy can be drawn between the measurement problem in quantum mechanics (QM) and the liar paradox.  This aside is just meant to draw out those intuitions.

The liar paradox amounts to more or less the following statement.   ‘This sentence is false.’  You know the drill.  If the sentence is true, then it must be false (for it asserts its own falsity).  And if the sentence is false, then it must be true (for the negation of its falsity is its truth).  In light of this (and to avoid infinitely ‘looping’ through the truth-values of the sentence), we say that we cannot ascribe any truth-value to the sentence at all, dub it a paradox, and call it a day.

Another account of the measurement problem can be found here.  Nevertheless, here’s the gist.  The dynamic equations of motion (DEM) (the third axiom of QM) are thought to certainly determine the states and motions of all particles (all states and motions are calculable [via the Schroedinger equation]).  By DEM, if we measure the color of a hard electron, the measurement outcome should be in a superposition of being both black and white.  But this isn’t actually what happens (and is where the fifth axiom of QM comes in).  The measurement outcome is always either definitely black or definitely white (with each result have a probability of exactly .5).  (Somehow measurement ‘disrupts’ the outcome, collapsing the superpositional state into just one of its terms.)

Say our goal is to identify what ‘the liar paradox’ would look like in a physical, rather than linguistic, system.  Superposition seems like a good candidate.  When the hard electron is going through the color box, it is in a superposition of being both black and white.  But we only really understand what superposition means in a negative sense.  An electron in a superposition of being black and white is not black, nor is it white, and it is not definitely both black and white, but nor can it be neither — and what that means, we don’t really know (so we introduce the term, ‘superposition’).  In one sense, it seems that, prior to the measurement outcome, a color-property simply cannot even be predicated of the electron.  With regard to its color, literally nothing can be said.  (Until it emerges from the device, but this isn’t as relevant.)

And this starts to look like a liar paradox.  We refuse to ascribe a truth-value to ‘this sentence is false,’ in the same way we refuse to ascribe a color-property to the hard electron going through the color box.

DEM says that the result of a measurement is superposition, but the collapse postulate predicts a probalistic outcome of .5 for black.  (And how could you ever even see a superposition?)  Suppose the outcome is black.  When you measure a second hard electron, the outcome will necessarily be white.  And when you measure a third, the outcome will be black.1  This sounds like saying: suppose ‘this sentence is false’ is true.  Evaluate the truth-value of the sentence again; it must be false.  And on the next evaluation, it must be true.

The difference between the two is that, empirically, measurements must have outcomes, while the liar paradox doesn’t demand a truth-value in the same way — we can reserve our judgment.


  1. We’re fudging a bit here, but bear with me.