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Rethinking the Synthetic a priori de re

Paul Burger
University of Bâle

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ABSTRACT: Hume and Kant destroyed the belief in the apriori de re, i.e. the rationalist’s doctrine of direct awareness of necessary facts about the nature of being. Later on, analytical philosophy told us that there are only two general classes of statements, synthetics a posteriori and analytics a priori. Quine eventually rejected the a priori in general and advanced a radical empiricism. However, both moderate and radical empiricism has recently been challenged by realistic minded philosophers. They have argued that ontological topics such as the nature of properties, laws or causation remain strongly undetermined by semantic ascent and Quinean ontological commitment, and announced an ontological turn. Are not ontological or metaphysical explanations a priori explanations? Despite his preferred talk in terms of a posteriori realism and inference of the best explanation, Armstrong’s defence of universals looks very much like an apriori one. Others, such as Barry Smith, explicitly defend that there are synthetic propositions a priori de re. I believe in both: Kant was right in claiming that an understanding of what metaphysics can teach us is dependent upon a clear concept of the synthetic a priori, but against Kant synthetics a priori de re are legitimate. In this paper I will defend synthetics a priori de re. However, I will reject the rationalist’s appeal to direct awareness of necessary facts as well as undeniableness or infallibility as necessary conditions for a prioris. Instead I will claim that all synthetics a priori express hypothetical truths.

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I shall start with a few remarks concerning the meaning of the terms in question. Still nowadays, ›a priori‹ is sometimes used in the sense of ›expressing ontological laws‹ or in Barry Smith's words: »The family of [ontological, PB] necessitation-relations extends […] to fill out the entire sphere of what, traditionally, had been seen as the domain of a priori knowledge« (Smith 1992, 309). Smith is committed to Husserl. In the 3. of his Logische Untersuchungen Husserl declares those pure laws as being synthetic a priori, in which the occuring non-formal terms are not formalizable salva veritate (Husserl, XIX/1, 260). Unfortunately, and despite my sympathy for Husserl's ontological view, such a claim does not tell us what kind of knowledge really is at stake. Smith at least seems to be willing to defend the a priori-view by appeal to »an innate capacity to discriminate between instances of categories«. Moreover, he continues that »hand in hand with this innate capacity goes the ability to grasp the associated relations of necessitation« (320). There is no point in denying some kind of innate capacity. Nevertheless, what such an appeal does not explain is in what cases and by what criteria a discrimination made is true or false. Furthermore, there is at least one hypothesis which cannot be based upon innate capacity without falling into a vicious circle, the hypothesis of having the innate capacity itself. In addition, there are those like David Armstrong who prefer to talk about ontological laws in terms of inference to the best explanation. One of the aims of this paper is to argue that ontological laws are a priori. However, I am not ready to follow Smith or rationalists such as BonJour (1992). I restrict the use of ›a priori‹ strictly to epistemic contexts. It is a common place today that much confusion was generated by logical positivists by their treating ›analytic‹ and ›a priori‹ as synonymous or as coextensional. Instead the analytic/synthetic-distinction is a semantic, the a priori/a posteriori an epistemic disctinction. The former yields information about reference or applicability of the expressions in question whereas the latter tells us what kind of evidence or thruth is involved. An analytic sentence is true even if its relevant expressions do not refer or are not applicable in the given world whereas any synthetic sentence, be it a priori or a posteriori, has to be applicable in order to be true.(1) Semantics provides us with a necessary condition. Synthetics a priori have to be applicable in some senseful way. Applicability on the one hand and evidence or truth on the other are most certainly supposed to be mutually dependent but they are obviously categorical different.


That there are no synthetic propositions a priori was the shared belief of classic analytical philosophers. That there are no synthetics a priori de re has been the shared belief of antimetaphysicians since Kant. Whereas a metaphysician claims that statements like

(1) The Universe is the only natural system with no environment.

(2) The Universe is the only strictly necessary substance.

