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Kripke's Modal Argument Against the Identity Thesis

Updated on July 31, 2014
Example of a Predicate Logic model.
Example of a Predicate Logic model.
Here is another first-order model, with identity added. Can you tell which of the expressions written in red are true, and which are false, in this model?
Here is another first-order model, with identity added. Can you tell which of the expressions written in red are true, and which are false, in this model?

The Identity Thesis

What is known as the Identity Thesis in the Philosophy of Mind posits that mental states (thoughts, emotions, beliefs, etc.) are the same as brain states (firing of synapses in the brain.) The thrust of this view is Eliminativist: mental states are nothing but electrochemical events more or less in the way in which the primitive's punitive thunderbolt turns out to be electric discharge. Long before the modern breakthroughs and astonishing advances in the study of the brain, the Materialist persuasion in classical philosophy was pushing toward the eliminativist direction - although this is not an entirely accurate characterization since the classical discussions had fewer categories in the philosophy of mind, into which to put their claims and, so, it is uncertain how exactly to map ancient views on this issue onto the various contemporary schools of thinking. There is a reigning view today, presumed eminently scientific, that seeks to to outlaw as "folk psychology" references to the spooky ontology of the mental. As primitive folklore fussing about the punitive thunderbolt was crushed by scientific progress, so will the pretenses about a "mind" and its ethereal contents be demolished when the brain has been mapped out completely. This view comes under attack in the philosophy of mind - an area that is, unfortunately, beyond the everyday ken even of educated people. More often than not, the attacks on claims like that embodied in the Identity Thesis are subtle. But we need first to restate the Identity Thesis itself before we proceed to examine what is known as Kripke's Modal Argument against this thesis.

We should be speaking of "mental states" and "brain states" as names or, if you will, labels whose referents or denotata are the objects we are to talk about. This shift paves the way for setting up the critical argument but it is also, in itself, motivated by certain philosophic considerations:

There is a prominent view that traditional metaphysical queries - investigations about what kinds of things do and may exist and what attributes such things do or may have - run into grief in the most fundamental ways. Mostly, the problem consists in abuse of language. If and when this happens (think of Carrol's deliberate misuses of language in Alice in Wonderland) then we end by with nonsense. This is easy to detect in a statement like "a triangle has four angles" (definitions of wods are violated, resulting in a nonsensical and, as such, necessarily false proposition being expressed.) Yet, nonsense is not always as straightforwardly available for detection. Psychologically, one may be persuaded that what is indeed nonsense... makes sense and be adamant about it. On the view that broad metaphysical qeries (investigations undertaken across the board, as when it is asked "what exists within the totality of things" or "why does anything exist?") are based ultimately on misuse of language; it is not surprising that traditional metaphysics is plagued by a plethora of puzzling issues and apparent paradoxes - and the result has been endless debate. A way around the problem is to consider ontologies (accounts of what things exist and what attributes they have) as confined to specific theories - in a broad sense of "theory." Such views are, as usual, at least implicit in Ludwig Wittgenstein's later work but the most perspicacious exponents of the view that ontologies are to be restricted internally to theories have been Rudolph Carnap and his student (up to a point) W. V. O. Quine. As we restrict ontologies to theories we are ready to employ the precious resources of Predicate Logic (also called First-Order Logic or Quantification Theory.) We can even model what we are talking about. We have a domain with our objects (we are welcome to them since they are posited internally rather than across some obscure firmament of the totality of things); we have quantifier phrases so we can quantify over them; and we have names or constants to use in tagging or labeling our domain objects. That's it.

Classical Predicate Logic, stubbornly defended by philosophers like Quine, actually comes to grief for certain technical reasons - and it has unintuitive consequences, as by not allowing for empty or non-referring terms. A more interesting formal alternative is the family of what are known as Free Logics. We are not interested in such details here. The point is that we have a deeper, philosophically motivated reason, for talking about "brain states" and "mental states" as the names that refer to or denote the objects we have in the debates (and the scientific study) of those putative entities.

Reformulating the Identity Thesis accordingly, we have: the names "mental states" and "brain states" co-refer - they have the same things as their referents. This, of course, means that mental states are not different from brain states (the referents are the same thing.) The object to which the term "brain states" refers is well understood, amenable to scientific study and free of paradoxical consequences. We cannot say this of "mental states" - at least not if the issue is engaged by default on the grounds of scientific inquiry. It follows that there is no prospect of attempting a rejoinder along the lines of "fine, the two terms name the same thing but this thing may well be mental."

The Kripke argument attacks the IT (Identity Thesis) as reformulated in the preceding paragaph.

Brain and Mind

Do the terms "Brain" and "Mind" refer to the same thing?

