Hauptli’s Lectures on Goldman’s “A Causal Theory of Knowing”[1] [1967]


     Copyright © 2013 Bruce W. Hauptli


1. Introduction:


Goldman will deal with cases of empirical knowledge—he believes that the Gettier counter-examples to the JTB thesis apply only to such knowledge claims.  The undiscussed contrast here is that between empirical knowledge and a priori knowledge (in mathematics and logic, for example).  Why doesn’t Goldman propose that his account be used to account for the latter sorts of claims? 


     Goldman wants to explain why Gettier’s examples undercut knowledge in the particular examples, and he wants to offer a more adequate analysis of empirical knowledge. 


18 He recounts Gettier’s “second case” involving Smith, Jones, Brown, a Ford, and Barcelona (either Jones owns a Ford or Brown is in Barcelona—with strong evidence for the former and no evidence for the latter; but where the former is not the case and the latter, coincidentally, is the case). 


-19 “Notice that what makes p true is the fact that Brown is in Barcelona, but that this fact has nothing to do with Smith’s believing p.  If Smith had come to believe p by reading a letter from Brown postmarked in Barcelona, then we might say that Smith knew p.  Alternatively, if Jones did own a Ford, and his owning the Ford was manifested by his offer of a ride to Smith, and this in turn resulted in Smith’s believing p, then we would say that Smith knew p.  Thus, one thing that seems to be missing in this example is a causal connection between the fact that makes p true...and Smith’s belief of p.” 


What Goldman wishes to add to the traditional analysis is the requirement is that there be such a causal connection.  As I have noted, in his An Introduction to Contemporary Epistemology, Matthias Steup distinguishes between a lucky guess (where given S’s evidence, the truth of p is not a likely outcome), and a lucky truth (where in relation to the relevant facts, p’s truth was not a likely outcome).  As Steup notes:


-justification is what prevents a true belief from being a lucky guess, but not from being a lucky truth. 

  ...What the Gettier problem shows us is that in order for a true belief to qualify as knowledge, it must satisfy two conditions; it must not be a lucky guess (that is, it must be justified), and it must not be a lucky truth.  A true belief that isn’t a lucky guess—like Smith’s belief...may still be a lucky truth, and thus fall short of being knowledge.  Hence in order to solve the Gettier problem, epistemologists have to figure out what kind of condition can prevent a true belief from being a lucky truth.”[2] 


As we can see, Goldman appeals to causal connections to ensure that we have empirical knowledge rather than, merely, lucky truths.  Goldman’s strategy consists of considering a number of differing sorts of knowledge claims and showing how causal connections of the appropriate sort can help us distinguish knowledge claims from what we might call cases of “Gettier luck.” 


     Traditionally epistemologists have generally recognized the following different sources of knowledge (of justification or evidence): perception, introspection, reason, memory, and reliable (or appropriate) authority (that is, testimony).  One of the virtues of Goldman’s article (besides its attempt to overcome Gettier’s problems) is his focus upon a variety of sources of evidence, and his careful analysis of what must be the case if these sources are to yield knowledge. 


2. Perceptual Knowledge:


19 Building upon Paul Grice’s causal theory of perception,[3] Goldman claims that “...a necessary condition of S’s seeing that there is a vase in front of him is that there be a certain kind of causal connection between the presence of the vase and S’s believing that a vase is present.” 


-19-20 “Deformed Case:” suppose that there is a vase, but there is also a holograph of a vase between S and the vase (which blocks S’s view, etc.). 


--S could know about the vase if someone else told S about it and the holograph.  Here the vase (the actual vase) would be the causal ancestor of S’s belief, but, clearly, we would not have a case of perceptual knowledge. 


--Note that Goldman assumes that perceptual knowledge is non-inferential.  While one may disagree with him about this, he does give an account of inference in what follows, and would hold that this assumption only “simplifies things,” to those who disagree.  Note, however, that many who hold that perception is one of the sources of knowledge want to hold that it is non-inferential so that it may provide a “foundation” for our empirical knowledge claims. 


