Logic, What is It Good For?

A student in my introductory logic course expressed some frustration with the course this evening. What do you think of my response?

A student in my introductory logic course expressed some frustration with the course this evening asking, “Does logic speak in terms of the English language??” Another student amplified that frustration. She replied, “Apparently not. I rather thought Philosophy was not all formulas.” I took both of their comments as a frustration with the relevance of logic. What good are all these formulas and terms and how do they relate to “real life?” Below is my response.

What do you think of how I answered them?

Symbolic logic is a system that symbolizes the structure of thought. A formal language (like English) symbolizes things in the world. So for example, the word "tree" is a symbol for a class of things in the world, namely, all trees. The sentence "That tree." is meant to specify a particular tree when used by a speaker to pick out an object in the world. It's still symbolic. Of course a formal language can be used to symbolize other things including other symbols (think of poetry here).

But logic symbolizes how ideas should relate to one another. So modus ponens for example symbolizes how two things should properly relate to each other in thought. If p then q, p, therefore q essentially is a symbolic representation for the relationship p ought to stand to q in order thought. Just like a formal language has a grammar ("a singular subject takes a singular verb, while a plural subject takes a plural verb"), ideas have a grammar and that's captured in logic.

Ideally, as you learn the grammar of ideas, you'll become better at seeing and using those relationships to make arguments. Here's an example.

Suppose you want to get me to believe that Apple makes the best computers on the market. I ask you why. You could say, "I dunno, they just do." or "You'd have to be stupid not believe that." or "Because apples grow on trees and that's what makes them good." You've given me no reason why I should believe Apple computers are better than other kinds of computers. So, in a sense, our conversation really can't go anywhere.

But suppose you give me a modus ponens argument. You say, "If a computer maker uses the highest quality materials in their workmanship, their computers will be better than everyone else's. Apple uses the highest quality materials in their workmanship. So Apple computers are better than everyone else's." Now we have something to discuss. I can disagree that highest quality materials are the only factor in "being the best" (your first premise) or that Apple uses the highest quality materials (your second premise) etc.

For this to work you don't have to think to yourself, "I must now give a modus ponens argument." just like you don't generally think, "In order to write a complete sentence, I must have a noun, a verb, and an object." Once you learn English grammar well enough, you just write complete sentences. The same should be true of logic. Once you master the rules, the "proper" formation of arguments will just come naturally.

So in once sense, you can think of early studies in logic as an elementary grammar for ideas. If it feels odd or "fake" and disconnected from the real world, it might be because you're learning a new grammar. If you just started studying English grammar for the first time (without knowing another language) it too would most likely feel fake (what does noun, verb, and object have to do with anything? you might think in a sort of non-linguistic way—assuming that’s possible). If you invest in this though and stick with it, it will pay off.

The Gettier Problem: A Study--Part 3

On the surface, Gettier’s scenario seems to present a clear case against the sufficiency of JTB. Smith has justified, true, belief but clearly doesn’t have knowledge so JTB is inadequate. But if we examine the belief we'll see that something has gone wrong with the case, not with JTB.

Which Condition Isn’t Met?

The basis of the tripartite analysis of knowledge begins not with truth but with belief. Typically, philosophers view knowledge as a species with belief being the genus. Knowledge is belief that has been modified or strengthened or improved upon. Belief, then, is the basis of the structure of knowledge and any analysis of knowledge has to include a robust account of what it means to believe. Many Gettier cases end up not being about belief at all and this is where they go wrong. The cases exchange terms about belief but end up describing a problem about the relations between the terms in the case and not about what the person described in the case actually is said to believe. Many cases run afoul based on an equivocation of terms used to describe propositional belief and an actual description of the contents of what the believer actually has as the object of belief.

By way of illustration, let’s look at Gettier’s first case[1] in which he describes Smith coming to have good evidence that the following proposition is true,

P1: Jones is the man who will get the job, and Jones has ten coins in his pocket.

He then comes to believe

P2: The man who will get the job has ten coins in his pocket

based on the fact that P2 is entailed by P1. Gettier tells us that Smith is clearly justified in believing P2 based on the evidence that he has accrued in coming to believe P1. As it turns out, Smith ends up getting the job and Smith has ten coins in his pocket. Thus P2 is true, Smith believes it, and Smith is justified in believing it. But our intuitions are clear: Smith does not have knowledge.

