Thoughts on Kearns Possible Worlds and Modality

I found the section on Epistemic modality to be of particular interest because of its relation to the deflationist definition of truth. During the take home exam, I thought a lot, as all of us did, about what it means for something to be true. Under the deflationist theory of truth, the definition holds no meaning because we have no divine insight into what is actually true. To them, the words true and truth are simply conveniences to convey a perception of truth. Epistemic modality differs from logical modality in a similar way to how deflationist truth theory differs from coherence theory. This form of modality expresses what may be possible or necessary, given what is known. Epistemic modality does not guarantee that the contained proposition is true, only that it logically follows what is understood to be true. This fits into possible worlds the same way: if there exists a world where the inhabitants have reason to believe a possibility or necessity. I find it hard to conceptualize other worlds in the concrete way that the reading demands, but am trying.

Evaluating Theories of Truth

While trying to evaluate various theories of truth, I have found that most theories are self-serving to one’s personal interpretation of truth, rather than distinct ways of viewing the same concept.  Compare these two quotes regarding truth: “Truth is rarely writ in ink.  It lives in nature.” (Martin H. Fischer), and “Every truth bends and is reshaped by other forces.” (Leslie Woolf Hedley).  Fisher, a psychologist, presents an understanding of truth very compatible with realism.  Truth lives independently of us, regardless of our (mostly unsuccessful) attempts to capture or describe it.  He would agree with correspondence theories of truth, although here he contends that most human propositions fail to fully capture these truths.  But if truth is something that exists independently of humans, what does that say about the “truth” of anything intangible that humans create?  Realism states that reality, the state of the world, is consistent for everyone.  However, pragmatics counter that one’s reality is not the same as another’s, and therefore two truths can occur simultaneously because they are relative to the conceptual scheme in which they exist.  This understanding of truth is what Hedley was getting at.  On a spectrum that ranges from “fact” to “opinion”, Hedley’s interpretation of truth would land much closer to “opinion” than Fisher’s.  To me, it is unclear whether either truth theory is more valid than another.  They are both completely acceptable and sound depending on one’s definition of truth, and each become implausible when applied to the other’s understanding of truth.

I’m wondering what course a debate between a realist and a pragmatist would take if they were to agree on a common conception of truth beforehand, of if that would be possible.  As people with less stake in the outcome of the debate are we allowed to have various definitions of truth, and change them to fit our situation as needed?  It seems as though it is necessary to consistently follow one truth theory but is it possible to separate out the situations in which the various theories are applicable?

A Paradox of Ecological Rationality?

I just wanted to share a paradox that occurred to me as we concluded our discussion about Gingerenzer’s theory of ecological rationality.

If we measure rationality to be heuristics that produce “actual success in solving problems” (Gingerenzer, Bounded and Rational, 123), it may lead us down a slippery slope. Humans are not the only organisms that exhibit rational heuristics by this definition — take a dog, for example. A dog acts very friendly towards its owner, which is a very reliable heuristic for securing a stable food supply and place to live. Thus dogs are also rational. We could continue to find examples of increasingly simpler beings and find heuristics that we could call rational. But at what point could we draw the line? Can we draw a line? If a line can be drawn, wouldn’t the definition of rationality consist in (or be defined by) that line?

Here’s a phrasing of the paradox that mirrors the sorties paradox. Humans are rational when they use effective ecological heuristics. A slightly less complex being is rational when using effective ecological heuristics. By induction, a rock is rational when using effective ecological heuristics. One such heuristic is being hard, which solves the problem of persistence, since on Earth hard things tend to exist the longest.

The paradox consists in that it is exceedingly implausible that a rock is to any extent rational. I’ve thought of two different resolutions to the paradox: (1) accept that rationality admits to degrees, or (2) claim that rationality also depends on adaptability to different environments.

Supposing (1), we could say that less complex beings are less rational. In effect, rationality would be a function of successfulness of ecological heuristics and cognitive complexity. From this position, it would follow that we could conceive of some extremely rational being with equally extreme computational power. But this entity would be essentially the same as the omniscient being from the unbounded rationality camp. Supposing (2) also takes us down a similar path, where an infinitely adaptable being would be infinitely rational, but I think infinite adaptability approaches to content-blind rationality, since isn’t a rule for determining which set of rules (corresponding to a particular environment) to apply after all environment-independent?

Thoughts on rationality & content-blind norms

I found Gigerenzer’s argument for the ecological rationality of heuristics and his argument against content-blind norms to be compelling. Specifically, I’d like to share some of my thoughts about content-blind norms.

Intuitively, it seems to make sense that rationally parsing meaning should be a content-blind process. After all, if it weren’t, wouldn’t content-dependent interpretation already require a preconception of the content’s meaning? If so, it seems this would amount to infinite regression, or a recursively defined meaning-generating function that accepts meaning of the sentence as input.

Let M be a function that maps from a sentence s to a meaning m (so we could say M(s)=m). Let D be the incomplete meaning-generating function from the above paragraph, where D maps a proposition (P) and meaning (m) to a (hopefully more complete) meaning. With this, we could write M(s) = D(P, M(s)). To clarify, proposition P corresponds to the content-blind syntactic structure of sentence s, while the meaning is the complementary context-sensitive component of sentence s.

Clearly, function D doesn’t do anything except call itself ad infinitum. It does, however, indicate what properties a correct semantic interpretation function C must possess: a base case for generating meaning that requires no precomputed meaning, and a means of reducing the extent of precomputed meaning required. That is, C(P, ε) must be defined, and C must satisfy M(s) = C(P, M(s’)), where s’ is a “less meaningful” sentence than s in some way.

