Profile on epistemology: from cheshire cats to deep disagreement

Published: June 28, 2018

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The tri-campus Department of Philosophy is very proud of the breadth of specialists we have in all branches of philosophy, and we’ve started to feature brief reflections from a diverse range of our scholars on key issues in their particular fields. In the last issue of our annual magazine, Philosophy News, we focused on epistemology, the branch of philosophy concerned with the theory of knowledge and related concepts such as truth, belief, and justification.

In addition to Professors Benj Hellie (UTSC), Jennifer Nagel (UTM), Gurpreet Rattan (UTM), Jonathan Weisberg (UTM), Franz Huber (St. George), Lecturer Kenneth Boyd (UTSC), and PhD students Jessica Wright and Julia Smith, our complement of epistemologists was expanded by the arrival of Professor David Barnett (St. George) last year and Postdoctoral Fellow Stefan Lukits (St. George) this year. In what follows, four of these scholars share some of their contemplations on various problems in epistemology.

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PhD Student Julia Smith: Theoretical Rationality and Belief

Brain with strings flowing through it (illustration)

The question of theoretical rationality is the question of what beliefs we should have, if we are rational. There is plenty of disagreement among epistemologists about what the requirements of theoretical rationality are. Directly bearing on this disagreement is an interesting question about whether it is ever possible to be rationally mistaken about what theoretical rationality requires.

On one hand, if a rational person can never be wrong about what rationally requires her to believe, we get the odd result that one’s total evidence regarding the requirements of rationality can never be misleading. This is unusual because our everyday lives are rife with misleading evidence (for example, false testimony from a usually reliable source), so it would be strange if evidence about the requirements of rationality were different. On the other hand, if a rational person can sometimes be wrong about what rationality requires her to believe, we get the odd result that there are cases in which agents ought to believe Moore-paradoxical propositions of the form “P, but it’s not rationally permissible for me to believe that P.” So, can mistakes about what we ought to believe be rational? Deep exploration of this question will help shed light on the nature of rationality, a key norm in epistemology.

Postdoctoral Fellow Stefan Lukits: Cheshire Cat Partial Beliefs

Illustration of cheshire cat in a tree

Illustration d’origine (1865), par John Tenniel (28 février 1820 – 25 février 1914), du roman de Lewis Carroll, Alice au pays des merveilles.

In metaphysics, Nietzsche complains that Descartes’s conclusions about the existence of a thinking self are based on grammar rather than sound logical inference. My current project is to pursue a Nietzschean-type criticism in formal epistemology. The culprit is again Cartesian, but this time it is the Cartesian coordinate system that implements a grammar misleading us to unwarranted epistemological conclusions.

Statisticians think of the set of normal distributions as manifolds—sets that behave locally like Euclidean space. Normal distributions, for example, are characterized by the mean and the standard deviation, which serve as coordinates that map normal distributions onto Euclidean space.

It is a current trend in formal epistemology to evaluate competing belief states using a scoring rule or some metric. Compromise is necessary between informative and accurate beliefs. Formal epistemologists want to use mathematical models to provide useful descriptions of this compromise. A scoring rule will ideally reveal the conditions of commensurability between informativeness and accuracy (given a number of assumptions). A proper scoring rule ensures that the belief state of all and only true beliefs fares well.

Coordinate systems are useful in creating these mathematical models. The Brier score or information entropy are interesting examples of these models. Deceptively, sometimes we begin to think of credal states as geometrically embodied in their parameters rather than represented by them.

My Nietzschean criticism encourages a move away from coordinates towards the manifolds of differential geometry. When you first learned what the constant angle sum of a plane triangle was you most likely absorbed the news in coordinate-free geometry. Later on, however, geometry became easier by using coordinates, usually Cartesian coordinates.

In modern physics, just as in epistemology, dependence on a particular representation in coordinates can become more of a liability than an asset. Modern physicists often do not want to think of space in terms of coordinates. Relativity theory especially has accelerated the transition from the vectors of the Cartesian grammar to the tensors and fibre bundles of differential geometry. The relevant relationships are now no longer between parametric representations (for example, the mean and standard deviation of the normal distribution), but between derivations (generalized derivatives, thus the name differential geometry) and a metric based on an inner product defined on tangent spaces (such as the Fisher information matrix).

For the categorical distribution with a finite event space (for example, die rolls and coin tosses) the finite set of probabilities is usually considered to be the set of parameters or coordinates of the belief state—in order to characterize the probabilities 60% for heads and 40% for tails I would consider the point (0.6, 0.4) in a Cartesian coordinate system. But then highly counterintuitive things happen!