Philosophical Aside:


In his discussions of the different sorts of empirical propositional knowledge here, Goldman talks about the connections between our beliefs and the causes of our beliefs.  Some theorists contend that his orientation is flawed because it doesn’t matter how we come to hold a belief initially, what really counts is why we continue to believe it.  A belief might be caused by a bad slice of pizza, but if one continues to believe it because of an appropriate connection with the relevant state of affairs, that is what is crucial. 

3. Knowledge Through Memory:


20-21 According to Goldman, “remembering, like perceiving, must be regarded as a causal process.  S remembers p at time t only if S’s believing p at an earlier time is a cause of his believing p at t.  Of course, not every causal connection between an earlier belief and a later one is a case of remembering.  As in the case of perception, however, I shall not try to describe this process in detail.  This is a job mainly for the scientist.  Instead, the kind of causal process in question is to be identified simply by example, by “pointing” to paradigm cases of remembering.” 


-21“Deformed Case: “someone initially perceives something, forgets it, the belief that it was perceived is artificially stimulated, and then s/he “remembers” perceiving it.  Such a case is not a case of knowledge through memory. 


4. Knowledge Through Inference:


21 As he uses the term here, ‘inference’ does not imply that S went through an explicit and conscious process of inference.  “My belief that there is a fire in the neighborhood is based on, or inferred from, my belief that I hear a fire engine.  But I have not gone through a process of explicit reasoning....” 


The Lava Case: S perceives solidified lava throughout the surrounding countryside.  When coupled with various “background” beliefs, S concludes that a nearby mountain erupted centuries ago.


-“Let us assume that this is a highly warranted inductive inference, one which gives S adequate evidence for believing that the mountain did erupt many centuries ago.  Assuming this proposition is true, does S know it?  This depends on the nature of the causal process that induced his belief.  If there is a continuous causal chain of the sort he envisages connecting the fact that the mountain erupted with his belief of this fact, then S knows it.  If there is no such causal chain, however, S does not know that proposition.” 


(p) ®®®®®®(q) ®®®®®® BS(q)

mountain               lava is                     S believes *

erupted                 now                         lava is now   *

                            present                     present            *


                                                                           S believes mountain erupted





                                                     S believes background claims (r)


® represents causal connections, and ** represent inferential connections. 


-21-22 “Deformed Case: “suppose someone, somehow removes all the lava and then, later, someone else decides to make it look as if the mountain had erupted. 


--22 “In the suggested variant...the...arrow [connecting p and q] would be missing, showing that there is no continuous causal chain connecting (p) with S’s belief of (p).  Therefore, in that variant case, S could not be said to know (p).” 


--“I am inclined to say that inference is a causal process, that is, that when someone bases his belief of one proposition on his belief of a set of other propositions, then his belief of the latter propositions can be considered a cause of his belief of the former proposition.  But I do not wish to rest my thesis on this claim.  All I do claim is that, if a chain of inferences is “added” to a causal; chain, then the entire chain is causal.” 


5. Knowledge Through Testimony:


22 “There is a continuous causal chain from p to S’s believing p, and thus, assuming that each of S’s inferences is warranted, S can be said to know p.” 


                                                                                    BS(r)                    BS(v)

                                                                                         *                         *

                                                                                            *                          *

(p) ®®® BT(p) ®®®  AT(p) ®® BS(AT(p)) ®®®BS(BT(p)) ®®®®BS(p)

                 T believes        T asserts          S believes          S believes                S believes p

                      p                       p              T asserts p          T believes p                 *

                                                                                                 *                        *

                                                                                            *                          *

                                                                                       BS(q)                BS(u)


q, r, u, v are background propositions (pertaining to T’s sincerity, etc.). 

® represents causal connections, and ** represent inferential connections. 


23 “In this case, as in the lava case, S knows p because he has correctly reconstructed the causal chain leading from p to the evidence for p that S perceives, in this case T’s asserting (p).  This correct reconstruction is shown in the diagram by S’s inference “mirroring” the rest of the causal chain.  Such a correct reconstruction is a necessary condition of knowledge based on inference. 


