Abstract
Deploying distinctions between ignorance of \(p\) and ignorance that \(p\) (is true), and between knowledge of \(p\) and knowledge that \(p\) (is true), I address a question that has hitherto received little attention, namely: what is it to have knowledge of propositions? I then provide a taxonomy of ontological conceptions of the nature of propositions, and explore several of their interesting epistemological implications.
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Notes
As Zagzebski perceptively notes: “The nature of truth, propositions, and reality are all metaphysical questions. For this reason epistemologists generally do not direct their major effort to these questions when writing as epistemologists, and so discussions of knowledge normally do not center on the object of knowledge, but on the properties of the state itself that make it a state of knowing” (1999, p. 92).
One could say that Pritchard only has in mind true propositions. As I shall argue in the next section, however, it’s important to distinguish between knowledge of a proposition that is true, and knowledge that a proposition is true.
As we’ll see in what follows, considering what ignorance of a proposition consists in sheds light on what knowledge of propositions consists in.
It seems pretty clear that, whatever they are, propositions have truth-conditions. Whether they are nothing but their truth-conditions is more controversial and I think untenable, but I shall not address that issue here.
This is because \(p_{3}\) (the Twin Prime Conjecture) remains an unsolved problem in number theory.
These examples help to illustrate a distinction between what we may call “preconceptual” and “postconceptual” ignorance of a proposition: one is preconceptually ignorant of a proposition if one lacks the conceptual wherewithal requisite for having an attitude relative to it, whereas one is postconceptually ignorant of a proposition if, though having this conceptual wherewithal, one has not deployed it so as to have such an attitude. To be sure, one can be preconceptually ignorant relative to some propositions without being preconceptually ignorant relative to others, and one can be postconceptually ignorant relative to some propositions without being postconceptually ignorant relative to others.
For a defense of the complementariness of knowledge and ignorance, see Le Morvan (2010, 2011, 2012, 2013). For an alternative view, see Peels (2010, 2011, 2012). Taking knowledge and ignorance to be complements has considerable lexicographical support. For instance, the OED’s definition 1a of ‘ignorance’ is as follows: “The fact or condition of being ignorant; want of knowledge (general or special).”
As a general point (that is, one that extends beyond the question of the knowledge of propositions), knowledge how and knowledge of seem to be different kinds of knowledge, and it is far from evident that knowledge of can be reduced to knowledge how. In fact, I think that one cannot have knowledge how without knowledge of, but I shall not argue for that point here.
Someone who is ignorant of \(p\) cannot know that \(p. \)For instance, since Hypatia was ignorant of \(p_{4}\), she was in no position to know that \(p_{4}\) is true.
Just because I know of \(p\), it does not follow that \(p\) is true, or that I believe that \(p\), or that my believing that \(p\) (if I do so) meets the \(+\) condition.
This is a mistake even if \(p\) is true, for even in such a case, knowledge of \(p\) is necessary but not sufficient for knowledge that \(p\). Accordingly, knowledge that a proposition is true should not be conflated with knowledge of a proposition that is true.
Recall that I shall not be arguing that any of these accounts are true; I am only interested for the purposes of this paper in what follows epistemologically if they are true.
I am classifying as a realist theory of propositions any account that quantifies over propositions. This sense of ‘realism’ is orthogonal to the sense according to which a realist theory is one that holds that propositions exist independently of propositional attitude holders. A theory can thus be realist in one sense and not in the other, be neither, or both.
I am classifying as an anti-realist theory of propositions any account that does not quantify over propositions. This sense of ‘anti-realism’ is orthogonal to the sense according to which an anti-realist theory is one that holds that propositions do not exist independently of propositional attitude holders. A theory can thus be anti-realist in one sense and not in the other, be neither, or both.
They are thus not thoughts in the Fregean sense of the term. This conception of propositions as thoughts in the mind is suggested by Aristotle in the sixth book of Metaphysics where he writes that the true and false are in the soul. See Aristotle (1941). It can be found in the work of scholastic philosophers such as Jean Buridan. For a helpful discussion of Buridan’s conception, see Hughes (1982). It is also found in the works of non-scholastics such as Locke and other figures in modern philosophy. On Locke’s view, mental propositions are nothing but a bare consideration of ideas. See Sect. 1 of Chap. V of Book IV of Locke (1975).
See David (2009) for an excellent discussion of the distinction between the Russellian and Fregean conceptions of the nature of propositions.
This view has been revived by others, for instance Moltmann (2003).
Quine (1960) and Prior (1971) among others provide prominent metalinguistic approaches to propositional attitudes. An anonymous reviewer of this journal has suggested to me that the intensional isomorphism of Carnap (1947) may fit into this category as well. By my lights, the metalinguistic approach developed by Sellars (1963) is the richest and most powerful of these approaches.
I am simplifying matters in using “we” here; to be more precise, one could write for any \(S\), \(S\) is ignorant (or, in a weaker form, for some \(S\), \(S\) is ignorant). This precision will not matter for my purposes.
Global Scepticism\(_{\mathrm{of}}\) holds that, for any \(p\), we are ignorant of \(p\), whereas Local Scepticism\(_{\mathrm{of}}\) holds that, for some \(p\), we are ignorant of \(p\). Global Scepticism\(_{\mathrm{that}}\) holds that, for any \(p\), we are ignorant that \(p\) is true, whereas Local Scepticism holds that, for some \(p\), we are ignorant that \(p\). These distinctions will not matter for the purposes of the paper.