(3) Particulars are bundles of universals.

have to be true or false, antimetaphysicians will at best be willing to accept these statements as general elements of a grammar (Wittgensteinians) or as ideas (Kantians) or as elements of a categorical framework to organise our experience (Körner 1984).(2) They believe that propositions like (1)-(3) have to be excluded from the class of true or false sentences. For the sake of argument let us take it for granted that antimetaphysicians are wrong and that our examples are synthetics a priori. In that case, we can start with two observations:

(i) Example (3) obviously indicates that synthetics a priori cannot be necessarily true as it has normally been demanded of aprioris. First, there are alternatives to (3). Second, (3) cannot be true because it would presuppose the principle of the identity of indiscernibles to be necessarily true — which it is not (cf Armstrong 1978, chap. 9). Since (3) can be true or false (acceptable or deniable), criteria such as certainty or infallibility can barely get generally accepted for aprioris.

(ii) The realistically minded metaphysician will defend some concept of nonepistemic truth. She will not accept the reduction of truth to warranted assertibility or to some meaning-based truth-conditions. Furthermore, she will call for extralinguistic truthmakers. Unfortunately, it won't help much to simply claim that our examples are true or false independent of our means of knowing. She will claim the same in regard to a posteriori truths. The demand for extralinguistic truthmakers does not dispense her from giving an account of evidence for the propositions in question. Metaphysicians who claim to work in a field of what could be called total science are obliged to give an account of the kind of knowledge they are expecting to find.

Despite their antimetaphysical attitude it may be worth reminding the reasons that Kant and the logical positivists had for rejecting the synthetic de re. Some may still be good, from others there may be lessons to learn in regard of a defensible account of synthetics a priori.

First, think of the notion of ›force‹. Suppose what seems to be a good working hypothesis that the term ›force‹ stands for some generic trait of being. Now, if you accept the rationalist's basic assumption that the mind has some direct awareness or acquaintance of necessary facts about the nature of being you are expected to have some insight in basic facts about force such that you can grasp the true propositions about it. Moreover, as a realist, you need extralinguistic entities of any kind whatever to make your sentences true. Unfortunately, and this is true even for those like me who favour a non-Humean view on causation, as far as ›force‹ is concerned there is no argument at hand demonstrating that we are acquainted with the truth-maker in question. It is a well-known fact that both Hume and Kant got influenced by this point.(3) It undermines any attempt (such as BonJour's 1992) to restore a rationalist position since in order to defend his view, the rationalist would have to show, (i) why in the case of ›force‹ there is no acquaintance with this generic trait of being although in other cases the acquaintance is supposed to be available and (ii) whether there is any case of acquaintance in necessary facts outside of logic at all.

Secondly, Kant adopted from rationalism an orientation towards certainty and undeniability. Kant believed in the coextensionality of ›a priori‹, ›strong general‹, ›necessity‹ and ›certainty‹ (cf. Critique A XV, B 3/4, »apodiktische Gewißheit«), where certainty means, as is again proposed by Van Cleve (1992), ›not truly deniable‹.(4) Kant explicitly excludes hypotheses from the domain of the apriori (A XV). Now remember our examples. Maybe (1) is a candidate for not truly being deniable. If someone claims that the universe has an environment we will readily treat what we earlier called ›universe‹ and what we now declare as its environment both as parts of the Universe, and so on. Nevertheless, someone who believes in God's creation of the Universe may deny (1). Therefore, it seems most reasonable to look upon (1) and possible alternatives as general hypotheses. (3) too is a general hypothesis based upon assumed ontological entities such as universals. Certainly, universals will never be empirically identified. The hypothetical character of at least (1) and (3) indicates that things could be just the other way round than Kant suggested. Kant's criticism on rationalism was not decisive enough as he still accepted its orientation towards certainty. If we are willing to give up the coextensionality of certainty and a priori it may become reasonable to work alongside the suggestion that all synthetics a priori are hypothetical.

Thirdly, Kant never denied that all knowledge stems from experience. Instead he could be read to take into consideration the difference between context of discovery and context of justification originally (Critique B 1). Despite the experience-dependence of knowledge there may be a class of statements for which no justification is available by inductive generalisation. We can restate Kant's point in Quineian terms. It may be the case that progress in science will force us to look for new logical systems. However, this will never change the fact that criteria for justification of logical systems cannot be empirically grounded. If we exclude the problem of whether there are a few very general nonfallible principles such as noncontradiction or consistency Quine could be done justice without any commitment to empiricism. Aprioris are true or false. However, any apriori which we are ready to give up, i.e. we believe to be false will always have to be replaced by another apriori.

