PHIL 2100: Introduction to Philosophy
Dr. Robert Lane
Lecture Notes: Friday June 16, 2010


[4.3.] Necessary and Sufficient Conditions.


The concepts necessary condition and sufficient condition, used in the previous section, are very widespread in philosophy.


To illustrate how these concepts work, I’ll apply them to the concept bachelorhood.


(In the following, “S” is a variable standing for some person or other; it comes from the word “subject.”)


(y) S is a bachelor


(a) S is an adult                        necessary, but not sufficient, for being a bachelor

(b) S is male                 necessary, but not sufficient, for being a bachelor

(c) S is unmarried        necessary, but not sufficient, for being a bachelor


Each of the three conditions (a), (b) and (c), taken by itself, is a necessary condition of bachelorhood. If any one of these is not the case, then S is not a bachelor.


On the other hand, neither (a), nor (b), nor (c), taken by itself, is sufficient for bachelorhood. None of them on its own is enough to make someone a bachelor.


However (a), (b), and (c), taken together, are sufficient—combined, they are enough to make S a bachelor. In other words, those three conditions are jointly sufficient for bachelorhood. We can combine these three conditions into a single statement:


(x) S is an adult unmarried male.


Now consider the following:


(x) is a necessary and sufficient condition of (y).


This combines two distinct claims:


(x) is a necessary condition of (y)


in order for (y) to occur, (x) must occur


if y, then x


x if y

(x) is a sufficient condition of (y)


in order for (y) to occur, it is enough that (x) occur


if x, then y


x only if y



So “(x) is a necessary and sufficient condition of (y)” means: x if and only if y.



[4.4.] Defining “Knowledge”.


One way to answer the question “What is knowledge?” (referring to propositional knowledge) is to provide necessary and sufficient conditions for knowledge, to fill in the following blank:


S knows that p if and only if ______________________________


Two of the necessary conditions are obvious:


(a) S believes that p

(b) It is true that p


But these two are not jointly sufficient… together, they are not enough for knowledge.


In his dialogue Theaetetus, Plato maintained that lawyers can convince a jury to believe a claim, sometimes by illegitimate means, and even if the claim is true, those jurors won’t know that claim.

·         Suppose that I commit a crime, and the DA cannot prove that I did it by legitimate means—she simply does not have enough evidence. So she manufactures evidence to convince them of my guilt. They have a true belief (it’s true because I actually committed the crime), but should we say that they know that I did it? It seems natural to say that they do not know that I did it, even if they believe that I did it and it is true that I did it.


What else is needed? Many philosophers think that the missing ingredient is justification.


(c) S is justified in believing that p.


Of course, now we need to explain what “justified” means; we need some explanation of what it is to be justified in believing something. A very rough explanation is this: someone’s belief that p is justified when she has good reasons for believing that p.[1]


In my example, the jury did not have good reasons to believe that I did it, since their belief that I did it was based only on lies told to them by the DA. (They thought they had good reasons, but that’s different than actually having good reasons.)


Adding the three conditions, a, b, and c, together, we get what it called JTB Theory:


Justified True Belief (JTB) Theory, a.k.a. the standard definition of knowledge:

S knows that P if and only if all three of the following conditions are met:

(1) it is true that P;

(2) S believes that P; and

(3) S is justified in believing that P.



[4.1.4.] Gettier Counterexamples.


Edmund Gettier (1963) argued that JTB is not sufficient for knowledge. He argued this point by providing a counterexample to the JTB theory.


counterexample (df.): an example that contradicts what some theory or claim says; for example, if the original claim is that “All As are Bs,” a counterexample would be an A that is not a B.


Gettier’s counterexample is a case of JTB that is not a case of knowledge.


Smith goes to interview for a job…


The secretary tells Smith: “Jones will get the job.” But she is wrong; in fact Jones will not get the job. Smith will get the job—he just doesn’t know it yet.


So Smith ends up believing: “Jones will get the job.” (F)


Because earlier he was peeking in Jones’ pocket, Smith also believes: “Jones has 10 coins in his pocket.” (T)


So Smith ends up believing: “The man who will get the job has 10 coins in his pocket.” (T)


That belief is true, because Smith also has 10 coins in his pocket.



Smith’s belief that the man who will get the job has 10 coins in his pocket is:

·         true (because that man—Smith—does have 10 coins in his pocket) and

·         justified (Smith has good reason to believe it—the secretary is an authoritative sour of information about who will get what job; and Smith has seen for himself that Jones has 10 coins in his pocket), but

·         it is not a case of knowledge (according to Gettier).


Cf. Russell’s example of the clock in the town square (p.153).


If Gettier is right, then JTB is not the same thing as knowledge.



[4.1.5.] Strong and Weak Concepts of Justification.


Whether this kind of counterexample really works against the JTB theory depends on how strong one’s concept of JUSTIFICATION is…



weaker conception: justificationw


If we mean by “S is justified in believing p” that S has very good (but not perfect) reasons to believe / evidence that p




the counterexample does work against JTB, since Smith has have very good (but not perfect) reasons/evidence for p. He is justifiedW, but does not have knowledge.