On the surface, Gettier’s scenario seems to present a clear case against the sufficiency of JTB. Smith has justified, true, belief but clearly doesn’t have knowledge so JTB is inadequate. But if we examine the belief component in light of Gettier’s case, something has gone wrong with the case, not with JTB. Gettier tells us that Smith believes P2 and is justified in so believing because of his justified belief in P1. The difference between P1 and P2 is that the particular term “Jones” in P1 has been replaced with the general term “the man” in P2. The claim is that Smith believes both. But what does Smith actually believe when it comes to P2? It seems he could believe one of three things.

Smith could believe that “the man” refers to Jones where the referent of the term picks out the specific person Jones. In other words, when Smith uses the term “the man” the content of his belief is the specific person Jones and the two linguistic elements “the man” and “Jones” have the same referent. Insofar as what Smith believes, the term “the man” does not refer to any other human being. If this is the case, then Smith ends up not having knowledge precisely because he does not have justified, true, belief and not because he has justified, true, belief but requires something else in addition. His belief was not about something true, namely, he believed that Jones would get the job.

We might also read this case such that “the man who will get the job” refers to Smith himself such that the content of his belief references only the person Smith. In this case, Smith would not have knowledge either because he was not justified in believing “The man [Smith] who will get the job has ten coins in his pocket.” He had no evidence to support this belief. JTB remains intact and the belief fails to be knowledge because Smith is not justified in believing that he will get the job.

A final option is that Smith could believe that “the man who will get the job” refers to any man whatever. The content of the belief has no specific referent and means something like “whoever gets the job will have ten coins in his pocket.” Remember the claim here is that this is what Smith believes. But again, it should be clear that if this is Smith’s belief, he fails to have knowledge on JTB because Smith had no evidence whatever that any man with ten coins in his pocket would get the job; as with option 2, he was not justified in his belief.

In Gettier’s original argument, Smith derived the belief “the man who will get the job” from the justified belief “Jones will get the job.” In making this move, Gettier seems no longer to be analyzing the content of Smith’s beliefs. Gettier analyzes Smith’s knowledge in terms of the generalized sentence “the man who will get the job has ten coins in his pocket” where the term “the man” in the sentence can refer to any man whatever. But JTB describes what Smith must believe in order to have knowledge and, assuming Smith is rational, it seems entirely misguided to think that, for Smith, the term “the man who will get the job” has no specific referent or different referents depending on who gets the job. However, on any reading of the case where we’re concerned with Smith’s beliefs, we have no reason to believe Smith has knowledge and no reason to believe JTB is in any way inadequate. In each case, Smith has not met the requirements of JTB and that is why he does not know.

Admittedly, the description above is imprecise and addresses perhaps the simplest and most straightforward of the Gettier-style examples. It also doesn’t account for a number of epistemic tools on which we rely and ones that we most likely want to preserve: things like entailment relations in first-order logic. As noted above, there are many solutions that easily deal with Gettier’s original cases but fail with more complex cases and some of the more creative examples that deserve to be labeled Gettier-style cases. In order to see if the above account can be applied to the more complex cases, it will be necessary to articulate the above argument in more precise language and then apply the argument to further cases.

Index


[1] Edmund Gettier, “Is Justified True Belief Knowledge” in Analysis 23 (1963). Reprinted in Sven Bernecker and Fred Dretske, Knowledge: Readings in Contemporary Epistemology (Oxford: Oxford University Press, 2000), 13-15

CFP: Edinburgh ‘Aims of Inquiry and Cognition’ Conference

The Epistemology Research Group in Edinburgh will be hosting a conference next May on ‘The Aims of Inquiry and Cognition’. Invited speakers include Ted Sider (Cornell), Carolyn Price (Open University), Asbjørn Steglich-Pedersen (Aarhus), Stephen Grimm (Fordham) & Kristoffer Ahlstrom (Copenhagen). There’s a call for papers here. There’s also a rudimentary conference webpage here, on which further details about the conference will be posted in due course.

Reposted from Certain Doubts

The Gettier Problem: A Study-Part 2

Gettier cases assume a particularist methodology in that they appeal to our intuition about what knowledge consists of. When encountering a Gettier case, we tend to say, “I may not know why, but that’s not a case of knowledge.” Pure intuitions are quite different, however.