Fourthly, the logical positivists rejected the synthetic a priori for two reasons. On the one hand, they refused it because of the reference of ist advocators to an inner sense as an extralinguistic mean of evidence. Not only are there no acquintances with extralinguistic truthmakers for aprioris de re there also is no extralinguistic evidence for aprioris de dicto. I agree with that. On the other hand, the synthetic a priori de re got eliminated by logical positivists because (i) they favoured sensualism, (ii) they held the semantic doctrine that meaning determines reference and finally (iii) they accepted the rationalist's orientation towards certainty too. As all of this premises got seriously criticized none provide good reasons for eliminating the synthetic a priori de re any longer — at least if one avoids appeal to inner sense or awareness of necessary facts.

So far, we get the following results regarding our defence of an account of synthetics a priori:

(i) There is no direct acquaintance with extralinguistic entities in question guaranteeing that we grasp true propositions .

(ii) Nondeniability or certainty are not necessary conditions of the apriori.

(iii) Hypotheses may very well be the general form of aprioris.

(iv) For all synthetics a priori, if a synthetic a priori will be given up it will be replaced by another synthetic a priori.

Still, nothing has been said about what kind of knowledge we gain with synthetics a priori.


In his Ontological Investigations Ingvar Johansson proposes the following threefold distinction (1989, ch. 16):



synthetic a priori

synthetic a posteriori









where T stands for ›true‹, F for ›false‹ and NT for ›necessarily true‹. He claims that synthetic statements a priori are false just in case their subjectterms do not refer, i.e. are not applicable. On the contrary, if the terms in question are applicable then the statements will be necessarily true. Although I agree with the thesis of fallibility of synthetics a priori (5) Johansson's suggestion needs refinement in order to become acceptable. Remember our examples:

(1) The Universe is the only natural system with no environment.

(2) The Universe is the only strictly necessary substance.

For (1) and (2) to be true ›Universe‹ has to be a referring expression, a denoting proper name. Moreover, (2) implies that ›Universe‹ is a referring expression in every possible world. I take (2) to function as a statement where by pure rational means a rigid designator is introduced. Of course, it is not a rigid designator like ›Socrates‹ or ›water‹. There is no demonstrative baptism. Nevertheless, it is a rigid designator as (i) it holds its reference for all possible worlds, (ii) there is no meaning in (2) involved, and (iii) science, cosmology, tends to discover as good as possible what the Universe does consist of. It is the accepted cosmological model at a given time which provides the meaning such that a analogue kind of identity-statement to ›water is H2O‹ becomes available: ›The Universe is xyz‹, where xyz stands for the group of the fundamental assumptions of a cosmological model.

I should say more about that. However, consider a sentence, well-known in todays cosmology:

(4) The Universe is homogenous and isotropic.

As ›Universe‹ is always applicable, according to Johansson, (4) would have to be necessarily true. Unfortunately, cosmologists teach us that the Universe may not be totally homogenous. (4) is at best an idealized approximation and that seems to go well with Johansson's concept of truthlikeness (or partial truth). The difficulty is that truthlike statements cannot be accepted as necessarily true. Again, the appeal to a nonepistemic concept of truth won't help. The point is not that we will never have adequate empirical criteria to decide conclusively, but that a statement like (4) does not need to be necessarily true only because the subjectterm is applicable. What Johansson should say or presumably meant to say is that if the referring expressions in the statement are applicable and if the latter is true then it expresses some kind of necessity de re: in regard to physics, that the physical world could not be different, in regard to ontology, that the general structure of being could not be different. It is not truth by itself which is necessary, but that a true synthetic statement a priori de re would express some necessary fact about reality.

Let us elucidate the point further. Remember

(3) Particulars are bundles of universals.

For a challenge, we can attack the bundle-view or we can deny that there are universals. Suppose for now that there are universals i.e. that ›is a univeral‹ is applicable. Unfortunately, Johansson's suggestion again fails to be satisfying. Despite our acceptance by hypothesis that ›being a universal‹ is applicable only one of the following sentences can be true:

(5) For all x, if x is a universal then necessarily there is at least one instance of x.

