According to Kant, what knowledge is analytic a priori?


According to Kant, what knowledge is synthetic a priori?

















(1) All bodies are extended.

(2) All bodies have weight.

(3) Gold is a yellow metal.

(4) 7 + 5 = 12.

(5) A straight line is the shortest path between two points.

(6) All substance is permanent (compare:  Law of Conservation of Matter or Law of Conservation of Energy).

(7) F = ma.

(8) Every effect has a cause.

(9) Every event has a cause.

(10) Principle of Sufficient Reason

(11) Pure mathematics (includes Euclidean geometry)

(12) Pure physics (includes Newton's laws)

(13) Law of Excluded Middle

(14) Law of Non-Contradiction






Kant's Formula for the Synthetic A Priori:  Propositions that must be confirmed by all possible experience.  No experience could disconfirm them.


Quine will point to recalcitrant data from the history of science:

Replacement of Newtonian physics and Euclidean geometry by Relativity Theory (with a non-Euclidean geometry) and quantum mechanics (with probabilistic rather than strictly causal relations).














(1) What are the two dogmas?


(2) Why does Quine think that they are at root the same?


(3) Why does Quine think that there are no statements that are confirmed no matter what? 














The verificationist picture:  Each sentence’s meaning can be given by an ordered pair of:

<confirmation (verification) conditions, infirmation (disconfirmation) conditions>.


When all possible experience counts as a confirmation condition and no possible experience is an infirmation condition, the sentence is analytic.


This assumes that individual sentences have confirmation and information conditions.  This is called meaning atomism.








Quine’s Holist Alternative: 




Confirmation and disconfirmation are holistic, not atomistic. 


Radical revisability. 


The examples of Euclidean geometry and Newtonian physics.


For Quine, even the laws of logic are in principle revisable.


This is called meaning holism. 










(1) No unmarried man is married.


(2) No bachelor is married. 


Correct the text (395): 


(3) All and only bachelors are unmarried men.


(3) is analytic. 


(4) Necessarily all and only bachelors are bachelors.


(5) Necessarily all and only bachelors are unmarried men.


The "closed curve in space"(395):  analytic, a priori, necessary, true by definition or in virtue of meaning.


       Are there any exceptions?  What about the Pope?


Consider Kant’s list again.


For Quine, there is only one kind of epistemic justification.  It is holistic and empirical.
























I.  Two Roles for A Priori Insight

      1.  Source of premises

      2.  Validate steps of reasoning. 
















Examples of propositions justified a priori according to BonJour:


1.  All bachelors are unmarried.

2.  Nothing can be red and green all over at the same time.

3.  Nothing can be red and blue all over at the same time.

4.  If A is taller than B and B is taller than C, then A is taller than C.  (Transitivity of "taller than")

5.  There are no round squares.

6.  2 + 3 = 5 (Compare 2+2 = 4 with 25 – 5 = 33).

7.  A cube has 12 edges.

8.  Logical example:  Inference that David ate the last piece of cake (105).

9.  Law of Non-Contradiction

10.  Philosophy is a priori (106).


Example of reasoning justified a priori according to BonJour:




Either David ate the last piece of cake or else Jennifer ate it.


Jennifer did not eat the last piece of cake (perhaps because she was at work for the entire time in question).


Conclusion:  David ate the last piece of cake.










II.  Skepticism about All A Priori Justification = Intellectual Suicide

      Why does BonJour believe this?


III.  Skepticism about Synthetic A Priori Justification

      What is BonJour's Reply? 
















BonJour's "Companions in Guilt" Defense of Synthetic A Priori Justification


The Inadequacy of Accounts of Analyticity


(a) Conditional Accounts

      (i) Kantian and Fregean

      (ii) also Kant's alternative formulation


(b) No Epistemological Insight

      (i) Lewis

      (ii) Salmon: "empty of factual content"

      (iii) true by virtue of meaning


(c)  Too Obscure or Too Implausible

      (i) true by convention

      (ii) implicit definitions







IV.  BonJour's Moderate Rationalism

      1.  Intuitive apprehension of necessary truth (rational insight or rational intuition)

      2.  Fallibility (apparent rational insight or apparent self-evidence)

      3.  Externalist Requirements:  (1) the condition of cognitive sanity; (2) conditions for apparent rational insights; (3) reliability of memory.  (There are actually other externalist conditions in BonJour’s account.)













The Fallibility Problem for Epistemology and for Philosophy Generally



What Do BonJour and Quine Agree On?


