Saul Kripke's 'Identity and Necessity'

Saul Kripke begins his paper by stating his general metaphysical position. That is, although it is a contingent a posteriori fact and a discovery of astronomy that Hesperus and Phosphorus are one and the same thing, their identity is still necessary. Our epistemological and scientific findings are irrelevant to Hesperus and Phosphorus's numerical identity. Perhaps the problem is that ‘Hesperus’ and ‘Phosphorus’ are not proper names at all; but substitutes for definite descriptions. That is, 'Hesperus' really means "the star seen at night…" So if 'Hesperus' were an abbreviated description and not a bona fide name, then what would be an example of a bona fide name? According to Bertrand Russell, only demonstratives like "this" and "that" are genuine names. They're genuine names because they're not dependent on descriptions. They are essentially contentless. More precisely, according to Russell, "this" and "that" are uninterpreted, indescribable and unconceptualised sense data; they are the objects of our own "immediate acquaintance".

But even ‘this’ and ‘that’ must rely on some kind of descriptive content; at least for the speaker. That is, even though he doesn’t have a name or even an explicit description, he must have still individuated the this or the that. Otherwise how will he know what he's in fact referring to? “Which this?” or “Which that?” This is certainly the case for the hearers. Though how does the speaker himself distinguish various this’s from various that’s? After all, in an act of ostensive definition one could be pointing at the brown on the table, or the cup on the table, or whatever. So ostension alone can't individuate a this from a that. And if it’s all a question of sense-data, how does the speaker know that the hearer will have the same kinds of sense-data? Even sense-data for the speaker can't in and of itself individuate a this or a that. Sense-data presupposes individuation; otherwise it wouldn’t be the data of something. Although, according to traditional sense-data theorists, we move from sense-data to the objects in the external world. Though without prior individuation, how would the sense-data theorist distinguish between relevant and irrelevant bits of sense data? Presumably when the theorist has sense-data of, say, a table, he'll also have sense data of, say, the things on the table, the colour of the table, and the objects in his general field of vision.

One can see why Kripke was concerned to argue that proper names have no descriptive content because the definite descriptions of Hesperus and Phosphorus didn't coincide. So it followed, to Kripke, that proper names mustn't rely on their descriptive content. Indeed they have no descriptive content at all; otherwise how could they be in fact identical. Similarly, how could we know that they are one and the same thing? Therefore proper names can't and mustn't rely or depend on any descriptive content.

Further into the paper Kripke again tackles the problem of the necessity of certain identity statements. He begins with the example of a pain and whether or not it's identical with a particular brain state. (This is tackled in greater detail later on in Kripke’s paper.) He then tackles the identity of heat with molecular motion and water with H
2O. Again, he admits that the identification of heat with molecular motion and water with H
2O are both contingent a posteriori discoveries. However, this has no effect on their necessary identities. Indeed there's another contingent fact about these necessary identities. Kripke says that of course we can "imagine heat without molecular motion" and a mental state "without any corresponding brain state". None of this affects the necessary identities. (Note: Kripke believes that the identity of heat with molecular motion is necessary; though he doesn't think the same about the identity of a particular mental state with a particular brain state.)

Heat is molecular motion; whereas, say, pain is a result or a product of molecular motion. There could of course be the feeling of heat without molecular motion. Though heat would still be molecular motion. The feeling of heat in our sensory receptors isn't actually heat. Therefore we could have an equivalent feeling from, say, light waves or sound waves (as Kripke also argues). 

The same is true of H
2O and water. There may be other examples of stuff that has the macro-qualities of water; though it would not thereby be water. In Kripke’s case, the macro-properties of water aren't the standard by which we determine or define water. That standard falls within the ambit of water’s micro-properties – that is, H
2O molecules. It is these micro-properties that make water a natural kind, not water’s macro—properties; which may, after all, be shared by other substances. Water is also H
2O whether or not we discover this to be the case. 

Why doesn’t all this apply to mental states and brain states? Because mental states are defined exclusively in terms of their phenomenal qualities; unlike water. That is, if we come across phenomenal qualities that don’t coincide with particular brain states, then such mental qualities aren't necessary identical to such brain states. There is, however, a contingent identity between mental states and brain states. There is no distinction between macro- and micro-properties when it comes to mental states.