See results
Saul Kripke
Saul Kripke

Kripke's Argument Against the Identity Thesis

We will spell out the argument first. Next, we will need to detour through another point due to Kripke - which we can call the "Strengthening of Identity". This latter claim furnishes one of the premises of the argument against the Identity Thesis (IT).

Let us call the Modal Argument against the Identity Thesis MAIT.


  1. If two terms co-refer, then it is necessarily true (in a certain sense of "necessarily") that they co-refer. [this is the "Strengthening of Identity" claim (SI)]
  2. Therefore, if the terms MS and BS co-refer, then it is necessarily true that MS and BS co-refer. [from 1 and 2]
  3. But it is conceivable that MS and BS do not co-refer: we can conceive, without absurdity, that some species (possibly even we) are or could be so constituted that some mental state (for instance, pain) has a different corresponding BS (not C-fiber firing as the case is with us but some other brain synapses firing.) [this is a plausible claim]
  4. Conceivability of a proposition not-p implies that it is possible that not-p -- in the sense of "possible" used in this argument. [Claim about how conceivability is related to necessity, ConcNec]
  5. Therefore, it is possible (in the sense of necessary/possible in this argument) that MS and BS do not co-refer. [from 4 and 5]
  6. Therefore, it is not necessarily true that MS and BS co-refer. [from 6 and given how necessity and possibility are related, NecPoss]
  7. Therefore, the terms MS and BS do not co-refer. [from 1 and 6, by application of the inferential rule known as Modus Tollens.]

MAIT schematically (informally, and omitting quotation marks around the terms "MS" and "BS.")

  1. (term1 = term2) => Nec(term1 = term2) SI
  2. (MS = BS) => Nec(MS = BS) 1-instance
  3. Conc(not-(MS = BS))
  4. Conc(not-p) => Poss(not-p) Conc/Nec
  5. Poss(not-p) => not-Nec(p) Poss/Nec
  6. Conc(not-p) => not-Nec(p) 4, 5 - Inference Rule: Hypothetical Syllogism
  7. Conc(not-(MS = BS)) => not-Nec(MS = BS) 6-instance
  8. not-Nec(MS = BS) 3, 7 - Inference Rule: Modus Ponens
  9. not-(MS = BS) 2, 8 - Inference Rule: Modus Tollens

Now that we have the argument, we can scrutinize its premises. The argument is valid - all the inferential deductive rules applies are valid in the standard deductive system, which means that we cannot possibly get a false proposition when we apply such rules to true propositions. Whether the argument is also sound depends on whether all its premises are warranted or well-supported so as to be accepted as indeed true. We can look into that now but we also have to specify what necessity species is at stake here (the sense in which "necessarily" and "possibly" are used in this argument); and we have to explain how premise 1 (Strengthening of Identity: SI) is to be supported.

Metaphysical Necessity

The meanings of "necessarily" and "possibly" required for the argmetn to go through belong to the species called Metaphysical Modalities. What needs to be defended is, first, that there are more than one species of necessity (or modality, if you will) and, next, that the term "metaphysical necessity" as defined makes sense and is a distinct species indeed.

The details could detain us for long but we will, instead, take some liberties and cut to the point.

Think of "necessarily" and "possibly" as always qualifying propositions. We are not interested at all in the use of these words as adjectives - e.g. in "water is necessary for survival." Instead, we take the preceding sentence to be making the point of the sentence "it is necessarily true that p" where p stands for "survival depends on having water." The sense of "necessarily" here we don't dissect yet.

A proposition is logically necessarily true (false) if and only if the meanings of the words in it make it so that checks as true (false) in every logically consistent (and complete) description of a situation. For instance, keeping language and the definitions of the words constant, the meaning of the sentence "all triangles have three angles" is logically necessarily true because it has to be true (remember that the language is kept fixed) in every consistent and complete account of any situation we can come up with. The same is the case with the statement we make when we say "either triangles are rectangles or triangles are not rectangles" - in this case the words whose meanings matter are "all" and "if-then." There is no logically conceivable situation in which this statement can be false. Such propositions are known as analytic. So, logical necessity is analyticity on this view (it is not the only view around...)

What about a statement like "Superman flies"? Is it logically impossible? There is nothing in the meaning of the words in the proposition expressed, which make it analytically fixed that this is true - or false for that matter. And yet, there is a sense in which we say that what Superman is presumed to be able to do is "impossible." This is not the logical sense; it is a sense we can call physical. It is logically possible but physically impossible that someone who is human flies. Actually, we might need a more fine-grained distinction of species of necessity and possibility than just logical and physical. (The impossibility in the case of Superman might not be physical exactly sionce the laws of nature do allow for other anatomically correct species to fly - although they do not allow humans to do so...)

