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.


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.


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.)


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.