a priori relativo de friedman

Soochow Journal of Philosophical Studies, No. 16�August 2007�, pp.51-68©2007 Soochow University

51

The Limits of the Relative A Priori�

Christopher Pincock��

Abstract

��

��

notion has some chance of success.

� Proofreaders: Donald James Sturgeon, Ya-Ting Yang, Kuan-Jung Kao�� Associate Professor, Department of Philosophy, Purdue University, U.S.A.

Soochow Journal of Philosophical Studies, No. 16

52

I. Situating the Relative A Priori

Debates about the a priori have been dominated by two camps, which we

could call the absolutists and the nihilists. Nihilists about the a priori, like

Quine, argue that there is no interesting collection of a priori justified beliefs.

��

beliefs that were said to have been a priori justified turned out to be false.1

Here we might think of claims about the Euclidean structure of space or the

conservation of mass. Absolutists about the a priori have usually responded by

adopting a fallibilist conception of a priori justification. On this approach, we

may sometimes be mistaken when we make judgments concerning a priori

justification for this or that belief. It may seem justified, but actually be

unjustified and even false. Still, the absolutists continue, unless we can

articulate some defensible collection of a priori justified beliefs, widespread

skepticism results (Peacocke, 2004).

A key strategic move made by some absolutists is to shift from talk of

justification to the broader notion of an epistemic entitlement.2� ��

influential formulation, an entitlement to a belief by an agent at a time has

�� !��

�� "�� !� �� !�� !��

��!�� #��, 1993: 458). Among

other things, a focus on a priori entitlement makes it clearer how we could

1 See also Kitcher (2000).2 Bonjour (1998) rejects this based on a more general form of epistemic internalism.

The Limits of the Relative A Priori

53

make mistakes about which beliefs are genuinely a priori.

My topic today, though, is on a much more radical proposal concerning

the a priori than anything that absolutists like Burge or Peacocke have offered.

This is the claim that there are relative a priori beliefs. In his Dynamics of

Reason and elsewhere, Michael Friedman has argued that Quinean nihilism

about the a priori can be defeated by focusing on the role that certain beliefs

have in a given scientific theory. Here he draws on Reichenbach and Carnap,

who argued that the lesson to be drawn from radical scientific change is that

the collection of beliefs that are a priori will change from theory to theory. For

Friedman, this change does not undermine the importance of these a priori

beliefs or the need to clarify their special significance.

It remains to be seen, however, whether the beliefs that Friedman focuses

�� !� �� !��

epistemic sense. Again, appealing to Burge, an entitlem��

justificational force is in no way constituted or enhanced by reference to or

reliance on the specifics of some range of sense experience or perceptual

!�� #��, 1993: 458). It is hard to see how any a priori entitlement could

be relative to a scientific theory. If it is a priori, it is not constituted by

experience, perception or any more generous notion of experimental testing.

And if we have an entitlement, then it seems like, other things being equal,3

we have a timeless and context-independent right to the belief. If we introduce

entitlements that are relative to a theory, it seems a short step to a full blown

relativism about epistemic notions like warranted belief and even knowledge.

3 See Peacocke, 2004: 8-10, for the need for this qualification.


54

This is, after all, where Carnap ende� �� $ �� % ��

&�� '�*�� !��+

It seems to me that he can, but the costs are higher than Friedman or

anybody else defending the relative a priori has realized. All I can argue here is

that there is a defensible account of the relative a priori according to which it

seems that there are relative a priori entitlements. A definitive argument that

these entitlements exist must be pursued elsewhere. But in addition to

clarifying what relative a priori entitlements require, I also want to argue that

there is no relative a priori entitlement for pure mathematics. In future work I

hope to argue that absolute a priori entitlements exist here, but that they are not

sufficient to ground our scientific knowledge without the aid of experience and

relative a priori entitlements.

II�� Theories

Friedman begins to articulate his notion of the relative a priori using a

distinction from an early work of Reichenbach, The Theory of Relativity and A

Priori Knowledge:

Reichenbach distinguishes two meanings of the Kantian a

priori: necessary and unrevisable, fixed for all time, on the one

�� !��

/��;�� '�<��!��gues, on

this basis, that the great lesson of the theory of relativity is that

the former meaning must be dropped while the latter must be


55

retained (Friedman, 2001: =>�� ?'