-“Deformed Case:” a newspaper reporter (T) and a reader (S) where there is a typo in the newspaper so that the story asserts ~p.  But “when reading the paper...S fails to see the word ‘not’, and takes the paper to have asserted p.  Trusting the newspaper, he infers that p is true.  Here we have a continuous causal chain leading from p to S’s believing p; yet S does not know p.  S thinks that p resulted in a report to the newspaper about p and that this report resulted in its printing the statement p.  Thus, his reconstruction of the causal chain is mistaken.  But if he is to know, his reconstruction must contain no mistakes.  Though he need not reconstruct every detail of the causal chain, he must reconstruct all the important links.  An additional requirement for knowledge based on inference is that the knower’s inferences be warranted....Reconstructing a causal chain merely by lucky guesses does not yield knowledge.” 


--We need to carefully examine the relevant footnote (#8) here: what exactly is the “correct reconstruction” requirement, and how does one determine which elements in the causal chain must be reconstructed correctly? 


--In his Contemporary Epistemology, Ralph Baergen maintains that what goes wrong in the Gettier cases is: “the target belief is true, but the way in which it is true isn’t what the subject has in mind.  One has the feeling that these beliefs are only accidentally true, and this seems to be what prevents us from regarding these beliefs as knowledge.  The weakness of the JTB theory, then, seems to be that it doesn’t rule out the possibility that the target belief could be true only accidentally.”[4]  According to Baergen, “...it is important that your mental reconstruction of the causal chain be correct; any error would prevent the belief from counting as knowledge.  For example, suppose you read a newspaper account of a hockey game and form the belief that the final score was 3 to 1 for Chicago.  This is the correct score, but the newspaper has actually misprinted it as 8 to 1; in your copy of the paper the left-hand side of the “8” is faded and you misread it as a “3.”  In this case your belief is true and justified, but because your reconstruction of the causal chain is incorrect it does not count as knowledge.  Your reconstruction of it would go something like this: The final score was 3 to 1 for Chicago, the sports reporter observed this, the newspaper printed it (this is the mistaken part—what it printed wasn’t the correct score), and I read it.  You might think that this constraint is just another example of Internalism, but actually it has another motivation.  Placing this restriction on reconstructions prevents accidentally true beliefs from counting as knowledge (as in the Gettier cases).”[5] 


6. Michael Clark’s Analysis:


23 The traditional analysis of knowledge refers to only three features of the diagrams we have examined thus far: (1) p must appear in the diagrams, S must believe p, and (3) S’s inferences must be warranted.  In addition to the traditional analysis, in his “Knowledge and Grounds: A Comment on Mr. Gettier’s Paper,” Michael Clark maintains a fourth condition is necessary in the analysis of knowledge: he contends that each of the beliefs in S’s chain of inference must be true.[6]  Thus, there must be facts “behind” each of the background beliefs (etc.).  Goldman uses his discussion of Clark’s proposal to help clarify his own analysis of knowledge, and the point is indeed relevant to our larger discussions.  Goldman’s discussion of Clark is interrupted by a discussion of what he calls the “second pattern” of our knowledge claims, and I will ignore the interruption for the moment here (and then discuss of the two patterns).  According to Goldman, there are two central problems with Clark’s analysis:


The first problem Goldman finds with Clark’s analysis is that we can construct cases where each of the beliefs in S’s chain of inference to p is true, but S does not know that p.  In such cases S’s believing that p is not causally related to p.  For example, S believes that Jones owns a Ford because Brown told him so, Brown is reliable, Brown’s information is correct, but Brown sells his Ford and then wins one in a raffle.  “Smith’s belief in p is not only justified and true, it is fully grounded, e.g., we [can] suppose that each link in the...chain of Smith’s grounds is true.”  [Chart on p. 26.]  “Smith’s lack of knowledge can be accounted for in terms of my analysis.  Smith does not know p because his believing p is not causally related to p, Jones owning a Ford now.” 


