On Truth and Self Reference: A Return to the Realms of Philosophy

Posted: September 21, 2009 in Uncategorized
Tags: , , ,

I started a philosophy class, and immediately got sick, so I missed the second class. However, in a very interesting attendance policy, I was required to write a paper about the readings we discussed the day I was absent. As I was writing it, I figured it would help to post it here. So here are my thoughts on paradox and self reference:

In order to truly understand the nature of paradoxes, it is first imperative to understand both the concept of truth and of self reference. For truth, we turn to Michael Glanzberg’s entry on the subject in the Stanford Encyclopedia of Philosophy, and for self reference we turn to Thomas Bolander’s entry on the subject in the same publication.

Glanzberg discusses truth first by going through some of the theories of truth. Where we might think that there is only one Truth (with a capital C), it turns out that how we define something as true has an inherent and very important decision about the world. For example, the correspondence theory, which Glanzberg attributes to GE Moore and Bertrand Russel, states that “a true propositions is identical to fact,”1 which contains in it the assumption that the language which forms propositions is connected to the ‘real world’ in a significant way. That is, there is access to reality through language, and that the signs in language actually do signify reality. Moore and Russel prefer a phrase like “A belief is true if and only if it corresponds to a fact,2 as this more accurately represents the world view. It is also interesting to note that Plato said that knowledge consisted of Justified True Belief3; this phrase and the whole correspondence theory of truth resonate in in this idea.

There is also the neo-classical view of truth, which states that “a belief is true if there exists an appropriate entity—a fact—to which it corresponds. If there is no such entity, the belief is false.4 This brings with it an interesting epistemic view: that there must be existence, there must be reality that exists outside of language. This is an important presupposition.

Glanzberg goes on to gain make reference to Plato’s Justified True Belief when discussing Coherence Theory, giving it the slogan “A belief is true if and only if it is part of a coherent system of beliefs.5 Coherence theory demands that truth be part of a whole, that there is only one Truth, though there may be other truths that the Truth is made up of. Thus, in order for something to be true, it needs to be coherent with the rest of the Truth. Coherence, then, would be a stronger requirement than Consistency. That is, it’s not enough that something be consistent (ie, non-contradictory) with the structure of the truth as a whole. It must also be coherent.

Next the article moves on to discuss sentences as truth bearers. These sentences being what Quine (1960) called ‘Eternal Sentences’6; that is, their meaning is not context-dependent.7 These sentences are part of a fixed language whose sentences are fully interpreted. This leads us to Convention T, which states “An adequate theory of truth for L must imply, for each sentence Φ of L “Φ” is true if and only if Φ.”8 So if every sentence in L has a truth value (as it should if L is fully interpreted), then “Convention T guarantees that the truth predicate given by the theory will

be extensionally correct, i.e., have as its extension all and only the true sentences of L.”9

Moving on through the article, we eventually come to Glanzberg’s discussion of revisiting correspondence in light of facts and truth makers (A truth maker being something in the world that makes the sentence true.10). Facts he says, make good truth makers. He also makes the controversial claim that “Negative facts would be the truthmakers for negated sentences.”11 We say this is controversial because Glanzberg mentions that Russel is ambivalent about them, while Beall and Armstrong defend or reject them, respectively.

The remainder of the article covers realism, anti-realism, deflationism, and and the redundancy theory, which asserts “there is no property of truth at all, and appearances of the expression ‘true’ in our sentences are redundant, having no effect on what we express,”12 before finally moving on to the last thing we’ll talk about here: Truth and Language.

Theories of truth are theories of reality. Sentences to which Tarski’s theory applies “characterize the world as being some way or another, and this in turn determines whether they are true or false”13; in fact, “any theory of truth that falls into the broad category of those which are theories of truth conditions can be seen as part of a theory of meaning.”14 This is significant; as we have seen before, any theory of truth (that is a theory of truth conditions) is a theory of meaning: thus, any of these theories make epistemological claims about what is and what we can know.

What, though, is the point? To answer that question, we move on to Thomas Bolander’s article on Self Reference. Bolander starts his article by defining self reference. He says that it “is used to denote a statement that refers to itself or its own referent.”15 The most famous of these, of course, is the liar’s paradox (“This sentence is not true”). Self reference seems to be the source of many of the most difficult semantic paradoxes.