After this Kripke discusses definite descriptions again. Take "the inventor of bifocals" (i.e., Benjamin Franklin). Kripke's argument is that someone else - other than Benjamin Franklin - might have been the inventor of bifocals. The reason for this, as we shall see, is that "the inventor of bifocals" is a definite description; whereas 'Benjamin Franklin' is a proper name. Kripke christens "the inventor of bifocals" a "non-rigid designator”; whereas 'Benjamin Franklin' is a ‘rigid designator’.

Rigid designators necessarily designate the things or persons they designate. They can't designate any other things or persons. They designate these things or persons in all possible worlds. The description "the inventor of bifocals", on the other hand, could designate someone other than Benjamin Franklin at another possible world. Indeed we 
needn't go to another possible world to meet an alternative inventor of bifocals. In this world someone else might have invented bifocals. So "the inventor of bifocals" is a non-rigid (or flaccid) designator. It's non-rigid because the description refers to different persons at different worlds and might have referred to a different person even in our own world.

So, again, Kripke says that we can't rely on “the inventor of bifocals” to refer or identify Benjamin Franklin. What we can rely on is the proper name ‘Benjamin Franklin’. For a start, someone may not know that Benjamin Franklin was the inventor of bifocals; even if they know who he is in some kind of other way. Indeed at another possible world someone else might have been the inventor of bifocals. So the proper name needs to apply to Benjamin Franklin at all possible worlds. This in turn implies that he must have some kind of essence that's unchanging at different possible worlds. The proper name refers to the essence of Franklin; whereas definite descriptions capture only contingent or accidental properties of him.

Because of their non-contentful status, proper names must refer to Benjamin Franklin at all possible worlds. If we relied on definite descriptions, we may pick out someone who's not in actual fact Benjamin Franklin. So, yet again, Kripke wants to guarantee a necessary relation between reference and referent.

What is an example of a rigid designator? Kripke offers the example of "the square root of 25" which designates the number 5. Why is this designator rigid? Because at every possible world "the square root of 25" would designate the same thing - viz, the number 5. There can be no other object of designation when the designator is rigid.

Although "the square root of 25" sounds a little like a description, in fact it's not. It's a rigid designator. It must always refer to the same entity – viz., the number 5. That designator couldn't refer to anything else because of the precision of the quasi-description that is in fact a name. The same is true of, say, “the number below 6”. That too must refer to the number 5. However, “Johns favourite number”, if it is 5, isn't a name because it could refer to other numbers in our world and at other possible worlds. We can of course be wrong about “the square root of 25”; though that would simply be a fact about us. 

Why is “the square root of 25” the same as, say, “Tony Blair”? Again, the former appears to be in some sense descriptive; though the name “Tony Blair” doesn’t seem to be descriptive, at least not at a prima facie level.

When Kripke talks about rigid designators, he doesn't mean to say that the referents of these things need exist at all possible worlds. They're not necessary beings. What is necessary, however, is that the rigid designator would refer to the same entity at all possible worlds; even if in fact it only actually exists in one possible world – say, ours. The referents of rigid designators needn't be like, say, universals. 

Kripke gives his own example of necessary existents: mathematical entities. If we get back to rigid designations of non-necessary beings, such as Benjamin Franklin, then the name “Benjamin Franklin’ must designate Benjamin Franklin “in any possible world where the object in question does exist, in any situation where the object would exist”. Of course, if Benjamin Franklin didn't exist, the name would have no designation. It would have no referent.

Kripke isn't saying, however, that Tony Blair must be called ‘Tony Blair’ at all possible worlds. He may have a different name at other possible worlds. However, our name ‘Tony Blair’ refers to their Tony Blair even if their Tony Blair isn't actually called “Tony Blair”. Our name doesn't refer to their names, it refers to the object, Tony Blair, at all these possible worlds - even in the ones in which Tony Blair is named, say, “Harry Buttock”. 

Kripke is in essence emphasising the importance of objects rather than names. More than that, he's emphasising the essences of objects which make it possible for Tony Blair to exist at different possible worlds - even in those at which he has a totally different name. He'll still be the same object. Moreover, he'll still have the same essence.