-In short, Clark’s analysis is too weak.[7] 


27 Goldman’s second problem with Clark’s analysis is that “we need not require, as Clark does, that all of S’s grounds be true.  What is required is that enough of them be true to ensure the existence of at least one causal connection between p and S’s belief of p.”  The counter-example here consists of S having some false evidence, but sufficient true evidence.  This is important independent of the discussion at hand, as we often have multiple “reasons,” “justifications,” and “causes” (the latter are called cases of causal 0ver-determination—suppose two assailants attack a victim and simultaneously cut off his head and shoot him in the heart with a shotgun, clearly either of the actions alone would have resulted in the victim’s death). 


-In short, returning to Goldman’s point Clark’s analysis is too strong. 


--A variant of this problem arises where S has dispensable background assumption (which is false). 


7. Knowledge and “Background Causes”—“Pattern II Cases:”


24-25 The causal theory does not require that p be the cause of the belief—there could be something else q which is the common cause of the belief and of p:



                                    T’s going downtown on Monday



(q) T’s intending to go

downtown on Monday                                   BS(v)

          î                                                            *

                î                                                           *

                        (r)------------®BS(r)                        BS(p)

                T’s telling S                             *                         *                              

                  on Sunday that s/he                     *             *                      

                  intends to go down-                            *

                  town on Monday                             BS(q)




Pattern 2 Case                                   BS(u)


[the earlier cases were Pattern 1 Cases]


u and v are relevant background propositions regarding T’s honesty, resoluteness, etc. 

ì, î, and ® represent causal connections, *** represent inferential connections. 


With this example, Goldman enriched his account considerably without sacrificing its core idea. 


8. Logical Connections and the Causal Account:


26-27 Suppose Smith bases his belief (p) that someone in his office owns a ford on his belief in the following four propositions:


(q) Jones owns a Ford

(r) Jones works in his office

(s) Brown owns a Ford [this is false]

(t) Brown works in his office


                       (q) Jones owns a Ford

                       Ý                      î

                       Ý                           î

                       Ý                                î

                       Ý                                BS(q)

(p) ==== (q & r)                               Smith   *

someone          ß                             believes           *

in the               ß                             Jones owns       BS(q & r) ******BS(p)

office               ß                             a Ford          *                            *

owns a             ß                                             *                            *

Ford                ß                                          *                            *

                        ß                             BS(r)                            *     

                        ß                           Smith believes             BS(s & t)

                        ß                          Jones works                 Smith believes Brown

                        ß                         ì in the office                        owns a Ford and works

                        ß                       ì                                                                                             in the office

                        ß                      ì

                        (r) Jones works in the office


ì and î represent causal connections,

******* represent inferential connections. 

Ý, ß, and = represent logical connections. 


27 As we have seen, Goldman maintains that S may be said to know because while one of the causal chains involves a falsehood (which would violate Clark’s analysis), the other causal chain is unproblematic. 


9. Goldman’s Overall Analysis of Knowledge:


28 S knows that p iff[8] the fact that p is causally connected in an “appropriate” way with S’s believing p.”  Where “appropriate ways” are:


(1) perception


(2) memory


(3) a causal chain, exemplifying either Pattern 1 or 2, which is correctly reconstructed by inferences, each of which is warranted (background propositions help warrant an inference only if they are true)


(4) combinations of (1), (2), and (3). 


-28 “...the causal requirement and the correct-reconstruction requirement are absent from...older analysis[es].  These additional requirements enable my analysis to circumvent Gettier’s counterexamples to the traditional one.  But my analysis is weaker than the traditional analysis in another respect.  In at least one popular interpretation of the traditional analysis [JTB], a knower must be able to justify or give evidence for any proposition he knows.  For S to know p at t, S must be able, at t, to state his justification for believing p, or his grounds for p.  My analysis makes no such requirement, and the absence of this requirement enables me to account for cases of knowledge that would wrongly be excluded by the traditional analysis.” 


--Goldman claims, for example, that his belief that Lincoln was born in 1809 is knowledge even though it is grounded by memory, and where he has forgotten the memory grounds. 


--29 Goldman contends that “keeping the list of “appropriate processes” open is important as we might discover causal connections where we believed they did not exist. 


--Goldman would treat knowledge of one’s own mental states as a causal situation wherein there is an identity between what is believed and the believing in the normal situation—a “degenerate causal chain” which is “zero links long.” 