The necessary existence of a base case suggests that at there must be some class of sentences whose meanings are entirely content-blind. I take this to mean that rationality is ultimately rooted in some fundamental set of processes that are entirely context-blind. That is not to say, of course, that rationality can be defined by content-blind norms—only members of this fundamental set can be defined by them.

I do not think this conclusion contradicts Gigerenzer’s view on viewing rationality in terms of content-blind norms. As Matheson puts it, “that cognitive virtue cannot be located entirely within the mind does not imply that it is located entirely outside the mind” (143). Supposing content-blind norms alone cannot be used to measure rationality, this question arises: can solely content-sensitive along with content-blind norms be used to measure rationality? For those two types of norms to suffice would require rationality to be purely self-blind. That is, for a given sentence, there would be one unique rational way to interpret it (ignoring situations of ambiguity). But is this the case? Each individual obviously interprets identical sentences in nonidentical ways. If rationality is self-blind, then, although no one may actually be 100% rational, we could conceive of someone who is 100% rational, the epitome of human rationality norms. Moreover, this would suggest that there could exist no two people who are fully rational yet with different minds.

I think it likely that rationality is also self-sensitive; that is, rationality needs to be evaluated with respect to the (ir)rational agent.

Thoughts on theories of truth

Because I’ll be missing class on Thursday, I decided to write a blog post with some of my thoughts about the reading (specifically Glanzberg’s survey of theories about truth in the Stanford Encyclopedia of Philosophy).

At first glance, the Correspondence Theory of truth seemed convincing in its simplicity and its similarity to the truth-conditional theory of meaning. Glanzberg’s slogan for the theory, “a belief is true if and only if it corresponds to a fact” (section 1.1.1), is enticingly intuitive — after all, isn’t truth inherently fact-based? Facts aren’t subjective, nor is truth, seemingly. I interpreted that “the existence of facts is the ‘first truism'” (section 1.1.2) to mean that the existence of facts gives rise to the concept of truth. Although I do think it is important for a theory of truth to describe from what truth arises, I am not convinced of this particular explanation. For one, it doesn’t answer what gives rise to falsity. Perhaps one could say nonexistence does, but that is prematurely introducing a logical negation that operates on bivalent truth values, which presupposes the existence of truth and falsity to begin with.

Here’s a thought experiment (I know “Schroedinger’s cat” is a bit overused, but it serves well to make my point — if you’re tired of hearing about it and just want it to be dead already, just imagine a photon with uncollapsed polarization instead). What is the truth-value of the proposition “Schroedinger’s cat is alive”? I’m not sure how correspondence theorists would handle this. The claim that the statement didn’t correspond to any fact in the real world and was therefore false would imply that the statement’s negation, “Schroedinger’s cat is not alive,” is true, but I would argue it is not, even in a correspondence theorist’s paradigm — in what characteristic(s) of the real world would the fact corresponding to Schroedinger’s cat not being alive consist? Certainly not the cat’s state inside of the box, since that is not only unknown but undecided. Perhaps the corresponding fact could be in the lack of a dead or alive state, but I would argue that that is simply a fact about the nonexistence of a fact. Although that could possibly work, it leaves me unsatisfied. I’m curious to hear what other people think about this thought experiment.

I found Tarskis’ theory of truth (section 2), particularly “Convention T,” difficult to follow. It seems that his theory doesn’t provide a solid, fundamental basis for truth or ground it in the actual world. (I’m sure the recursive nature of his definition of truth contributes to this notion.) One advantage his theory offers, though, is that it determines whether languages are consistent or inconsistent. In inconsistent languages, such as those that contain the Liar Paradox, I gather that truth isn’t a universal quality in that every sentence must be true/false. Perhaps the idea of an inconsistent language could help resolve the questions raised in the thought experiment I proposed in the previous paragraph.

Reading about consistent vs. inconsistent languages led me to the following questions: in an empty language, does truth exist? What about in a language describing an empty world?  To combine what I’m getting at with both those questions, can truth exist without meaning? Can meaning exist without truth? As I see it, truth is not something inherent to the universe. Nothing in the physical world exhibits falsity, I would argue. Falsity seems to arise in a language that is used to formulate propositions, which have truth value. To address the last question, I do think meaning can exist without truth. Consider the Liar Paradox and the opposite proposition, “This sentence is true.” Neither have truth values, but I would argue that they do have distinct meaning.

There’s a lot more to say about all the theories mentioned in Glanzberg’s article, many of which I didn’t even touch on. I will say that I’m most drawn towards the Coherence Theory of Truth, as it seems to hold up under most criticisms, including the “unknown quantum state” thought experiment.

(written by Nicholas Mosier)

Welcome

Using logical and mathematical tools, formal semantics answers the following questions: Why do sentences mean what they mean? How is reasoning possible? How does language structure our understanding of time, change, knowledge, morality, identity, and possibility? We will assess formal semantics as a theory of linguistic meaning and reasoning by comparing its predictions with linguistic and psychological evidence. We will also examine its philosophical assumptions. This course is well suited for students interested in computer science, linguistics, logic, mathematics, or philosophy. (Some prior familiarity with formal logic is recommended, but not required.)

Course meeting times and places:
Tuesday and Thursday: 9:30AM-10:45AM in Bicentennial Hall, Room 219
Wednesday: 11:15AM-12:05PM in Twilight Hall, Room 302
Office hours:
Wednesday: 2:30PM-3:30PM in Twilight Hall, Room 303A
Thursday: 11:30AM-1:30PM in Twilight Hall, Room 303A