Index

A Brief Remark on Intuitions and Gettier Cases

Gettier cases assume a particularist methodology in that they appeal to our intuition about what knowledge consists of. When encountering a Gettier case, we tend to say, “I may not know why, but that’s not a case of knowledge.” Pure intuitions are quite different, however, from intuitions that have been shaped by study or influence. 5585-WWU_smAn epistemologist who has studied the question of knowledge deeply may no longer be able to look at a specific case with virgin eyes. Her “intuition” may be deeply affected by what she consciously has come to learn about what knowledge should be or what she may be committed to in her theory. If this is true, then it might explain why Gettier cases continue to get more and more complex and why each case—and its subsequent solutions--may feed a new set of intuitions giving birth to new cases.

In an introductory philosophy course that I’ve taught for many years, at the beginning of each quarter I ask each batch of new students to create three columns on a sheet of paper and write “Faith,” “Belief,” and “Knowledge” at the top of each column. I then ask them to fill in the columns with examples from their own noetic structure. We then review the list. The knowledge column generally tends to contain the least number of items but typically contains things like “I am sitting in a chair” or “We are now located in Seattle” and the like. Being a philosophy professor, I forcefully challenge their knowledge column providing irrefutable evidence (at least irrefutable for beginning philosophy students) that they actually don’t know what they claim to know. When I then ask if they would like to change their minds, some students will easily move items from the “Knowledge” column to the “Belief” column now realizing they were “mistaken.”

This admittedly anecdotal experiment illustrates a difficulty in dealing with Gettier cases. The cases themselves demand that we rely on intuition in order to “see” that such cases do not constitute knowledge yet the intuitions we’re expected to appeal to are not pure and most likely are as varied as the people have them[1]. The more one studies Gettier cases, the more likely one may abandon their particularist intuitions and employ more of a methodist analysis simply because they know so much. I preface my own response to Gettier with this caveat. For my own intuitions are quite strong about why Gettier cases go wrong. But I fully acknowledge that my reader may not share them.

Index


[1] This may be why solving the Gettier problem tends to be so difficult. William Lycan goes further warning, “It is well to remind ourselves that no effort of analytic philosophy to provide strictly necessary and sufficient conditions for a philosophically interesting concept has ever succeeded.” (William G. Lycan, “On the Gettier Problem problem”) Lycan’s ominous claim applies not only to Gettier problems but to many problems in philosophy and is worth remembering at the beginning of this study to avoid too much frustration at the end.

The Gettier Problem: A Study-Part 1

Philosophers who believe that Gettier-style arguments pose a substantial problem for the tripartite theory of knowledge vastly outnumber those who do not. In this series, I’m going to throw my lot in with the latter group and argue that Gettier arguments do not present substantial counterexamples to the justified true belief theory of knowledge as commonly construed.

Index

Gettier – What’s the Problem?

Philosophers who believe that Gettier-style arguments pose a substantial problem for the tripartite theory of knowledge vastly outnumber those who do not. In this series, I’m going to throw my lot in with the latter group and argue that Gettier arguments do not present substantial counterexamples to the justified true belief theory of knowledge as commonly construed. I will argue that while Gettier arguments do surface some problems in epistemology, they do not undermine JTB. Specifically, I will argue that JTB describes the justification of beliefs while Gettier arguments merely show the limitations of language that reference beliefs. I will argue that most Gettier-style counterexamples fail to make a distinction between a proposition (or a statement that exemplifies a proposition) and beliefs about or of propositions.

Treatments of the Gettier problem are expansive, complex, and varied. In his excellent article “Conditions and Analyses of Knowing,” [1] Robert Shope places responses into 5 distinct classes each class having multiple variations. In general, philosophers tend to attack the problem by attempting to amend or shore up the justification condition or by attempting to establish a (heretofore elusive) “fourth condition.” It will be useful to rehearse Shope’s taxonomy in order to better categorize my own response in light of the current literature.

Under the largest category which Shope titles, “Challenges to the Justification Condition” he outlines two main sub-classes elucidating problems with each. Causal theories attempt to demonstrate that the justification condition is unnecessary by arguing that knowledge consists of beliefs that are directly caused by the object of the belief. Some have tried to add a “nonaccidentality requirement” which states that the causal chain that is responsible for the belief not include any causes that might accidentally bring about the belief in question.

Others have attempted to analyze Getter cases in terms of reliability requirements. These models have the belief being formed by way of reliable processes but not necessarily starting from the event or state of affairs that the belief is about. A variation on the model (which Shope labels “Reliable Indicator analyses”) does include the target event or state of affairs and views the connection between belief and its target as the indicator of the strength of the causal chain. A third variation (“Conclusive Reasons analyses”) uses subjunctive conditionals to state the reliability factor: if not h then S would not believe that h (this is one example among many variants).