(1)  Less important agreement:  No important difference between analytic a priori and synthetic a priori.


(2) Most important agreement:  If there is a priori justification, it is not infallible.


Is there a priori justification? 










V.  Issues Raised by BonJour's Account:

      1.  What is the difference between a putative, an apparent, and a genuine rational insight?

      [Why is BonJour an externalist about both apparent and genuine a priori insight?]

      2.  How can a mistaken rational insight be corrected?

      [Are all mistakes internally correctable?]

3.  Does reasoning require direct rational insight?

[What is the content of the insight?]

4.  Can any substantive position in philosophy be justified purely a priori—that is, by direct rational insight of premises and deductive reasoning from such premises?

[Isn't it relevant whether other people agree or disagree?]

5.  Can the rational degree of belief in a putative a priori insight itself be determined purely a priori?  [What led BonJour to become a fallibilist about apparent a priori insight?]

Stich's Challenge


Could human reasoning not be based on a priori insight into valid principles of inference?


I.  The evidence that people do not reason in accordance with valid principles:

      1.  Wason Selection Task:  Deductively invalid reasoning.

      2.  Inconsistencies in probabilistic reasoning.

      3.  Belief perseverance and debriefing.










Conditional:  If there is a vowel on one side, there is an even number on the other.























           a                      b                   c                          d



Conditional:  If a patron is drinking beer, s/he is 21 of older.























           a                      b                   c                         d



"If p then q" is equivalent to "‑(p&-q)"

Test for this:  -(Beer & under 21)



In the first example, the test would be:

-(Vowel & odd number).  Why don't people see this?



5.  Assume that the probability of a woman giving birth to a boy is the same as the probability of a woman giving birth to a girl (1/2 in both cases).  In families with two children of which at least one is a girl, what is the probability that the other child is also a girl?  


In families with two children, what is the probability that the first child is a girl? a boy?

In families with two children, what is the probability that the second child is a girl? a boy?



              GG:  prob = 1/4

G                                             These three

              GB:  prob = 1/4        outcomes are

                                                 equally probable.

              BG:  prob = 1/4


              BB:  prob = 1/4







More evidence:  False Proofs of Fermat's Last Theorem:


      “In 1908, the Wolfskehl Prize of one hundred thousand marks was offered in Germany for anyone who could come up with a general proof of Fermat’s Last Theorem.  In the first year of the prize, 621 ‘solutions’ were submitted.  All of them were found to be false.  In the following years, thousands more ‘solutions’ were submitted, with the same effect.  In the 1920’s German hyperinflation reduced the real value of the 100,000 marks to nothing.  But false proofs of Fermat’s Last Theorem continued to pour in.”[Aczel, p. 70] 








II.  Who sets the standards for Stich?

(1) Not individuals.

(2) Not majorities.

(3) Reflective equilibrium of experts.


III.  How reliable are the experts?  The Monty Hall Problem. 


IV.  Could good reasoning be a combination of useful heuristics that has been selected for by biological and cultural evolution rather than something that requires insight into necessary truths?   What is the status of deductive logic on this account?


V.  How would BonJour reply? 









The Monty Hall Problem



Setup:  3 doors. There are goats behind two of them and a car behind one.  You want the car, not a goat.


Key claim:  No matter which door you pick, the host can AND WILL always open a door with a goat.


Two Strategies: 


(1) Stay = Pick a door and stay (don’t switch) after the host opens a door.  What is the expected percentage of wins with this strategy?


(2) Switch = Pick a door and switch to the unopened door after the host opens a door.  What is the expected percentage of wins with this strategy?


In this case, powerful apparent a priori intuitions prevent learning.


Pigeons and the Monty Hall Problem

(Herbranson and Schroeder 2010).


Comparison of six pigeons and 13 undergrads:


On the first day, the pigeons STAYED 2/3 of the time and SWITCHED only one-third of the time, which indicates that they did not have any a priori intuitions about the situation.  By day 30, the pigeons SWITCHED more than 96% of the time.  The pigeons had effectively learned to SWITCH, with some random checking for changes in the payoff to the other strategy.


On the first day, the undergraduates SWITCHED slightly more often than they STAYED, which is compatible with the hypothesis that they did not think that any strategy had any advantage over the other.  By day 30, the human subjects SWITCHED 2/3 of the time, but they did not seem to be increasing from that level.


Which species is more sensitive to the pattern of pay-offs (experience)?