Now it will be interesting to see how Kripke departs from David Lewis in his view of possible worlds. According to Kripke, Lewis actually believes that, say, Nixon exists at many possible worlds. The man Nixon actually has some kind of existence at other possible worlds. Kripke, on the other hand, claims that there are only “counterparts” of Nixon at other possible worlds. These counterparts “resemble Nixon more or less, but none can really be said to be Nixon”. Indeed, at a prima facie level, it's hard to imagine what Lewis means by Nixon’s, as it were, multiple instantiation (or exemplification). On Lewis’s account, the man Nixon would be some kind of universal that's multiply instantiated at many possible worlds. Then we would have - wouldn’t we? - a particular that is also a universal at the same time. If that were the case, our Nixon wouldn't be the prototype: he'd instead be some kind of non-spatiotemporal Nixon universal outside of time. Kripke thinks that we can solve our modal problems by simply positing Nixon counterparts, rather than numerous trans-identical instantiations of the American ex-president.

According to Lewis, Nixon is multiply instantiated; though these Nixon duplicates don't also actually duplicate Nixon’s earthly life. The man is duplicated; though his actions etc. aren't. And these alternative actions and events actually occur at other possible worlds. According to Lewis, Nixon himself, not a counterpart, actually may not have suffered the Watergate scandal. This of course prompts the question: Why did Lewis insist on making Nixon multiply instantiated? Does this hinge on his realism about possible worlds?

As I said earlier, the names of numbers are seen as rigid designators. The name ‘9’ refers to the object 9 at all possible worlds. Now it's Kripke’s intention to make proper names rigid designators too. He wants the name ‘Nixon’ to refer to the same thing or person at all possible worlds. How does he argue his case?

Firstly he argues that it's easy to imagine Nixon doing things which he didn’t actually do. Perhaps we could imagine him having been awarded the Nobel Peace Prize for Literature. Perhaps his counterpart, not his instantiation, received this prize at another possible world. There's no problem with such possibilities. They aren't logically impossible. Can we imagine the man himself being different? Kripke argues that “we cannot say ‘Nixon might have been a different man from the man he in fact was’”. If Nixon had been a different man, we might ask: In what sense is he still Nixon? Could Nixon have changed all his properties and still remain Nixon? Clearly not. Could Nixon have had some of his properties changed and still remain Nixon? Possibly; though we would perhaps need to make a distinction between essential and contingent properties. We couldn’t change any of Nixon’s essential properties without changing Nixon into someone or something else. Or, more precisely, we would make Nixon cease to exist. Here we're faced with a Liebnitzian position in which all of a thing’s properties are essential to that thing. Or, tautologically, all the essential properties, however many, are essential to a thing or person.

Perhaps we can safely say that Nixon wouldn't have been Nixon had he a different brain. The brain of Nixon, therefore, was essential to Nixon. How does all this show us that ‘Nixon’ rigidly designates Nixon? If Kripke did indeed have certain or many essential properties, then a counterpart at another possible world that didn't have these essential properties couldn't be designated by the name ‘Nixon’. It would be designating something or someone else – a non-Nixon. If ‘Nixon’ designates anything, that thing must be Nixon and not a non-Nixon. On the other hand, the description "the thirty-seventh President" doesn't entail any essential properties; or, indeed, any properties at all except the property being the 37^th President of the United States. Anything or anyone might have fulfilled the role of being the thirty-seventh President of the United States. Can anything or anyone be Nixon the man? How can x be y if x and y are discernable objects? x would only be y if they were indiscernible objects – that is, if they shared all their properties (including relational ones).

Kripke offers us an analysis of the technical terms he'll be using in the remainder of the paper. 