Shope then considers analyses done in terms of defeasibility. This class and the two that follow attempt to add a fourth condition to the standard account. Shope describes a defeasibility condition as one that describes the impact that a hypothetical circumstance (typically stated in the form of a subjunctive conditional) might have on an aspect of the knower’s epistemology if that circumstance brought the knower, unsuspectingly, into some relation with a true proposition or propositions.

Before providing his own analysis, Shope reviews two more approaches the first of which are analyses in terms of virtue epistemology. On Shope’s read, virtue-based solutions involve reference to characteristics true of the knower rather than merely of the process of coming to believe. Reliabilist theories would fall under virtue analyses on this read. A more specific type virtue analysis involves a deontological component and would include “some positive normative characterization” of the way the knower goes about attaining epistemic goals.

Plantinga gets his own category in the final approach in Shope’s list. Plantinga’s proper functionalism combines elements of reliabilism and virtue epistemology but includes the idea of belief producing mechanisms aimed at truth in the proper environment as a background requirement.

Shope carefully explains that each approach above deals with a certain subset of cases but no approach deals with all variants of Gettier-style examples. As he unpacks each view, he isolates a variant that each solution fails to address. In addition to Gettier’s original two cases, Shope isolates 11 new strains (with clever titles like “Neurotic Grabit” and “The Careless Typesetter”) that pose problems for one or more of the solutions he examines. Shope’s own approach contains specific elements of mine so we will examine elements of his solution in a later article. Shope’s detailed survey, however, demonstrates the obvious complexity of an adequate analysis of knowledge and the enormous effort epistemologists have exerted since 1963 in an attempt to answer Gettier.

Index


[1] In this paper, Shope explores the various responses to the Gettier Problem (as well as surveys the critiques of the tripartite theory of knowledge in general). See Robert K. Shope, “Conditions and Analyses of Knowing” in Paul K. Moser, ed. The Oxford Handbook of Epistemology (Oxford: Oxford University Press, 2002). For the purposes of this paper, I will assume that the three conditions, justification, truth and belief, are individually necessary and jointly sufficient conditions for knowledge. My only claim at this point is that whatever belief, truth, and justification turn out to be, one does not have knowledge without meeting all three conditions. When the three conditions are met, one has knowledge.

Philosophy and Obscurity

In the 20 or so years I’ve spent trying to get people to appreciate philosophy, I’ve learned that most people find the discipline irrelevant, obscure, and kind of pointless.

In the 20 or so years I’ve spent trying to get people to appreciate philosophy, I’ve learned that most people find the discipline irrelevant, obscure, and kind of pointless. The general idea is that philosophy may be fun for some people but at the end of the day, it really doesn’t matter all that much to how people live and that’s where we really should put our energy. I tend to get verbal pats on the head, and the kind of smiles that one gives to small children who think they are doing something important. Few people I’ve met who aren’t in the discipline think philosophy has any bearing on the things that really matter in life.

I’ve kind of gotten used to it. I’m attempting to write an article for the Huffington Post and had a friend read my draft. His feedback was typical of what I usually get: you don’t draw any conclusions, you don’t take a position, you use a lot of big words that I don’t understand and the like. Of course he was absolutely right—all those things were true. But as I thought about his feedback, I had to admit that they were somewhat intentional. Philosophy is like that. It’s hard to take a hard-and-fast position on topics for which there shouldn’t be hard and fast positions. Big words help consolidate ideas that might take 2 or 3 sentences to describe. Opinions are legion so I try to avoid them. But in order to make my article palatable and relevant to a larger audience I have to break all the rules of philosophy (or become a better writer which is something I know I need to do).

I was browsing through my RSS feeds this evening and I came across a quote that somewhat summarizes the situation. The quote applies to poetry—an equally obscure discipline—but it applies to philosophy just was well. Paul Dirac said:

"In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite."

In philosophy its exactly the opposite as well. Philosophy attempts to dig into things most of us know and “unpack” them. It tries to go beyond the surface and bring clarity to ideas with a goal of understanding them better. What it ends up doing much of the time is bringing clarity only to other philosophers. Non-philosophers typically ask for a common sense rewording of the philosophical jargon and then respond with, “Oh, I already knew that. You needed all those big words to say that?” followed by the polite and slightly irritated smile and a request for more wine.

In response to the feedback on my paper, I joked to my reviewer that I would just add longer and deeper quotes. “So you like obscurity then . . .” he replied. Maybe I should look into poetry.

