Second Philosophy: A Naturalistic Method

Penelope Maddy

Oxford, Oxford University Press, 2007

x + 448 pp., ISBN 978-0-19-927366-9 (hardback)

This book is the culmination of Maddy’s efforts, for more than a decade, to delineate a sensible version of naturalism, in general philosophy and in the philosophy of logic and mathematics. The name ‘Second Philosophy’ is to emphasize its distinctive idea: a Second Philosopher is born native to scientific methodologies; she trusts scientific methods while admitting that they can be improved from within, but she rejects any demand for justifying her scientific knowledge from outside. In contrast, a First Philosopher tries to justify sciences by transcendental and a priori investigations. 

The book consists of four parts. Part I contains a general characterization of the Second Philosopher’s method, by comparing her account for knowledge and her answer to the skeptics with those accounts and answers offered by Descartes, Hume, Kant, Carnap, Quine and Putman. For instance, to respond to the Kantian idea that a transcendental investigation is required to identify the source and foundation of our a priori knowledge, the Second Philosopher recommends psychological investigations into human innate cognitive architectures selected by evolution, to see how much of human cognition is innately determined independent of experiences.

Part II of the book describes the Second Philosopher’s stance regarding truth and reference. Here, Maddy settles on disquotational truth and reference. She admits that a word-world correlation is necessary for accounting for the effects of human subjects’ behaviors induced by their beliefs, but she suggests that we do not need the semantic correspondence relation for this, and instead a ‘reliable indication relation’ is sufficient. An instance of the reliable indication relation is: my belief ‘it’s raining’ is a reliable indication of the physical state that it’s raining, because the latter physically causes the former.

Part III is a naturalistic account for logic. Here, Maddy argues for three theses: the world has some logical structure (as it is recognized by humans); humans have some innate cognitive architecture allowing them to detect and represent this logical structure; this is a result of evolutional selection. The logical truths thus innately represented belong to a rudimentary logic, which do not yet include all classical logical laws, mostly because there is indeterminacy due to vagueness in the world, which generates truth gaps in the representations. Then, Maddy discusses, in this naturalistic context, whether logic is universal, necessary, a priori, revisable, empirical, and analytic and so on. She also discusses how the full classical logic comes out from the rudimentary logic as idealizations.

In Part IV, Maddy first explains that the Second Philosopher sees van Fraassen’s doubts about unobservable things as something extra-scientific. Then, Maddy argues against three attempts to infer the objective existence of mathematical entities or structures from mathematical applications: the Quinean indispensability argument based on confirmation holism, the idea that applicability is due to objective mathematical structures in the world, and the idea that miraculous effectiveness of mathematics for applications must be due to the objective truth of mathematics. Then, on the positive side, Maddy recommends evaluating mathematical methods by their effectiveness for serving mathematicians’ purposes for relevant mathematical theories, and she recommends Thin Realism and Arealism. Thin Realism holds that mathematical entities are exactly the sort of things described by whatever mathematical theories accepted by mathematicians, no more and no less; Arealism explicitly denies the existence of mathematical entities. Maddy argues that there is no essential difference between these two positions, presumably because of thinness in Thin Realism.

The book contains rich content on many other topics. For instance, the survey on cognitive psychological studies on the logical and arithmetic cognitions among human infants in Part III is fascinating and enlightening. The discussions in Part IV for demystifying the alleged miraculous effectiveness of mathematics are also amazing. The book contains no (logical or mathematical) technical materials and is easily accessible to general philosophical audiences. Maddy is most well-known for her work in the philosophy of mathematics, especially, in the highly technical area of the philosophy of set theory, but this book definitely belongs to philosophy in general. It is about how to do philosophy under the Zeitgeist of naturalism.

Since I share with Maddy the conviction about naturalism, here I will only point out what I take to be ‘still not naturalistic enough’ in the book. First, I would rather distinguish between naturalism and anti-naturalism by their different views on the nature of a subject of cognition, not by the different methods they accept, transcendental or scientific. Is a subject a physical human brain that is a result of evolution, physiological maturation, and physical interactions with environments, or is it a transcendental Mind, standing opposite to an External Reality, with some mental capacity not reducible to physical interactions for accessing that External Reality? Transcendental methods clearly presuppose the latter, but sometimes scientific methodologies are also understood as a transcendental Mind’s best and only methods for knowing things in the External Reality. This should be inconsistent, because sciences clearly describe Homo sapiens as physical things, but the illusion of a transcendental Self is so deeply rooted in human nature that one frequently unconsciously assumes the stance of a transcendental Mind. For instance, the skeptics’ question “how do you know …” lures me to take myself as a transcendental Mind, not just this body and brain. Otherwise, my answer to it can only be a naturalistic description of the structure and history of this brain. If we consciously talk about brains only, we will naturally proceed differently on some issues than what Maddy did in the book. I can only briefly indicate two instances in this short review.

First, we will naturally embrace correspondence truth. It is supposed to be a relation between a neural circuitry C supposedly realizing a belief inside a brain and a physical state (e.g. it’s raining) outside the brain. Another physical state (e.g. a fake sound of raining) may also cause the same neural circuitry C. Therefore, statistically and causally, C is also a reliable indication of the latter physical state. Truth and the reliable indication relation are thus two different relations between physical things inside and outside a brain. We recognize these two relations for our own beliefs, and then in our scientific study of a human subject we assume that both relations exist for that subject’s brain. Indeed, characterizing truth scientifically is much more difficult than characterizing the reliable indication relation, but they seem to be technical difficulties due to the extreme complexity in a brain’s cognitive activities that realize the former relation. Since we are talking about brains, philosophical mists such as ‘one cannot jump out of the Mind to compare Reality with the Mind’ are irrelevant. I see no motivation for avoiding truth. In a footnote on page 226, Maddy appears to admit that it is possible to differentiate between these two relations scientifically but claim that it doesn’t matter which one is the ‘true representation relation’. However, suppose that we can characterize these two relations scientifically and we find that one has the features that we intuitively attribute to truth and the other has the features that we intuitively attribute to the reliable indication relation. Then, we have good scientific reason to claim that the former is truth. Maddy (pp. 154-156) also cites examples to show that in some special cases that reliable indication relation explains the effects of behaviors induced by a belief, but apparently in many simpler and more common cases where the reliable indication relation (e.g. sound of raining) is present but truth (e.g. raining) is absent, we need both relations to explain the effects (e.g. picking up an umbrella before going out but not using it). Things inside a brain can bear many kinds of relations with things outside the brain and truth is the most prominent one in our intuitive explanation of human cognitive activities. It seems quite improbable that truth becomes redundant in a scientific explanation of such complex phenomena. We naturally suspect that if one starts with that trivial reliable indication relation in explaining human cognitive activities, one will soon have to characterize truth or some equally complex relation.

Second, Thin Realism seems superfluous. Looking into a brain, we see that some neural circuitries bear that truth relation with physical states outside the brain. Then, for mathematical beliefs (as neural circuitries) inside the brain, which do not bear that truth relation with any physical states outside the brain, we will naturally study their cognitive functions within that brain other than ‘representing physical states’. For instance, it seems that mathematical beliefs help the brain to organize and represent other beliefs and finally produce beliefs that do bear that truth relation with physical states outside the brain. With these, we already have a complete scientific description of the natural phenomena of human mathematical practices. It seems gratuitous to insist that those beliefs represent mysterious ‘thin entities’. That idea comes from taking the subjective stance of a transcendental Mind and speculating about a sort of ‘thin existence’ outside the Mind. No one ever clearly explains what ‘thin’ entities are, while things inside and outside a brain are clear for sciences.