Unfortunately, the notion of constitution here is very opaque. To try to make it

clearer, Friedman isolates three parts for each scientific theory: (i) a wholly

mathematical theory that includes the background geometry along with

whatever is needed to articulate and solve the equations of the theory, (ii) a set

of coordinating principles that relate this mathematics to physical structures,

(iii) candidate empirical laws that can be tested experimentally. In Newtonian

mechanics we could put Euclidean geometry and some version of the calculus

in (i). Friedman argues that the coordinating principles of Newtonian

��@��G

(1) The law of inertia: Every object in a state of uniform

motion tends to remain in that state of motion unless an

external force is applied to it.

(2) F = ma

(3) For every action there is an equal and opposite reaction.

�� @��

gravitation. For any two objects a and b,

(4) F = G ma mb / d2

That is, there is a force of attraction between the two objects that is given by

the product of their masses, divided by the square of the distance between

them, and multiplied by some constant fixed by the units. Other physical

theories are said to have a similar tripartite structure.

Once this structure of physical theories is isolated, Friedman offers the


56

following response to Quine. Against the Quinean claim that testing proceeds

via a simple conjunction of mathematics, scientific hypotheses and auxiliary

��

d�� @�� #�� ,

2001: 35). First, the coordinating principles presuppose the mathematics:

[T]he mathematics of the calculus does not function simply as

one more element in a larger conjunction, but rather as a

necessary presupposition without which the rest of the putative

conjunction has no meaning or truth-value at all. The

�� @��

elements of the language or conceptual framework, we might

say, within which the rest of the theory is then formulated

(Friedman, 2001: 36).

Most obviously, (2) is given in terms of acceleration, which is the

instantaneous rate of change of velocity, which is in turn the instantaneous rate

of change of position. Without the mathematics of the calculus, (2) would be

impossible.

Second, the empirical laws presuppose the coordinating principles. A law

like (4) is meant to apply in a restricted class of reference frames called the

inertial frames. It can be more perspicuously rendered as the claim that there

exists an inertial reference frame and that in all such frames, (4).4 So, the law

is consistent with apparent motion due to a different kind of force law as long

4 The existential commitment ascribed to this law is debatable, but will prove useful later on inclarifying these presupposition relationships.


57

as these apparent motions are with respect to a non-inertial frame. As this

privileged class of reference frames is specified by the coordinating principles,

[W]ithout the Newtonian laws of mechanics the law of

universal gravitation would not even make empirical sense, let

alone give a correct account of the empirical phenomena. For

the concept of universal acceleration that figures essentially in

this law would then have no empirical meaning or application:

we would simply have no idea what the relevant frame of

reference might be in relation to which such accelerations are

��'� &�� @��

physics are not happily viewed as symmetrically functioning

elements of a larger conjunction: the former is rather a

necessary part of the language or conceptual framework within

which alone the latter makes empirical sense (Friedman, 2001:

36-37).5

Instead of a Quinean, holistic conjunction we get a stratified picture of theories

divided into these three levels, where the lower, empirical level presupposes

the higher levels.

Friedman argues that this stratification gives us all the resources we need

to reject Quinean holism, and so to defend some more modest version of a

priori justification. For in any given case where an empirical law has led to a

5 Absolute acceleration is acceleration with respect to any inertial frame and is an essentialfeature of Newtonian mechanics. Absolute velocity turns out to be dispensable. For furtherdiscussion see Friedman (1983).


58

prediction that turns out to be incorrect, we are justified in adjusting our claims

at the empirical level, and not at the levels of the mathematics or the

coordinating principles. To be sure, there are crises in the history of science

where revisions in the mathematics and coordinating principles are considered,

but these changes are not prompted by the failure of this or that empirical law

to get the phenomena right. Instead they result from more fundamental

misgivings about the adequacy of the entire framework. For Friedman, such

crises end by the adoption of a new mathematics/coordinating principles

framework, which allows the process of ordinary empirical testing to resume.