JTB fails and we need a new definition of knowledge.

stronger conception: justifications


If we mean by “S is justified in believing that p” that S has perfect evidence / reasons to believe that p




the counterexample does not work against JTB, since Smith does not have perfect reasons/evidence for p. He is not justifiedS and so his belief is not a counterexample to JTB.




(It might be the case that) no one ever has perfect reasons for believing anything, so accepting this notion of justification  pushes us toward skepticism, because it seems that we do not have any beliefs that are justifiedS.



This is a general problem with attempts to solve the problem of knowledge:


Ff you characterize justification in a weaker way, then

(a)    your definition of “knowledge” can be broad enough for it to turn out that we do have knowledge, but

(b)   that definition cannot be defended against counterexamples like Gettier’s… i.e., the JTB theory fails.


On the other hand, if you characterize justification in a very strong way, then

(a)    you can defend the JTB theory against counterexamples like Gettier’s, but

(b)   your definition of “knowledge” becomes so narrow that it turns out that nobody ever has it (this is skepticism).


[4.2.] Descartes’ Meditations.


René Descartes (1596-1650)


·         Born in Tourraine, France; spent most of his life (1628-1649) in Holland.

·         He wrote on wide variety of topics: physics, astronomy, music, human physiology and psychology.

·         He made important contributions mathematics, including the invention of analytic geometry, the analysis of geometric structures primarily by way of algebraic operations on variables defined in terms of position coordinates. “Cartesian coordinates” were named for him (based on his name having been spelled “Des Cartes”).

·         His main philosophical works were

·         Discourse on the Method of rightly conducting the Reason and seeking the Truth in the Sciences (1637, in French)

·         Meditations on First Philosophy in Which the Existence of God and the Distinction of the Soul from the Body Are Demonstrated. (1641, in Latin; 1647, French trans.) [we will be reading some of this]

·         In September 1649, he went to Sweden at the request of Queen Christina, who wanted to learn philosophy from him.  But the Swedish winter was harsh, and Christina made Descartes, who was accustomed to lying in bed until noon, come to her library at 5am every day, when it was very cold. He became very sick and died Feb 1650.


Descartes received a good education, which he himself admitted. But early in his life, he decided that no one knew anything worth learning (much like Socrates):


I found myself beset by so many doubts and errors that I came to think I had gained nothing from my attempts to become educated but increasing recognition of my ignorance. (Discourse on the Method 1.4)


So he gave up “the study of letters” (learning what other man had written) and began traveling, hoping to learn something of importance from his experiences. He turned his back on the teachings of others in the hope of discovering important truths on his own. This is indicative of the individualism of the Meditations.


Descartes tried to give an account of knowledge that avoided skepticism about knowledge of the world outside our own minds. His main concern was to overcome skepticism about the external world, to show that we do in fact have knowledge of the external world.


He is now classified as member of the philosophical movement called rationalism:


rationalism (df.): the epistemological view according to which the only, or at least the most important, source of knowledge about the world is reason, not the senses. [Prominent rationalists include Descartes, Baruch Spinoza, and Gottfried Leibniz.]


This is opposed to a very different epistemological tradition in European philosophy:


empiricism (df.): the epistemological view according to which knowledge, or at least the most important knowledge, is to be gained only through experience. Empiricists reject substantive claims about the world that cannot be justified by appeals to experience (e.g. John Locke, George Berkeley, and Hume).


The basic epistemological view adopted by Descartes is now called foundationalism


foundationalism (df.): the view according to which there are two types of justified beliefs: (i) basic beliefs, which are justified, but not justified by any other beliefs; and (ii) derived, which are justified by other beliefs.

·         There are different types of foundationalism, but all types make these two claims.


Descartes wanted to identify the most basic, fundamental beliefs, those that are epistemically certain (which absolutely cannot be false), and build up from there.


epistemic certainty (df.): S is epistemically certain that p when S believes that p and S cannot possibly be mistaken in that belief; certainty that requires the impossibility of error.


This is very different from


psychological certainty (df.): a feeling that a belief one has must be true, e.g., when I seem to see and feel desks in this room and come to believe that the room contains desks, I feel certain that there are desks in the room.

·         It is possible to feel certain that p even if it is false that p; e.g., a gambling addict might feel certain that she is going to win the next hand of blackjack, even if in fact she is not.



[4.2.1.] Descartes’ Method of Doubt.


Descartes’ so-called Method of Doubt test is like a filter for basic beliefs. If a belief can pass the method of doubt test, then it is epistemically certain and therefore qualifies to be a basic belief.


Here’s how the method works: attempt to construct a story in which you believe that p but it is false that p.

·         If you can, then set aside the belief that p—it is not absolutely certain. (It may be true, but it’s not beyond doubt.)

·         If you cannot, then the belief that p is indubitable (beyond doubt) and therefore basic (foundational).