Firstly he asks: "What do we mean by calling a statement necessary?" His answer is: Firstly, the statement is true. Secondly, "it could not have been otherwise". Contingent truth, on the other hand, is a matter of a statement being true; though it could have been the case that it isn't true. Kripke says that these are metaphysical issues. He then discusses a priori truth and says that such a thing "can be known independently of all experience". Because of the concern with our knowledge of these statements, they're assigned to the realm of epistemology. Questions of a priori truth are epistemological because they're concerned "with the way we can know certain things to be in fact true". As Kripke was well aware, traditionally it was thought that all necessarily true statements could be known a priori. Of course Kripke questions this assumption. In fact he offers his own alternative. Some things or statements may be necessarily true; though only knowable a posteriori (that is, our knowledge depends on experience). Kripke offers his own example: the Goldbach conjecture. This conjecture claims that every even number is the sum of two primes. Because this is a mathematical statement, it must be necessarily true (if it is true). However, the Goldbach conjecture isn't known a priori. Here Kripke qualifies the notion of the a priori. It's not simply a question of what is known independently of experience; but also what "can be known independently of experience". 

Another addition to the a priori argument, in relation to Goldbach's conjecture, is that part of its - possible - truth would be our ability to prove it true if it were true. Kripke denies this too. It's been known since Gödel, Kripke argues, that within certain mathematical systems there's at least one theorem that's not provable within that system. So there can be no absolute and total guarantor of truth within any mathematical system. This means, again, that not all mathematical truths are provable. Therefore they certainly aren't known to be true a priori. (Gödel’s stance on mathematical systems may be applicable to systems of various descriptions outside of pure mathematics.)

Essentialism

Kripke now goes into a different subject (though it ties in with everything else): the notion of essential properties. What are essential properties? According to Kripke, they're those properties that "are such that [an] object has to have them if it exists at all". If a particular object didn't have these properties, it wouldn't even exist as that object. There's another way of expressing this. If a particular object didn't have these essential properties, "it would not be this object". Kripke gives a possible example of an essential property of a lectern. He says that it must be made of wood, rather than ice. Wood is an essential property of the lectern.

What does it mean to claim that this lectern has wood, rather than ice, as an essential property? The essentialist claims, according to Kripke, "that this lectern could not have been made of ice". This claim is further glossed by saying that "in any counterfactual situation…we would have to say also that it was not made from water". If this lectern were made of water, it wouldn't be this lectern.

Now Kripke reverts back to arguments about the a priori. That is, to the argument that necessity doesn't depend on being known a priori. It terms on the lectern "we cannot know a priori whether this table was made of ice or not". However, and this is Kripke's primary point, "given that it is not made of ice, it is necessarily not made of ice". Kripke expresses this in symbolic logic:

P ⊃ P
P--------------P

This means: If the lectern isn't made of ice (P), then it's necessarily () the case that the lectern isn't made of ice (P). The lectern isn't made of ice (P). Therefore the lectern is necessarily not made of ice (P).

The important point to be extracted from the above is that the conclusion  P is known a posteriori "since one of the premises on which it is based [i.e., P] is a posteriori".

Kripke then gets back onto the notion of rigid designators. He offers us a more detailed characterisation of them. First of all he talks about two rigid designators, ‘a’ and ‘b’. Both rigid designators designate the same thing, viz, x. He says that “in every possible world, a and b will both refer to this same object x, and to no other”. So if both ‘a’ and ‘b’ designate the same object, then “there will be no situation in which a might not have been b”. He goes on to say that that “would have to be a situation in which the object which we are also now calling ‘x’ would not have been identical with itself”. This would be a necessary identity between two names that designate the same object, namely x. 

To get back to the example that opened the paper, Kripke says that “one could not possibly have a situation in which…Hesperus would not have been Phosphorus”. So if both names rigidly designate the same object, say, Venus, then both names are necessarily identical.

Kripke pre-empts the possible critiques of his position. He says that some “people tend to regard identity statements as metalinguistic statement”. To put this very simply. Metalinguistic statements are statements about sentences and names rather than things and events. So instead of

Hesperus is Phosphorus.

We have

“'Hesperus’ and ‘Phosphorus’ are names of the same heavenly body.”

Kripke isn't talking about the necessary identity of names, . He's talking about the necessary identity of things. Of course the identity of names may have been false. We may have called Phosphorus ‘Juniper’ and Hesperus ‘Klink’. Though if they both rigidly designated the planet Venus, then their designations would be necessarily identical. However, the names themselves aren’t necessarily identical. How could they be? Names, signs and inscriptions are of course arbitrary and contingent. 