At any given stage, then, Friedman insists that there is a serviceable distinction

between the relatively a priori parts of the theory and its empirical claims.

Ordinary testing is sufficient to rationally adjust the empirical claims, while

only a scientific revolution can displace what was once relatively a priori

(Friedman, 2001: 45-46).

III. Presupposition

Two big questions remain, though. First, what exactly is the

presupposition relation that Friedman has in mind here and are there genuine

instances of beliefs standing in this relation? Second, what grounds our

entitlement to the beliefs that are presupposed by a given theory? Again

��<��!��*��

these questions suggest an unholy mixture of semantic and epistemic elements.

We see this in Carnap, when he says that the a priori parts of his frameworks

are presupposed by the other parts because they constitute a linguistic


59

framework. Friedman also clearly has a semantic relation in mind when he

�� %�� !��^��

_��!�� G�

To say that A is a c��" ��`��

�� !��

�� '� "� ^�� "�

�^��_��!��

one and only one present King of France, in the sense that the

proposition in question lacks a truth value if its accompanying

presupposition does not hold. Similarly, in our example from

Newtonian physics, the law of universal gravitation essentially

employs a concept { absolute acceleration { which has no

empirical meaning or application (within the context of

Newtonian physics) unless the laws of motion hold. Within the

context of Newtonian physics, that is, the only way in which

we know how to give empirical meaning and application to the

law of universal gravitation is by presupposing that the laws of

motion are true: if the latter principles are not true (in the sense

that there exists a frame of reference in which they hold) then

the question of the empirical truth (or falsity) of the law of

universal gravitation cannot even arise (Friedman, 2001: 74).

@�� ^�� _�� !��

��!�� <��

descriptions. But we can s��


60

invocation of this example as a way of explaining what he takes the

presupposition relation to be.

Something has gone wrong, though, as the following simple objection

demonstrates. According to Friedman, (4) presupposes (1)-(3) in the sense that

without (1)-(3), (4) would lack a truth-value. This appears to mean that (4)

would lack a truth-value if (1)-(3) were not true. But (1)-(3) are not true. As

Friedman admits in this passage, the combination of (1)-(3) assert the

existence of a certain kind of frame of reference. But there is no such frame of

reference. So, (4) must lack a truth-value. But I hope it is not too controversial

to insist that (4) does have a truth-value, namely false. That is, far from it

be�� |�� #��

��?�� |��

arise and scientists have answered it by saying that the law is false.6 This is

especially obvious if we take the content of the law of universal gravitation to

include the claim that there is an inertial frame. If this is removed, then the law

takes on a hypothetical character: in all inertial frames, (4). Then the law will

come out vacuously true and so will still have a truth-value.

@��

a series of semantic assumptions about the relationship between the meanings

of sentences and the coordinating principles of frameworks. He may think that

(4) as uttered by us expresses a different proposition than what a Newtonian,

who accepts (1)-(3), would express by uttering the same sentence. Such a tight

link between meaning and framework principles entails a strong form of

6 ^�� |�� have interpreted the proposal in terms of ordinary truth and falsity.


61

semantic incommensura!�� _�� }�!��

�� !�� !�� ~��

�� '� �� !��

approaching semantics, so it is hard to know if he would take this line. In the

absence of any new arguments I think it is fair to dismiss semantic

incommensurability in light of our manifest ability to understand scientific

theories that depart in dramatic ways from our own best theories. In fact,

without believing that Newtonian mechanics is true, I can honestly say that I

understand it much better than the general theory of relativity, which I believe

to be our best theory of large-scale physical phenomena.7 Among other things,

I can understand the notion of an inertial frame and at the same time know that

there are no such frames.

Once we set aside these semantic assumptions we arrive at a more

traditional picture of sentences expressing language-independent propositions.