So Descartes sets out looking for indubitable beliefs to serve as the foundations of knowledge. Before we see how he applies his method, let’s get clear on exactly what dubitability is.

·         It is not a psychological property – for a belief to be dubitable is not for any human being to actually be able to take seriously the possibility that it is false.

·         It is a logical property – it has to do with whether a certain kind of story is logically possible. If it is logically possible for you to believe p while at the same time it is false that p, then p is dubitable.


So Descartes is searching for beliefs that are true and that cannot possibly be false. So we can be epistemically certain that the belief is true.


Descartes does not have to examine his beliefs one at a time. That would take far too long! (“Is it possible that my belief that this is an ice cube is false?” “Is it possible that my belief that this other thing is an ice cube is false?”)


He instead wants to apply his Method of Doubt test in way that, if it shows a belief to be dubitable, it will show a whole group of beliefs to be dubitable:


… owing to the fact that the destruction of the foundations of necessity brings with it the downfall of the rest of the edifice, I shall only in the first place attack those principles upon which all my former opinions rested. (Med I, Sober, 207)



[4.2.2.] The Method of Doubt vs. A Posteriori Beliefs


The first group of beliefs to which Descartes applies the method of doubt test is a posteriori beliefs:


a posteriori (df.): an a posteriori belief or statement is one that could be known or justified only by sense experience: e.g. “I am wearing a baseball cap”; “I am lecturing right now”; “the sky is blue,” “ice is cold,” etc.

·         They are called  a posteriori because they can be known only after (posterior to) sense experience.


Says Descartes, a posteriori beliefs fail the Method of Doubt test. There is always a possible reason to doubt any belief based on sense experience, namely, that the senses have deceived us before, so they might be deceiving us again:


All that up to the present time I have accepted as most true and certain I have learned either from the senses or through the senses; but it is sometimes proved to me that these senses are deceptive, and it is wiser not to trust entirely to anything by which we have once been deceived. (Med I, Sober 207)


In response to this, Descartes grants that there are some things that we should not trust the senses about (“minute objects”), but asks whether it is possible to doubt what the senses tell us is near at hand:


But it may be that although the senses sometimes deceive us concerning things which are hardly perceptible, or very far away, there are yet many others to be met with as to which we cannot reasonably have any doubt, although we recognise them by their means. For example, there is the fact that I am here, seated by the fire, attired in a dressing gown, having this paper in my hands and other similar matters. And how could I deny that these hands and this body are mine, were it not perhaps that I compare myself to certain persons, devoid of sense, whose cerebella are so troubled and clouded by the violent vapours of black bile, that they constantly assure us that they think they are kings when they are really quite poor, or that they are clothed in purple when they are really without covering, or who imagine that they have an earthenware head or are nothing but pumpkins or are made of glass. But they are mad, and I should not be any the less insane were I to follow examples so extravagant. (Med I, Sober 207-208)


But at this point Descartes realizes that there is another possible reason to doubt any belief based on sense experience, viz. it is always possible that we are dreaming.


At the same time I must remember that I am a man, and that consequently I am in the habit of sleeping, and in my dreams representing to myself the same things or sometimes even less probable things, than do those who are insane in their waking moments. How often has it happened to me that in the night I dreamt that I found myself in this particular place, that I was dressed and seated near the fire, whilst in reality I was lying undressed in bed! At this moment it does indeed seem to me that it is with eyes awake that I am looking at this paper; that this head which I move is not asleep, that it is deliberately and of set purpose that I extend my hand and perceive it; what happens in sleep does not appear so clear nor so distinct as does all this. But in thinking over this I remind myself that on many occasions I have in sleep been deceived by similar illusions, and in dwelling carefully on this reflection I see so manifestly that there are no certain indications by which we may clearly distinguish wakefulness from sleep that I am lost in astonishment. And my astonishment is such that it is almost capable of persuading me that I now dream. (Med I, Sober 208)


There is no sure criterion to judge whether one is dreaming or awake. In dreams we are (at least sometimes) just as sure that we are awake as we are when we are actually awake.


So with this point about dreaming, Descartes thinks that he has shown that it is always possible to doubt a posteriori beliefs. So there is nothing in the physical sciences (“physics, astronomy, medicine”) that is indubitable. If we are to find epistemically certain, basic beliefs, we must look elsewhere…



Stopping point for Wednesday June 16. For next time, read Descartes’ Meditation II (pp.210-16) and III (pp.216-222 only), then all of Sober’s chapter 13. We have fallen behind so this reading does not line up exactly with what is on the syllabus. Tomorrow (Thursday June 17) is the last day to withdraw from class with a “W”.




[1] Sober suggests an alternative, rough account: “We should think of individuals as having certain duties concerning how their beliefs should be formed. A belief is justified if the process by which it was formed does not violate any duties that the person has.” (151) This sounds somewhat like a recently popular approach to epistemology called virtue epistemology. For more information, see John Greco and John Turri, “Virtue Epistemology,” The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward N. Zalta (ed.), URL = <>.

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