Kripke gives an excellent example of what’s at issue here. Take the statement “2+2=4”. If we're talking names exclusively, this statement wouldn't be necessarily true, or perhaps even true at all. If we're talking about the accepted designations of these inscriptions, then the statement is necessarily true. Kripke elaborates. He says, “’2’ and ‘4’ might have been used to refer to two different numbers” (to the ones they do now refer). If the inscription ‘2’ referred to the mathematical object 3, then the statement “2+2=4” would be necessarily false. In this instance, “2+2=4” should be “2+2=6” because, again, the inscription ‘2’ refers to the object 3.

The opponent of Kripke is still not entirely convinced. He says: “’Look, Hesperus might not have been Phosphorus’”. Kripke’s adversary then goes onto say that if “things had turned out otherwise, they would have been two different planets…so how can you say that such a statement is necessary?””.

Kripke dissects this opposition. He says that there are two things that the adversary could mean. The adversary can mean that he can't know a priori that Hesperus is Phosphorus. Of course we can’t; and Kripke has already conceded that. Alternatively, the adversary could mean that there could be circumstances - or perhaps possible worlds - in which Hesperus wouldn't have been Phosphorus. This is all a question of mixing up names and the objects of names. How could we say that two numerically identical things - namely Hesperus and Phosphorus - might not have been the same? Again, the adversary’s problem is easily explained. He says that at another possible world the people of that world may well have named Venus ‘Phosphorus’; though, contrarily, used ‘Hesperus’ as a name for Mars. In that case, “Phosphorus is Hesperus" wouldn't have been a necessary identity statement. Again, we're not talking about names: we're talking about things. Whatever names we give Venus, if they rigidly designate the same object, Venus, they'll form necessary identity statements. Hesperus and Phosphorus are numerically identical, no matter what names we use. We're talking about their designations, not the names of those designations.

Names and Descriptions

For Kripke's enterprise it's important that names are clearly distinguished from descriptions. In certain parts of the tradition, they were thought to be closely related. As Kripke says, it was thought that "we fix the reference of the term 'Cicero' by use of some descriptive phrase, such as 'the author of these works'". After the reference has been fixed, according to Kripke, it was the case that 'Cicero' rigidly designated the man who wrote these works. Though if the descriptive phrase were important or necessary for the fixing of the name, then if someone else wrote the works mentioned earlier, then he would be Cicero. According to Kripke, we "do not use [the name] to designate whoever would have written the works in place of Cicero". In fact it seems, at a prima facie level, ridiculous to think that someone else could have wrote the works of Cicero. However, what Kripke wants to argue is that the name alone fixes the reference, not a description.

Traditionally, the name and a description used to fix the reference were taken to be synonyms. Kripke argues that we can't depend on the description. If we did, at another possible world someone else could have written the works written by Cicero. Therefore the name 'Cicero' would apply to that person if name and description were synonymous.

Kripke then offers his wider critique of identifying names and descriptions. He says that “suppose that we do fix the reference of a name by a description”. What would be the consequence of this for a theory of reference? He argues that name and description would still not be synonymous. The name would still rigidly refer to the object in question “even in talking about counterfactual situations where the thing named would not satisfy the description in question”. Indeed Kripke goes further than this. He says that the “reference of names is rarely or almost never fixed by means of description”. Is this because the relation between description and referent is contingent; whereas the relation between name and referent is necessary?

Kripke gets to works on examples. 

Take ‘heat’ and ‘the motion of molecules’. Both terms could be seen to refer to the same thing. That heat is the motion of molecules is a scientific fact. It is an a posteriori judgment. The motion of molecules isn't “contained in the concept” - as Kant would have put it - of [heat]. As Kripke put its, “scientific investigation might have turned out otherwise”. However, the discovery was indeed contingent or a posteriori; though the connection between heat and the motion of molecules is necessary. (Note: not between the names ‘heat’ and the desctiption ‘the motion of molecules’). Regardless of our knowledge, our words, etc., there's a necessary connection or identity between heat and the motion of molecules.

