Kripke on A Priori Knowledge and

Necessity

Traditional views• Kripke: historically, philosophers have assumed two things:

1.All a priori knowledge is of necessary truths.– Recall such diverse thinkers as Chisholm, Kant and Ayer.– Even Quine’s denial of necessary truths is part of his argument that there is no a priori knowledge.

2.All a posteriori knowledge is of contingent truths.– Again, Chisholm, Kant and Ayer.– Quine: all knowledge is both empirical and revisable.

• Kripke argues that both principles are mistaken.

Names• Old Theory (Frege-Russell): Names are abbreviated descriptions:– E.g.: we know that Aristotle was Plato’s greatest student.

– So: ‘Aristotle’ means ‘Plato’s greatest student’.•Note: this is a very simplified example.

• Kripke: If ‘Aristotle’ means ‘Plato’s greatest student’, then:– ‘Plato’s greatest student is not Aristotle’ is a contradiction.

– Equivalent to ‘Plato’s greatest student is not Plato’s greatest student’.

– This is necessarily false. (Note this)

A problem• Kripke: this can’t be necessarily false. Here’s why:

• It is plainly possible that someone else might have been Plato’s greatest student.– Aristotle could have chosen not to study philosophy at all.

– He might have gone into politics or become a soldier.– These are simply not contradictions.

• So, ‘it might have been the case that: Plato’s greatest student is not Aristotle’ is true!

• The old theory of names is wrong.

Identity and necessity• Kripke: Aristotle might not have been Plato’s student, a philosopher, etc.– These are contingent features of Aristotle

• But: it is not true that Aristotle might not have been Aristotle.

• Try to imagine a possible world in which Aristotle exists, but is not Aristotle.

– If that person is not Aristotle, then it is not a world in which Aristotle is not Aristotle.

– If that person is Aristotle, then it is not a world in which Aristotle is not Aristotle.

Identity and necessity• Kripke’s conclusion: there is no possible world in which Aristotle is not Aristotle.

• If X = X, then NECESSARILY, X = X.– (Let’s call this the ‘Kripke Formula’)

• There are no contingent identities!

Rigid designators• X is a rigid designator if and only if it designates (i.e. refers to) the same entity in every possible world (in which the entity exists). 

• Kripke: We can see that ‘Aristotle’ is a rigid designator:

1. In our world, ‘Aristotle’ designates Aristotle.2. In every world in which he exists, Aristotle = Aristotle.3. So, the person we refer to by ‘Aristotle’ retains his identity

across all worlds in which he exists.

• In other words, our word ‘Aristotle’ picks out a person who exists in many possible worlds, so when we we use the name, we refer to a single person who in fact exists in multiple worlds.

Names and descriptions• Kripke: since names are rigid designators:

– ‘Aristotle’ refers to a particular individual person.– If we want to consider what could have been true of him, we must imagine him but with different properties.

• The contingent descriptions that attach to Aristotle have nothing to do with the content of the name ‘Aristotle’.– Names pick out individuals and do nothing else.– They are like tags, not abbreviations. – There only function is to designate something (not to describe it).

Names are tags• Any kind of term can be used to tag/name someone.

• You don’t need to know anything about these people to be able to use their names refer to them.

• You may think that Alpha is a doctor, for example, but perhaps she is in costume; – You can still use ‘Alpha’ to designate her.

Jane Alpha

E2reqd933d

A thought experiment• You are taught that ‘Hesperus’ refers to that bright object that you often see in the sky before sunrise.– You are also taught that ‘Phosphorus’ refers to that, bright object you often see in the night sky.

– Your teachers tell you: ‘Hesperus is the morning star and Phosphorus is the evening star’.

• Later on, Astronomers perform some observations:– The morning star is Venus; so is the evening star!– ‘Hesperus’ refers to Venus and ‘Phosphorus’ refers to Venus.

• Since Hesperus = Phosphorus, necessarily Hesperus = Phosphorus (remember the Kripke formula).

Empirically discovered necessities

• Kripke: Hesperus = Phosphorus was an empirical discovery.– Astronomical observations were required to learn it.– So, it is a posteriori. – However: what is learned is necessary. 

• So, some propositions are necessary but a posteriori. 

• Some other necessary a posteriori propositions:– Water = H20– Temperature = mean kinetic molecular energy.– Math proofs done by computer.

A historical detour• Venus has an interior orbit so, it can never appear all that far away from the Sun in the sky.

– Venus is, therefore, usually seen not long after sunset or not long before sunrise.

– It is also, usually, the brightest object in the sky.

– At first, observers thought there were two stars there, not one planet.

Contingent a priori

• The official, scientific measurement society (OSMS) has been asked to determine the exact, official length of one meter.– Whatever they decide will, by international treaty, become the universal standard measure of a meter.

• So, all members of the OSMS gather in Paris:– With support of all members, the lead scientist stands up, holds a bar of length L in front of the scientists, and says:

– “The length of this bar is hereby declared to be the standard meter”.

– Kripke: what follows from this declaration?

Contingent a priori• The scientists know that the bar’s length, L, is 1 meter.– They don’t have to measure anything; It is known a priori!

– it follows from the declaration itself (in context)

• But is this claim necessary?

• Kripke: No.– If it were necessary, it would be impossible for the bar to be any length beside L.

– But this is not impossible:– If the bar had been hotter when the declaration was made, it would have been a different length.

Reference fixing• When the declaration is made, the scientist aims to single out or a certain length (one that in fact equals 39.37 in.) – She uses the length of a particular bar to pick out this length.

– In other words, the length of the bar at that time fixes the reference of ‘one meter’.

• Kripke: it does not follow that this length is essential.– Whatever length the bar has at that time is contingent: it might have been otherwise; it might change.

– (Note: one metre = length L remains necessary). 

• Conclusion: some claims are a priori but contingent.

Conclusion• Kripke: The: a priori/a

posteriori distinction does not track the: necessary/contingent distinction.

• This may appear to be a subtle point, but it in fact carves out a philosophical position that few (if any) thinkers prior to Kripke considered to be possible.

A priori A posteriori

Necessary

‘All bachelors are unmarried’

‘Hesperus is Phosphorus’

Contingent

‘This bar is one meter long’

‘Toronto is Canada’s biggest City’

The Kripkean position• If Kripke is right, then:

1. Synthetic a priori knowledge is possible (contra Ayer, Quine, Hume, etc.). 

2. Synthetic a priori knowledge does not require that the world conform to the mind (contra Kant)

3. A priori knowledge is possible even if there are no analytic claims (contra the empiricists).

4. A priori Knowledge is not limited to necessary claims (contra Chisholm).

• So his position would be almost unique among philosophers (Ruth Barcan Marcus appears to have anticipated much of Kripke’s reasoning).

Kripke and essentialism• If water = H20, then, for Kripke, necessarily water = H20.

– But this claim is not necessary in virtue of the meanings of words.

– It is not part of the meaning of ‘water’ or ‘H20’ that they be identical. 

• This is a kind of essentialism: water has a necessary property: being H20.– Anything that is not H20 is not water, even if it is liquid, colourless, tasteless, etc.

• What do you think: are there some features of objects or people that are necessary in this way? – Could something be water even if it had molecular structure XYZ? – Is this an unduly strong commitment to chemical theory?