When Foucault talks about sexuality, he uses the Cheshire Cat of Alice in Wonderland as an illustration of “smiles, happinesses, pleasures, and desires as qualities without an abiding substance to which they are said to adhere. As free-floating attributes, they suggest the possibility of a gendered experience that cannot be grasped through the substantializing and hierarchizing grammar of nouns and adjectives” (Judith Butler in Gender Trouble, page 32).

The current ambition in formal epistemology is to highlight parameter invariance as a discriminating feature between mathematical models. Following successes in physics and statistics, I am looking for ways in which the parameters can become an afterthought rather than a determining constituent of how we think about the relationships between different belief states. Let the doxastic landscape be, as Foucault expresses it in a very different context, “a world of pleasures in which grins hang about without the cat.”

Associate Professor Gurpreet Rattan: The Intellect and Its Limits

Comic panel of man thinking hardThinkers have a capacity to evaluate and improve their own and others’ thinking, even at the most fundamental levels of belief and method. At these most fundamental levels, the relevant kind of evaluation involves targeting not only what one thinks, but also the conceptual and methodological resources used to think and reason at all. The intellect is the faculty of mind that underlies these capacities. Although significant attention has been paid to the cognitive bases of much of our rational belief and knowledge—including perception, memory, metacognition, introspection, communication, and inference—the intellect has been, in contemporary philosophy at least, largely overlooked.

In my current project, I aim to correct this oversight and to provide foundations for future work by giving an account of the intellect. On the view that I develop, the intellect is concerned with establishing a proprietary kind and quality of knowledge—knowledge that is informed by epistemic values of conceptual understanding, methodological understanding, intersubjective understanding, and objectivity. Knowledge infused by the intellect aspires to clarity of thought and method, deep understanding of conflicting perspectives, and objectivity in the evaluation of one’s own and conflicting perspectives.

This account of the intellect lands the intellect at the centre of a network of fundamental philosophical debates about truth, disagreement, and relativism. My account of the intellect is the basis for unified answers to some hard questions in these debates, like: what difference does possessing the concept of truth make for our knowledge? What is the epistemic significance of deep disagreement? And: how should the doctrine of relativism be formulated and evaluated?

Finally, my project is concerned not only with the nature of the intellect, but also its principled, necessary, limits. Ultimately, my account of the intellect is meant to cast illumination on the trenchant difficulties involved in justifying our fundamental beliefs and methods, in changing one’s framework for thinking, in persuading others with whom one is in deep disagreement, and for claiming an objective basis for one’s perspective. For the last 50 years or so, the doctrine of relativism has held out the promise of explaining some of these difficulties. The main innovation for thinking about these difficulties that I would like to introduce is to suggest a move away from relativism and towards an appreciation of the role of the problem of other minds.

Professor Benj Hellie: Epistemology with Mind-First Logic

In my view, epistemology is about rationality in belief, which is a psychological matter, and hence one for philosophy of mind; but philosophy of mind should start with the “semantics” (theory of meaning) for mental language; and semantics is ultimately based on logic.

Since the dawn of the analytic philosophical tradition, the dominant assumption, presupposed in almost all work, has been that logic is about truth, which is determinately fixed by the world, authoritatively, once and for all, setting the standard of correctness for what to believe.

Stars in galaxyBut what if logic isn’t about truth? In particular (as on the “partial logic” of the 1980s), maybe logic is about endorsement, a relation to mental conditions (especially belief states). Where there is only one world, there are many belief states: mine now and at various times in the past and future, yours now and at various times in the past and future, and so on. None of these belief states are fully determinate (we are all uncertain about the exact number of stars in the galaxy), disagreement is widespread among them (I used to think that goats eat cans, but I changed my mind), and no one’s belief state sets the standard of correctness for anyone else’s.

An endorsement-logical foundation has big ramifications through the rest of philosophy. Truth-based semantics treats a mental claim and a chemical claim alike, as “describing” the world, as encoding a condition the world has to meet in order for the claim to be true. But endorsement-based semantics can treat these claims very differently: a chemical claim still conveys information which is potentially controversial, but a mental claim merely “expresses a sentiment”— “I do not believe the galaxy has an odd number of stars” merely puts my uncertainty on display without conveying any controversial information, while “Fred believes that goats eat cans” merely puts on display my simulation (a.k.a. mindreading) for Fred.

Now, language that is “expressive” is a well-known source of “faultless disagreement”: if I express my simulation of Fred as believing that goats eat cans and you express your simulation of Fred as not believing this, neither of us has entered into controversy. And once we are in a position to allow faultless disagreement over someone’s mental condition, epistemology starts to look very different. After all, many long-standing problems (Frege puzzles, self-knowledge versus content externalism or attitude externalism, retraction of earlier belief, self-location) are framed in terms of forcing philosophy to take sides in a conflict between our take on someone’s mental condition and their own take. But if the conflict is faultless, philosophy is not forced to choose—and the problem vanishes.