10. An Aside: Internalism and Externalism:


An important distinction in contemporary epistemology is that between the orientations of “externalism” and “internalism.”  In his Unnatural Doubts, Michael Williams maintains that:


the essence of externalism...is to allow knowledge when a person in fact meets certain conditions, whether or not he knows he meets them.  These conditions may be “external,” not just in not being represented in the person’s knowledge or beliefs, but in having to do with his actual situation.  The capacity for knowledge is thus like any other capacity: it depends partly on the powers of the individual and partly on the circumstances in which he is required to exercise them.[9] 


As we have seen, in his “Understanding Human Knowledge in General,” Barry Stroud says that externalist accounts of knowledge:


316  ...would explain knowledge in terms of conditions that are available from an “external,” third-person point of view, independent of what the knower’s own attitude towards the fulfillment of those conditions might be.[10] 


In his Contemporary Epistemology, Ralph Baergen maintains that:


...internalists perform their epistemic evaluations from the first-person point of view, taking into account only that which was available to the subject when the belief being evaluated was formed (or maintained, or revised), while externalists evaluate from the point of view of a fully informed observer—what one might call the third person point of view.[11] 


The importance of the distinction is emphasized by Robert Fogelin in his Pyrrhonian Reflections On Knowledge and Justification:


...justificatory performances come in a variety of forms ranging at the extremes from those that involve complex ratiocination to those that rely upon the unreflective use of a perceptual power or capacity.  Both can be carried out in a responsible or an irresponsible manner; both can establish or fail to establish the truth of some belief.  Both are sources of knowledge.  Until relatively recently, philosophers have often tended to think of knowledge as solely the product of intellectual activity.  The externalists have made an important contribution to epistemology by breaking the spell of this intellectualist prejudice.[12] 


     We need to ask: “Does Goldman’s causal theory constitute an instance of “externalism”?”  Not quite, I contend—his “correct reconstruction condition” seems to leave him with at least one foot in the internalist camp!  As Fogelin recommends, Goldman may appear to have inclinations both ways.  The central motivation for the “causal theory,” however, is strongly externalistic—it is the appeal to “external,” “third-person,” causal connections which is to overcome the Gettier problems and ensure the adequacy of the analysis of knowledge!  And the issues which Goldman raises in his discussion of the various cases center upon whether the causal connections obtain, not whether the individual is aware of their obtaining.  Fogelin maintains, however, that as Goldman shifts from simply demanding the existence of unbroken causal chains to demanding that the individual be able to also offer the right sort of “reconstruction,” his view shifts significantly:


that these are very different positions is clear because the first condition would not disbar animals from processing knowledge, whereas the second condition presumably would.”[13] 


11. Goldman’s answers to possible objections:


30 To those who maintain that he offers a bad analysis of the meaning of ‘knowledge’:


-Goldman maintains he is interested in only giving the truth conditions for knowledge.  Goldman’s reply to such critics above is important.  The distinction between providing an analysis of the meaning of a term and providing an account of the truth conditions for the application of a term will be important as we continue through the course. 


To those who complain that his analysis makes it difficult to tell whether someone knows something:


-Goldman maintains that “verification conditions” (rather than truth conditions) are what are important relevant to this issue, and he it is the latter he is concerned with—thus he is not concerned with the issue of verifying whether individuals have knowledge. 


--Goldman, then, is not attempting to answer the questions "What do we mean by `knowledge'?" or "How can we tell when we know?"  Instead, he is only interested in answering the question "What is knowledge?" 


To those who raise skeptical problems:


-Goldman maintains that he has not attempted to respond to skeptical problems. 


Goldman recognizes that his analysis deviates from a strong tradition in philosophy which separated questions of justification from questions of causation. 