(6) For all x, if x is a universal then there may be no instance of x.

Applicability is not accompanied by ›necessarily true‹. Rather, we have a hypothetical or conditional situation: if either (5) or (6) is true, than the true sentence will express a necessary fact about reality. The same goes for another famous example:

(7) For all x, if x is an instantiation of a colour then x is extended.

I want you to interpret (7) as a synthetic statement.(6) In that case, if (7) is true it will express a necessary dependence between colour and (spatiotemporal) extension. Unfortunately, the sentence once again is not necessarily true. Suppose we advocate what Armstrong tells us to be the best version of a trope-theory, the suggestion that tropes are pointlike non-extended qualities (Armstrong 1989, 115). In that case (7) is a false proposition as an elementary colour-instance is not extended. All we get are hypothetical truths depending on the chosen ontological framework. Applicability as well as truth itself are assumed by hypothesis. Either the synthetic a priori functions as a primitive or it is a consequence of primitives.

If the truth of synthetics a priori is not guaranteed but hypothetically assumed the question arises about how to evaluate between competing proposals. Surely, apart from standard criteria such as economy, comprehensiveness, non-ciricularity, we will expect some explanatory goal regarding basic features of our experience (or better: our scientific world picture). If we agree with the latter a second question will arise. If actually all synthetics a priori are hypothetical would it not be more reasonable to prefer what Peirce called abduction instead of synthetics a priori? Peirce himself had an empiricist's view of abduction. His first and third »cotary propositions« restrict abduction to perceptual judgements.(7) I believe that Peirce let unconsidered that there are two kinds of abductive hypotheses at hand.

The well-known example »Water is H2O« may serve as a paradigm for the empirical type. On the left hand side we have a demonstratively introduced kind-term, on the right hand side a component of a scientific theory for which evidence is added by predictions, observations and experiments. Abductive hypotheses are empirical (a posteriori) iff demonstratively introduced (first order) terms and predictions, observations or experiments are involved.

It is evident that the examples discussed hitherto do not fit in this scheme. Although ›Universe‹ functions as a rigid designator (i) the entity is not demonstratively baptizable and (ii) neither observations nor experiments are available to support direct evidence for statements of the form »The Universe is F«. There is no point in claiming with Peirce that abductive statements concerning the Universe shade into some perceptual (or experimental) judgement about the Universe itself. The best what could be done is to confront (but not test) the consequences of a cosmological model with an observable region or the consequences of a naturalistic hypothesis such as (1) with the accepted scientific outcome at a given time. Nor does it make sense to talk of adding evidence for ontological statements via predictions, observations or experiments. We can think about ways for testing quarks, but not for testing universals or natural classes. Moreover and contrary to ›Universe‹, applicability for ontological terms is dependent upon the ontology defended. However, once assumed they become applicable in all possible worlds. Furthermore, there is a kind of demonstrative definition involved, although of a higher order: call ›a property‹ each case of being red, being round, having a certain mass etc. Universals or tropes and the like are then introduced in order to explain properties. As the list of properties is open and also dependent upon scientifically accepted candidates, the standard adequacy conditions of an account of properties(8) will not suffice. Any ontological theory, i.e. any synthetic a priori has to be confronted with the best available empirical knowledge at a given time.

A more detailed account of the outlined adequacy conditions would exceed the scope of this paper. However, in addition to the results of the preceeding section we get that, given we acknowledge the a priori/a posteriori distinction as epistemic, the discussed statements should be regarded as synthetics a priori. On the one hand they actually have to be considered as hypothetical: if they are true, they will express a necessary fact about the reality. On the other hand the standard criteria for aposterioris are unavailable in evaluating them. Nevertheless, there are rational criteria at hand. Plato would have said that the second best way is available only to human minds. Synthetics a priori have to have explanatorial power in regard of the best empirical theories at a given time. They have to be best explanations — they are abductive — but their means of justification are not grounded in experience — they are a priori. Certainly, they do not provide truth-criteria for empirical theories. General metaphysics can teach us what the most reasonable theory about the most general structure of being would look like. It is not nothing to know the pro's and con's for universals or the pro's and con's for a naturalistic world picture. Although such a result is not what rationalists believed to be the achievement of general metaphysics it is far more than antimetaphysicians have ever been ready to accept.