Bolander goes through these paradoxes in rapid fire, hitting Grelling’s paradox about whether or not “heterological” is heterological, where heterological is defined as “does not itself have the property it expresses,”16 then moving on to Set-Theoretic paradoxes like Cantor’s paradox and the Hypergame paradox17, before moving on to Epistemic paradoxes like the paradox of the knower18. Thankfully, after this he settles down to discuss the structure of paradoxes, setting up the idea that “even if paradoxes seem different by involving different subject matters, they might be almost identical in their underlying structure.”19 This is a helpful idea: if all these paradoxes do have identical, or even similar, underlying structures, then the same methods to solve one should help to solve all of them. Bolander goes on to show how all, or at least most, paradoxes of self-reference follow the same structure. Priest (1994), then presents the principle of uniform solution: “same kind of paradox, same kind of solution.”20

Bolander discusses why paradoxes matter, saying that “The significance of a paradox is its indication of a flaw or deficiency in our understanding of the central concepts involved in it.”21 So if we are to quest for knowledge, in particular for certain knowledge, then we must deal with these paradoxes. And there are several methods to try.

Bolander suggests two main methods: formalizing knowledge as a predicate in a first-order logic (syntactic treatment of knowledge) or formalizing knowledge as an operator in modal logic (semantic treatment of knowledge).22 The problem with these two is that it leads to problems of inconsistency, like Tarski’s theorum or Godel’s incompleteness theorum. Attempts to solve paradoxes of self references show one important thing: “there are limits to what can be proven and what can be computed,”23 which does not bode well for the idea of certain knowledge. Thankfully, Bolander moves on to a section about how to solve, or at least get around, these paradoxes.

The main point of the remainder of the entry is the idea of hierarchies. Of type theory. As Bolander writes, “The fundamental idea of type theory is to introduce the constraint that any set of a given type may only contain elements of lower types (that is, may only contain sets which are located lower in the stratification). This effectively blocks Russel’s paradox, since no set can then be a member of itself.” This also blocks the liar paradox, because “now a sentence can only express the truth or untruth of sentences at lower levels, an thus a sentence such as the liar that expresses its own untruth cannot be founded.”24

While this does move around the paradoxes, and therefor opens the door for us to still know things, it seems to me like a bit of a dodge of the issue. Bolander himself admits that it is a way around, rather than through, the paradoxes. Maybe there isn’t a solution; if there were, it probably would have been found already. If that is true, then we have to be satisfied with avoiding these paradoxes if we expect to know anything for certain. It may be, then, that the nature of a paradox is that it shows us where we need to make moves and add rules to ensure that we don’t run into them. That the paradoxes themselves are interesting intellectual exercises, but in and of themselves are not particularly valuable, at least in so far as favoring the development of a corpus of knowledge.

1Glanzberg, “Truth” in Stanford Encyclopedia of Philosophy, page 3.

2Ibid, page 5. Italics in original.

3In the Theaetetus.

4Glanzberg, “Truth” in Stanford Encyclopedia of Philosophy, page 5

5Ibid, page 8.

6Though it can easily be argued that there is no such thing as a true ‘eternal sentence,’ that is a subject for another time, so the idea will be granted for our purposes.

7Glanzberg, “Truth” In Stanford Encyclopedia of Philosophy, page 11.

8Ibid, page 12.

9Ibid, page 12. Italics in original.

10Ibid, page16.

11Ibid, page 17.

12Ibid, page 22. It should be noted that this particular theory seems to have a circular component to it: if there is no property of truth, how can we claim that redundancy is true?

13Ibid, page 25.

14Ibid, page 28.

15Bolander, “Self-Reference” in Stanford Encyclopedia of Philosophy, page 1.

16Ibid, page 3.

17Ibid, page 4.

18Ibid, page 5.

19Ibid, page 6.

20Ibid, page 8. Italics in original

21Ibid, page 9.

22Ibid, page 16.

23Ibid, page 19.

24Ibid, page 20. Italics in original.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s