(end of reading)


12. Selected Criticisms of Goldman’s Causal Theory:


1. Ralph Bergen maintains that:


one wonders whether, if and when we do arrive at a more complete understanding of causation, the causal connections in all these cases will be found to have much in common.  To put this another way, what reason have we to suppose that we’ll be able to point to a single sort of causal connection (or to a single set of features of such connections) and say that these and only these suffice for knowledge?  Why might it not be that the cases in which we judge a subject as having knowledge exemplify a wide range of causal stories, and that what is common to all these cases of knowledge is something other than causal origins?[14] 


     In addition, Baergen notes that many believe the notion of causation is itself bankrupt, and Goldman’s theory must have a response to these concerns. 


2. In his “Scientific Realism and Naturalistic Epistemology,” Richard Boyd maintains that:


...the issue in scientific knowledge is not the reliable production of beliefs.  The reliability which scientific practice displays is not so much a matter of how beliefs are produced or even of how they are initially accepted, but of the tendency over time for beliefs to be sustained only if they are approximately true and for beliefs to be modified in the direction of closer and closer approximations to the truth.  What is at stake is reliability in the regulation of belief (over time) rather than reliability in the initial production or acceptance of particular beliefs.  Indeed, I think that this will prove to be true in many cases of everyday belief as well.[15] 


3. Fred Dretske offers a criticism which arises out of Goldman’s “lava” case.  Dretske asks us to imagine two mountains, M and N, and a lava flow which comes from M but could have come from N.  Of this case Dretske says the following:


in such circumstances Goldman’s necessary condition is satisfied, but mine is not.  (2d) is false; it is false that the lava would not be there, and distributed in this fashion unless M had erupted.  For if, contrary to hypothesis, M had not erupted, N would have; leaving the very same (relevant) traces. 

  In such circumstances I do not think we could say that S knew that M erupted on the basis of the present existence and distribution of lava.”[16] 


4. In his “Epistemic Luck and the Purely Epistemic,” Richard Foley maintains that:


we can criticize the person’s intellectual character, or his cognitive equipment, without criticizing everything which is a product of that character or equipment.  A belief can be rational even though what prompts the believer to choose his belief or what cognitive equipment causes him to have the belief regularly produces epistemic howlers.  In such cases, we should admit...that the believer has been epistemically lucky.[17] 


5. A number of interesting criticisms are contained in Marshall Swain’s “Knowledge, Causality, and Justification.”[18] 


6. In his “The Gettier Problem and the Analysis of Knowledge,” Keith Lehrer offers a distinction which empowers a critique of causal theories of knowing like Boyd’s above:


Lehrer distinguishes between acceptance and belief: “to accept a proposition in this context means to assent to it when one’s only purpose is to assent to what is true and to refuse to assent to what is false.”[19] 


He clarifies: “a person may believe something for the wrong reasons, perhaps he cannot help but do so, and, nevertheless, know that it is true because he assents to it for the right reasons.”[20]  Believing something [causally] because the “stars” say it is so, but assenting to it on proper epistemic grounds. 


According to him, “this distinction...vitiates those causal theories of knowledge that maintain that whether a person knows something to be true depends on the causal relation between a person believing something and the fact that it is so.  Belief may arise in particular and sundry ways, but no matter how a person comes to believe something, and no matter how his belief is sustained, he may know that what he believes is true if he accepts the proposition in question on proper grounds.”[21] 


He offers an additional criticism of causal theories:


while considering modifications of the original Nogot example, I should also like to make it clear that a very simple modification of that example suffices to defeat attempts to deal with the Gettier problem in causal terms, for example, by requiring the fact that makes a proposition a person believes true be a cause of his believing it.  For, it may well have occurred to some readers of the original Nogot example to wonder why Nogot should have gone to so much trouble to deceive me into believing that he owned a Ford when he did not.  The answer, we may suppose, is that Nogot knows that Havit owns a Ford, and Nogot has a compulsion to try to trick people into believing true propositions by getting them to believe some false propositions.  Thus, the fact that someone in my class owned a Ford caused Nogot to cause me to believe that someone in my class owned a Ford.  So the fact that someone in my class owned a Ford is, indirectly, the cause of my believing that someone in my class owns a Ford.  But this is still not anything I know.  Moreover, the deception need not involve a human agent but might arise from some peculiarity in the natural cause of events, like a name fading in a peculiar way on a document.[22] 


Notes:(click on the note number to return to the text the note refers to)  

[1] Cf., Alvin Goldman, “A Causal Theory of Knowing,” The Journal of Philosophy v. 64 (1967), pp. 355-372.  The essay is reprinted in Knowledge: Readings in Contemporary Epistemology, Sven Bernecker and Fred Dretske, eds, (N.Y.: Oxford U.P., 2000(, pp. 18-30.  These notes are to the reprint edition, and emphasis is sometimes added to the passages. 