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(1) Such a view fits well with a Fregeian account of analyticity. According to his famous definition in Die Grundlagen der Artithmetik, § 3, an analytic truth is either a general logical law or such a law plus definition. The point is of course that logical terms do not refer and that definitions such as "All bachelors are unmarried men" are to be read by substitution as instances of the logical truth "All A which are B are B." Though I feel quite uncomfortable with Quinton's 1964 general account of the apriori, his four elements of analyticity provide a good base for a detailed account.

(2) Körner's use of "metaphysics" is similar to Strawson's "descriptive metaphysics."

(3) For details regarding Hume cf. Blackburn 1990.

(4) The argument often runs with the principle of noncontradiction (cf. Putnam 1983, Kuhlmann 1981).

(5) Metaphysical systems are empirically criticizable (Johansson, 331). Cf. also Bunge 1977, 1-25.

(6) It may also be interpreted analytically (cf. Schlick 1930/31). For a detailed account about how the very same sentence could be analytical and synthetical, cf. Lemos (1988).

(7) Cf. Peirce Lectures on Pragmatism § 181: 'Nihil est in intellectu quod non prius fuerit in sensu' and 'The third [...] is that abductive inference shades into perceptual judgement without any sharp line of demarcation between them.'

(8) Cf. Oliver 1996, 20-1.


Armstrong, David (1978): Nominalism and Realism (= Universals and Scientific Realism, vol. I), Cambridge University Press.

— (1989): Universals. An Opinionated Introduction, Westview Press.

Blackburn, Simon (1990): "Hume and Thick Connexion," Philosophy and Phenomenological Research, vol. 50 (1990), 237-250.

BonJour, Laurence (1992): "A Rationalist Manifesto," Hanson/Hunter, 53-88.

Bunge, Mario (1977): The Furniture of the World (= Treatise on Basic Philosophy, vol. 3), Reidel.

Frege, Gottlob (1884): Die Grundlagen der Arithmetik, ed. by Chr. Thiel, Hamburg 1988.

Hanson, Philip and Hunter, Bruce (eds.): "Return of the A Priori," Canadian Journal of Philosophy, supplementary vol. 18 (1992).

Husserl, Edmund: Logische Untersuchungen, reprinted in Husserliana vol. XVIII (ed. E. Holenstein) and XIX/1, XIX/2 (ed. U. Panzer), Hijhoff 1975/1984.

Johansson, Ingvar (1989):Ontological Investigations. An Inquiry into the Categories of Nature, Man and Society, Routledge.

Kant, Immanuel: Kritik der reinen Vernunft, Hamburg 1976.

Körner, Stephan (1984): Metaphysics: Its Structure and Function, Cambridge.

Kuhlmann, Wolfgang (1981): Reflexive Letztbegründung. Zur These von der Unhintergehbarkeit der Argumentationssituation, Zeitschrift für philosophische Forschung 35 (1981), 3-26.

Lemos, Ramon (1988): Metaphysical Investigations, Fairleigh Dickinson University Press.

Oliver, Alex (1996): "The Metaphysics of Properties," Mind vol. 105 (1996), 1-79.

Peirce, Charles Sanders: Lectures on Pragmatism, in: Collected Papers, vol. V, ed by Charles Hartshorne and Paul Weiss, Belkap Press 1962.

Putnam, Hilary (1983): "There is at Least One A Priori Truth," Realism and Reason, Philosophical Papers vol. 3, Cambridge University Press.

Quine, Willard Van Orman (1980): "Two Dogmas of Empiricism," From a Logical Point of View, Harvard University Press, 2nd. ed.

Quinton, Anthony (1964): "The A Priori and the Analytic," Proceedings of the Aristotelian Society, vol. 64 (1963/64), 31-54.

Schlick, Moritz (1930/31): "Gibt es ein materiales Apriori?," Gesammelte Aufsätze 1926-36, Hildesheim 1969, 19-30.

Smith, Barry (1992): "An Essay on Material Necessity," Hanson/Hunter, 301-322.

Van Cleve, James (1992): "Analyticity, Undeniability, and Truth," Hanson/Hunter, 89-111.

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