These propositions can be grasped by scientists who possess the relevant

concepts and it is of course possible to understand all these propositions in

advance of determining whether or not they are true. Is there any space left for

relative a priori entitlements? In his perceptive critical ��

book Lange notes two potential presupposition relations that fit with

�� '� ��

semantic relation, Lange also articulates an epistemic presupposition relation:

�`��Friedman, our observations can count as evidence for or against

@�� @��

7 Friedman does discuss a neo-Newtonian theory that is available from within the mathematicalframework of general relativity theory, but this is not what I have in mind here.


62

��~�� #��, 2004: 703). Although he says on

��}�� #��, 2004:

704), I take this to be a promising presupposition relation between propositions.

On this approach, A presupposes B when being entitled to A requires that we

believe B. The entitlement to believe A is only available to someone who

!��'�^��!��#�?��@�� '��

only if someone believes the laws of motion, and so actually believes that what

he is observing relates to an inertial frame, that empirical testing of (4) is

possible. In this theoretical context, the observations can tell in favor of (4).

Outside of this context, no entitlement to (4) exists.

To make this presupposition claim more plausible, consider an example of

testing within the Newtonian framework. In 1705 Halley made the prediction

that a certain comet would return in 1758. To make this prediction Halley

�� |�� @��

laws of motion. Crucially, this entitled him to the belief that the frame of

reference centered on the Sun approximates an inertial frame. Using the law of

universal gravitation along with some parameters like two points on the known

trajectory of the comet, Halley then was able to predict when it would return.

Later, when the prediction turned out to be correct, based on observation O,

this law received a boost in confirmation. I think there is a clear sense in which

this empirical test could not have been implemented by someone who did not

believe the mathematics and the coordinating principles. The calculations and

the intermediate result about the frame centered on the Sun would simply not

have been available to contribute to the confirmation of the law. More

schematically, O by itself does not constitute a reason to believe (4). It is only


63

a reason to believe (4) for someone who also believes (1)-(3), as only they are

able to ascertain the link between O and (4).

So far we have been discussing the sense in which the empirical laws

presuppose the coordinating principles. What about the alleged presupposition

relation between the coordinating principles and the mathematics? If the

current epistemic account of presupposition is to work we must argue that

there can be no entitlement to believe the coordinating principles unless we

believe the relevant mathematics. This seems incorrect, at least if we think of

the coordinating principles in a certain natural way. According to Friedman,

@�� }��

frames. These frames are specified using their mathematical properties as well

as their physical properties, such as spatio-temporal relations. But there is no

need to use exactly the same mathematics that Newton did in claiming that

these frames exist. In fact, the mathematics used to present Newtonian

�� !�� @��

Principia through to its most sophisticated presentation in what is often called

analytic mechanics. 8 This suggests that the relationship between the

mathematics and the coordinating principles is much looser than the

relationship between the coordinating principles and the empirical laws. While

the empirical laws presuppose those very coordinating principles, the

coordinating principles can occur along with a wide variety of mathematical

theories.9 To see the implications of this variability, we need to get clearer on

the basis of our entitlement to the coordinating principles.

8 Cf. Lange, 2004: 706.9 So the semantic presupposition relation defended by Friedman also fails here.


64

IV. Entitlement to Relative A Priori Beliefs

Suppose that everything I have said so far is correct and that there is an

epistemic presupposition relation between some empirical laws and

coordinating principles. Still, our entitlement to believe the coordinating

principles may be nonexistent or may turn out to be empirical. For example, an

absolutist about a priori entitlement may insist that what entitled Newton to

believe his laws of motion was a complicated inference to the best explanation

using the empirical data assembled by earlier scientists like Kepler. If this is

right, then the entitlement to the laws of motion is empirical and not relative to

a theoretical context in any interesting sense. For the mathematics, the

absolutist will either insist on traditional absolute a priori entitlements or opt

for empiricism here as well.

It remains unclear to me what Friedman would say to answer this

question, and I take it that the reason he does not face this issue is because he

has not isolated a workable presupposition relation. Can we at least articulate

an account of entitlement here that is consistent with some kind of relativity?

^�� !�� *�� !�� }��

questions and practical reasoning. For Carnap, genuine theoretical reasoning

can occur only for internal questions, and so only after the adoption of a

linguistic framework. What entitles us to choose this or that linguistic

framework is the practical point that it is only by adopting some framework

��'��

our purposes here.