[2] Matthias Steup, An Introduction to Contemporary Epistemology (Upper Saddle River: Prentice Hall, 1996), p. 9. 

[3] Cf., Paul Grice, “The Causal Theory of Perception,” Proceedings of the Aristotelian Society supplementary vol. (1961), pp. 121-152.  Grice’s analysis of knowledge appealed to a causal relationship between a state of affairs and a true first-person sense-datum report (that is, a report of one’s first-person sensory experiences—for example: “I see a footnote on the page”). 

[4] Ralph Baergen, Contemporary Epistemology (Fort Worth: Harcourt, 1995), p. 110. 

[5] Ibid., p. 117. 

[6] Cf. Michael Clark, “Knowledge and Grounds: A Comment on  Mr. Gettier’s Paper,” Analysis v. 24 (1963), pp. 46-48. 

[7] An analysis of a concept is too strong when it excludes cases which clearly fall under the concept—for example, an analysis of “triangularity” which held that “triangles are closed three-sided figures all of whose sides are of equal length” would be too strong as it excludes isosceles and scalene triangles!  An analysis is too weak when it includes cases which clearly do not fall under the concept—for example, an analysis of “triangularity” which held that “triangles are figures” would be too weak as it includes squares under the concept. 

[8] ‘iff’ stands for ‘if and only if’. 

[9] Michael Williams, Unnatural Doubts (Oxford: Blackwell, 1991), p. 319.  Emphasis is added to the passage. 

[10] Barry Stroud, “Understanding Human Knowledge in General,” in Knowledge and Skepticism, eds. Marjorie Clay and Keith Lehrer (Boulder: Westview, 1989), pp. 31-50, p. 40.  Reprinted in Knowledge: Readings in Contemporary Epistemology, Sven Bernecker and Fred Dretske, eds, op. cit, pp. 307-323, p.316. 

[11] Ralph Baergen, Contemporary Epistemology, op. cit., p. 9. 

[12] Robert Fogelin, Pyrrhonistic Reflections On Knowledge and Justification (N.Y.: Oxford U.P., 1994), p. 48. 

[13] Ibid., p. 54. 

[14] Ralph Baergen, Contemporary Epistemology, op. cit., p. 115. 

[15] Richard Boyd, “Scientific Realism and Naturalistic Epistemology,” in PSA 1980 v. 2, eds. P.D. Asquith and R.N. Giere (East Lansing: Philosophy of Science Association, 1981), pp. 613-662, p. 630. 

[16] Fred Dretske, “Conclusive Reasons,” in the Australasian Journal of Philosophy v. 49 (1971), pp. 1-22.  The essay is reprinted in Essays on Knowledge and Justification, eds. George Pappas and Marshall Swain (Ithaca: Cornell U.P., 1978), pp. 41-60, pp. 46-47, which is on Reserve in the Green Library. 

[17] Richard Foley, “Epistemic Luck and  the Purely Epistemic,” American Philosophical Quarterly v. 21 (1984), pp. 113-124, p. 121. 

[18] Marshall Swain, “Knowledge, Causality, and Justification,” The Journal of Philosophy v. 69 (1972), pp. 291-300.  The essay is reprinted in Essays on Knowledge and Justification, eds. George Pappas and Marshall Swain, op. cit, pp. 87-99, which is on Reserve in the Green Library. 

[19] Keith Lehrer, “The Gettier Problem and the Analysis of Knowledge,” in Justification and Knowledge, ed. George Pappas (Dordrecht: D.Reidel, 1979), pp. 65-78, p. 65. 

[20] Ibid., p. 66. 

[21] Ibid. 

[22] Ibid., p. 76. 

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