CFP: Extended Cognition and Epistemic Action

CALL FOR PAPERS
Special Issue of Philosophical Explorations on “Extended Cognition and Epistemic Action”

Guest Editors: Andy Clark (University of Edinburgh), Duncan Pritchard (University of Edinburgh) and Krist Vaesen (Eindhoven University of Technology)

Submission Deadline: September 15, 2011

Invited Contributors: Fred Adams (University of Delaware) & Ken Aizawa (Centenary College of Louisiana), Ronald Giere (University of Minnesota), Sanford Goldberg (Northwestern University), Richard Menary (University of Wollongong) and Kim Sterelny (Australian National University and Victoria University).

Background and Aim
According to the thesis of extended cognition, cognitive processes do not need to be located inside the skin of the cognizing agent. Humans routinely engage their wider artifactual environment to extend the capacities of their naked brain. They often rely so much on external aids (notebooks, watches, smartphones) that the latter become a proper part of a hybrid (human-artifact) cognitive system.

The thesis of extended cognition has been influential in the philosophy of mind, cognitive science, linguistics, informatics, and ethics, but, surprisingly, not in epistemology. The discipline concerned with one of the most remarkable products of human cognition, viz. knowledge, has largely ignored the suggestion that her main object of study might be produced by processes outside the human skin.

In this special issue of Philosophical Explorations we therefore are looking for papers that explore the ramifications of the thesis of extended cognition for contemporary epistemology in general, and for conceptualizations of epistemic action in particular. The special issue will include five invited papers (by Fred Adams & Kenneth Aizawa, Ronald Giere, Sanford Goldberg, Richard Menary and Kim Sterelny), plus two contributions selected from the papers submitted in response to this open call for papers.

We expect contributions discussing the impact of extended cognition on issues as: epistemic agency and responsibility, cognitive ability, ownership of belief, the distribution of epistemic credit, the sources of belief, artifactual testimony, the growth of knowledge, non-propositional knowledge, the evolution and reliability of extended cognitive processes, the varieties of extended epistemic action.

Submission Details
Please send a pdf-version of your paper (max. 8000 words) to Krist Vaesen, (k.vaesen@tue.nl). Contributions that do not make it to the special issue may be considered for publication in one of the regular issues of Philosophical Explorations.

Further Inquiries
Please direct any inquiries about this call for papers to Krist Vaesen, (k.vaesen@tue.nl).

New Books in Philosophy

The New Books Network has launched a new channel focusing on philosophy. “New Books in Philosophy features peer-to-peer discussions with philosophers about their new ideas as expressed in their newly published books. The program is co-hosted by Carrie Figdor (University of Iowa) and Robert Talisse (Vanderbilt University). Between the two of us, we will be exploring new books in ethics, epistemology, philosophy of mind, metaphysics, philosophy of science, social and political philosophy, history of philosophy, philosophy of language, and many other subfields.”

Info here.

Formal and Experimental Philosophy Workshop

This coming fall, Tilburg University (The Netherlands) will host a two day workshop titled, “Formal Epistemology Meets Experimental Philosophy.”  From the workshop’s website:

Over the years, the methodological toolbox of philosophers of science has widened considerably. Today, formal and experimental methods importantly complement more traditional methods such as conceptual analysis and case studies. So far, however, there has not been much interaction between the corresponding communities. Formal work is all too often conducted in an a priori fashion, drawing on intuitions to substantiate various assumptions and to test their consequences. Experimental work, on the other hand, is often limited to testing various assumptions and intuitions, and often does not identify or create new phenomena that can subsequently be integrated into a formal framework. The working assumption of this workshop is that philosophy of science can gain a lot from combining formal and experimental studies. By doing so, philosophy of science will become increasingly scientific as a crucial aspect of the scientific endeavor lies in the combination of formal theories and experimental insights.

This workshop aims to explore the relation between formal and experimental approaches to the philosophy of science. We invite meta-theoretical papers, but especially papers that fruitfully combine both methods to problems from the philosophy of science. This first Pittsburgh-Tilburg workshop will pay special attention to the philosophy of the social sciences, but a focus on other subfields of philosophy of science is also welcome.

Workshop info and call for papers here.

The Epistemology of Groups

Northwestern’s department of philosophy is holding a workshop on the epistemology of groups on August 1st, 2011. Talks include “A Deflationary Account of Group Testimony” and “Group Belief: Lessons from Lies and Bullshit”

Info here.