Suppose our goal is to understand some well articulated physical domain


65

like the motions of the planets or the patterns of the tides. On our picture so far

the propositions accounting for these phenomena are accessible independently

of our belief in any given package of coordinating principles. Still, belief in

some package is necessary in order to have access to any entitlements that

might exist for one or more of these propositions. In such a situation I claim

that an agent is entitled to believe one of these packages of coordinating

principles. This entitlement obtains at least until the putative law is

disconfirmed via ordinary empirical testing. At that time, the agent may

reasonably stick with that set of coordinating principles and test another

candidate empirical law, or else shift to another set of coordinating principles

that is needed to test some different kind of empirical law.

Is the entitlement in question a priori? It passes the letter, if perhaps not

�� G� ��

constituted or enhanced by reference to or reliance on the specifics of some

�� }�� !��' � ^�� !��

justificational force turns on the practical goal of confirming this or that

empirical law. The epistemic presupposition relation obtains independently of

the empirical contingencies that Burge mentions, and so it is a priori. But, then,

in what sense is this a priori entitlement relative to a theoretical context? It can

happen that a package of coordinating principles has been so thoroughly

explored that a wide range of candidate empirical laws that are confirmable

within that framework have been disconfirmed by experiment. With this

historical record at our disposal, I claim that we are no longer entitled to

believe this package of coordinating principles. As a practical means to the end

of confirming some empirical law that will account for the phenomena, this


66

package has failed. This is, after all, how we think of Newton�� '�

As coordinating principles, Newton and his immediate successors were entitled

to believe them. But we have lost this entitlement.

V. Mathematics is not Relative A Priori

Entitlement to believe this or that package of coordinating principles is

relative, then, in the sense that the accumulation of the historical record can

indicate that believing this package is a poor means to the end of empirical

testing. Nothing like this is available for mathematics, and until Friedman or

somebody else can explain their account of mathematics, it seems clear that

entitlements in mathematics are either absolutely a priori or empirical.

In favor of mathematical entitlement being absolutely a priori, it is first

important to notice that mathematical revolutions lack many of the features of

scientific revolutions. Even when Euclidean geometry was discarded as a

theory of physical space, it was still retained as a genuine mathematical theory

that we know to be true. This knowledge rests on entitlements tied to

mathematical proofs. It remains unclear what the basis of our entitlement to

the axioms and logic that allow these proofs is. But it is not plausible that they

rest on the role of mathematics in scientific experiment (Pincock, 2007).

Friedman himself se ��

�� <� �� "� �� !��

mathematical structures, whose distinctive theorems and principles are

�� #�� , 2001: 80). Here, then, we see that

a defensible notion of relative a priori entitlement may rest on a core of


67

absolute a priori entitlements.

If this is right, then, what is the presupposition relation between the

�� @�� @�� of motion? While I

argued earlier that no particular mathematical theory is required to have an

entitlement to believe the coordinating principles, I suggest that some

minimally strong mathematical theory is epistemically presupposed. Once this

minimal mathematics is in place, we obtain the entitlement based on the

practical reasoning sketched above. Without the mathematics, this practical

reasoning breaks down and the entitlement evaporates.


68

References

Bonjour, Laurence (1998). In Defense of Pure Reason. Cambridge.

Burge, Tyler (1993). Content Preservation. Philosophical Review, 102:

457-488.

Friedman, Michael (1983). Foundations of Space-Time Theories. Princeton.

Friedman, Michael (2001). Dynamics of Reason. CSLI.

Kitcher, Philip (2000). A Priori Knowledge Revisited. In Boghossian &

Peacocke (Eds.), New Essays on the A Priori (pp. 65-91). Oxford.

Lange, Marc (2004). Review Essay on Dynamics of Reason by Michael

Friedman. Philosophy and Phenomenological Research , 68: 702-712.

Peacocke, Christopher (2004). The Realm of Reason. Oxford.

Pincock, Christopher (2007). A Role for Mathematics in Physical Theories.

Nous, 41: 253-275.

a priori relativo de friedman

Documents