Scepticism\(_{\mathrm{of}}\) entails scepticism\(_{\mathrm{that}}\) because, as I argued earlier, being ignorant of \(p\) entails being ignorant that \(p\), but being ignorant that \(p\) does not entail being ignorant of \(p\).
If we have knowledge that \(p\), then scepticism\(_{\mathrm{that}}\) modulo \(p\) is false.
Parallel to how, more generally, scepticism\(_{\mathrm{of}}\) is stronger than scepticism\(_{\mathrm{that}}\) in entailing but not being entailed by the latter, so too Extra-Mental Scepticism\(_{\mathrm{of}}\) is stronger than Extra-Mental Scepticism\(_{\mathrm{that}}\), Cartesian Scepticism\(_{\mathrm{of}}\) is stronger Cartesian Scepticism\(_{\mathrm{that}}\), and Nominalist Scepticism\(_{\mathrm{of}}\) is stronger than Nominalist Scepticism\(_{\mathrm{that}}\).
The early Russell held that these objects are sense-data and therefore not mind-independent. If one divorces the Russellian theory from the early Russell’s commitment to sense-data and takes the objects in question to be physical and mind-independent, then such PA-knowledge does entail the falsity of Cartesian Skepticism\(_{\mathrm{of}}\).
In fact, characterizing incorrigible knowledge of a proposition \(p\) in terms of this bi-conditional is a bad idea, for it is possible to have knowledge of a proposition that is false.
I am very grateful to an anonymous reviewer of this journal and to Karen Le Morvan for helpful comments and suggestions.
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Appendix
Appendix
The following are some other representative examples of the equation of knowledge that \(p\) and knowledge of \(p\) that can be found in the literature:
(1) In Iannone (2013, p. 176) we find:
Philosophers distinguish various kinds of knowledge. One is propositional knowledge—i.e., knowledge of propositions—or knowledge that, e.g., of the proposition \(2+2=4\).
Notice here how Iannone—in a dictionary of world philosophy no less—equates without argument knowledge of propositions to be knowledge that (they are true).
(2) In Steup (2005, p. 1) we find:
There are various kinds of knowledge: knowing how to do something (for example, how to ride a bicycle), knowing someone in person, and knowing a place or a city. Although such knowledge is of epistemological interest as well, we shall focus on knowledge of propositions and refer to such knowledge using the schema ‘\(S\) knows that \(p\)’, where ‘\(S\)’ stands for the subject who has knowledge and ‘\(p\)’ for the proposition that is known.
Notice here how Steup, in the widely consulted Stanford Encyclopedia of Philosophy, equates knowledge of \(p\) with knowledge that \(p\).
(3) In Zagzebski (1999, p. 92) we find:
While directness is a matter of degree, it is convenient to think of knowledge of things as a direct form of knowledge in comparison to which knowledge about things is indirect. The former has often been called knowledge by acquaintance since the subject is in experiential contact with the portion of reality known, whereas the latter is propositional knowledge since what is known is a true proposition about the world. Knowing Roger is an example of knowledge by acquaintance, while knowing that Roger is a philosopher is an example of propositional knowledge (p. 92).
In this passage, Zagzebski takes knowledge of a proposition (that is true) to be equivalent to knowledge that it is true.
(4) In DeRose (2009, p. 14) we find:
I depict knowledge of p as requiring that p be true and that the subject’s belief as to whether is true match the fact of the matter, not only in the actual world, but in the ‘sphere of epistemically relevant worlds’ centered on the actual world...
DeRose in effect equates knowledge of \(p\) with knowledge that \(p\) by taking the conditions he specifies for the latter to be necessary for the former.
(5) In Plantinga (1993, p. 49) we find:
\(S\) has incorrigible knowledge of a proposition \(p\) if and only if it is not possible that \(p\) be false and \(S\) believe it, and not possible that \(p\) be true and \(S\) believe—\(p\).
Plantinga’s bi-conditional is presumably really about incorrigible knowledge that \(p\); but, in equating knowledge that \(p\) with knowledge of \(p\), he gives the bi-conditional in terms of incorrigible knowledge of \(p.\) Footnote 27
(6) In Pritchard (2006, p. 4), we find:
Think of all the things you know, or at least that you think you know, right now. You know, for example, that the earth is round and that Paris is the capital of France. You know that you can speak (or at least read) English, and that two plus two is equal to four. You know, presumably, that allbachelors are unmarried men, that it is wrong to hurt people just for fun, that The Godfather is a wonderful film, and that water has the chemical structure H\(_2\)O. And so on. (...) In all of the examples of knowledge just given, the type of knowledge in question is called propositional knowledge, in that it is knowledge of a proposition. A proposition is what is asserted by a sentence which says that something is the case.
Pritchard goes on to take truth and belief to be necessary conditions of propositional knowledge which he equates with knowledge of a proposition. He thereby equates knowledge of a proposition with knowledge that it is true, a distinction obscured by his use of the term ‘propositional knowledge.’Footnote 28
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Le Morvan, P. On the ignorance, knowledge, and nature of propositions. Synthese 192, 3647–3662 (2015). https://doi.org/10.1007/s11229-015-0712-6
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DOI: https://doi.org/10.1007/s11229-015-0712-6