The kind of necessity that is involved in the Kripke argument is metaphysical. This is what it means: it is metaphysically necessary that p if and only if p has to be true in every logically possible situation (or rather its complete description) that is exactly like our world with respect to how things work (what properties things have - at least when it comes to certain fundamental, especially natural, properties.) For instance, water is H2O in our world: we cannot tell that it is incompatible with the laws of nature to have something that has exactly the properties of water without having the chemical composition H2O. It is not physically but metaphysically necessary that water is H2O: in every world in which natural kinds have the same defining properties as they have in ours, water will have to be H2O there.

Next we have to lay out the case for what we called Strengthening of Identity (SI).

Wo is the actual world: "it is metaphysically necessary that p in the actual world" (Necm(p), Wo) means by definition that it is true that p in every world that is m-related to Wo - notice that the value of p in the unrelated worlds does not matter.
Wo is the actual world: "it is metaphysically necessary that p in the actual world" (Necm(p), Wo) means by definition that it is true that p in every world that is m-related to Wo - notice that the value of p in the unrelated worlds does not matter.

Strengthening of Identity

There was once an old puzzle that can be resolved by bringing metaphysical necessity. This result that can be accepted as non-puzzling anymore is what we call Strengthening of Identity.

It goes like this: if two names co-refer (for instance "morning star" and "evening star" turn out to be naming the same planet, Venus), then it must be necessarily true that they co-refer. This is puzzling: it is surely a contingent matter that those two names (which people coined to refer to what they thought are different celestial bodies) refer to the same object. How can it be a matter of necessity that two names, picked to refer to objects x and y, must refer to the same object if it turns out, after all, that x and y are the same object?

And yet, there is a proof of this - sketched very briefly here: since x and y are the same object, after all, they must have all their attributes in common. (This is called Leibniz's Principle of the Indiscernability of Identicals.) Now, x has the attribute "necessarily-identical-with-x" (self-identity is surely a matter of necessity.) Since y has all the attributes of x, then it must also have the attribute "necessarily-identical-with-x." So, y is necessarily identical with x if it so happens that it is just identical with x.

If the species of necessity involved is metaphysical we can give an account that dispels the apparent paradox: what we are saying when we use the strong identity is just that the item referred to is, after all, identical with itself as a matter of necessity. How do we bridge the gap between the thing referred to and the names referring to it? Kripke's point is that in every world metaphysically like ourse - where water has to be H2O etc. - the names must also be referring to the same object: so, in our actual world, it is metaphysically necessary that these names co-refer. This is a Nominalistic view that has no use for abstract things - or for what the Scholastics called "essential properties." This view has the consequence that you track an item "rigidly" throughout any possible situation in which the item may be said to exist by its name. (It is not intuitive, though, that "Nixon" would be called "Nixon" in every possible world... )

Now go back to the Kripke modal argument against the identity thesis and see how the strengthening of identity is used there as premise 1.

Given that any object named "a" possesses the self-identity property necessarily, any other object that happens to be identical with the object named "a" must also possess necessarily the property "identical-with-a."
Given that any object named "a" possesses the self-identity property necessarily, any other object that happens to be identical with the object named "a" must also possess necessarily the property "identical-with-a."

Kripke's Neo-Nominalistic Name-Rigidity

Kripke name-rigidity. In every logically possible world, the same tag or name is to be referring to what we are to take as the same individual object. We don't track the object by its properties - which properties would those be?
Kripke name-rigidity. In every logically possible world, the same tag or name is to be referring to what we are to take as the same individual object. We don't track the object by its properties - which properties would those be?

Another Modal Argument Against Materialism

Objections to Kripke's Argument

Obviously, any successful attack against at least one of the premises of the argument disarms it. If one can make a good case against premise 1, for instance, (the SI thesis), the argument is defeated. A vulnerable premise might be the one that traces metaphysical impossibility via claims about inconceivability. The latter comes across as a psychological category. It is possible that epistemic modalities (not psychological ones) are at issue: a situation in which "pain" names an event that is referred to by an expression other than "c-fiber-firing-states" would be knowable given our fixed terms for "pain" etc; contrast this with the identity between "water" and "H2O": Kripke takes denial of this equality (unlike the "MS" "BS" equality) to be "inconceivable". Why? It may be the case that the terms "water" and "H2O" fix terms in such a way that we couldn't make epistemically sense of a world that is said to be metaphysically like ours but has a water-substance that is not referred to by "H2O" even though it is referred to by "water." (Notice that this is about metaphysically similar worlds - not a matter of logical necessity.)

© 2014 Odysseus Makridis


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