Kripke, thankfully, offers us many possible arguments against his general thesis. For example, what if an increase in the motion of molecules didn’t cause sensations of heat in our sensory receptors; but, instead, the slowing down of molecules did? In that case, so the adversary argues, heat wouldn't be identical to the motion of molecules.

Another argument against Kripke thesis would be this. What if there were no people on this planet? If there were no people on this planet, then there would be no sensations of heat. Would we, in that case, say that heat didn't exist in this counterfactual world? Kripke would argue that heat still exists regardless of human sensory receptors. Why does he think this? Because if there were fires on this uninhabited planet, these fires would still heat up the air. Kripke’s general conclusion is that heat isn't necessarily identified by the feelings of certain sensations (those of heat). Indeed more strongly, heat has nothing to do with sensations, strictly speaking. (This could be seen as the opposite position to Berkeley’s idealism.)

Kripke offers another counter-argument against his general thesis. In yet another counterfactual situation, the creatures on our planet don’t get the sensation of heat when they're exposed to things that cause us to feel heat. In this counterfactual situation, Kripke imagines creatures that get visual sensations when they're exposed to sound waves.  Kripke here is also changing the example. Instead of heat being connected with sensations of heat, we now have sound waves being connected to visual sensations. Should we now say that sound waves would be light (visual sensations)? No. Light would still be necessarily identical to streams of photons; just as heat is necessarily identical to the motion of molecules. In both cases, the existence of counterfactual creatures and human sensations would be irrelevant to the necessary identifications.

Kripke backs up his position by saying that the terms ‘heat’ and ‘the motion of molecules’ are both rigid designators of the same thing. Both ‘heat’ and ‘the motion of molecules’ refer to the same thing or process at all possible worlds. In accordance with previous explanations, sensations can't be identical to particular things or processes at all possible worlds - as we've seen. To use Kripke exact argument, because “heat is in fact the motion of molecules, and the designators” ‘heat’ and ‘the motion of molecules’ are both rigid, then “it is going to be necessary that heat is the motion of molecules”.

Where are Kripke’s adversaries going wrong? In a sense, the answer to this is quite simple. We've identified something that is contingent to be part of the definition of heat. That contingent fact is that on this planet human beings happen to be sensitive to the motion of molecules. When we experience the motion of molecules we feel heat. So we identify heat, and therefore the motion of molecules, with our experiences of heat (say, of things being hot). Heat, and therefore the motion of molecules, “causes such and such sensations”. We identify heat with these sensations; whereas the only real necessary identity is between heat and the motion of molecules.

To clarify his point, he goes back to the Cicero example. Here too we identify a contingent property of Cicero with Cicero: that of writing such and such works. Kripke concludes that ‘Cicero’ and ‘heat’ must be used as rigid designators. ‘Cicero’ always stands for the thing Cicero; and not for any of his descriptive properties. ‘Heat’ always designates the motion of molecules; and not other contingent properties (e.g., heating up our hands to cause the sensation of heat).

Kripke’s adversary wrongly thought that heat could be identified with something that isn't the – increased – motion of molecules. His identification of heat with the sensation of heat is a contingent, not a necessary, identification.

To get this point across Kripke identifies a non-necessary - that is, a contingent - identification: the identity of a pain with a particular brain state. The Identity Theorists, contrary to Kripke, claim that there's a necessary connection between a particular pain and a particular brain state; or, more generally, between pains and brain states. What the identity Theorist commits himself to, according to Kripke, is that if we have pain state X, then we must be in brain state Y. Similarly, if we are in brain state Y, we must experience pain state X. Kripke I think would accept that there may well be a connection – not an identity – between pain state X and brain state Y; though that connection can't be necessary. This simply means that I can experience pain state X and not be in brain state Y. It's logically possible to feel pain state X and not have the corresponding brain state Y. The conclusion of this is that the Identity Theory must be wrong. Pain state X isn't identical to brain state Y. The Identity Theorist may say, according to Kripke at least, that the identity between pain state Y and brain state X is “contingent”. Kripke argues that the Identity Theorist can't claim that the relation is contingent. He says that the Identity Theorist must believe that “we are under some illusion in thinking that we can imagine that there could have been pains without brain states”.

Reference

Saul Kripke, ‘Identity and Necessity’, from Identity and Individuation (1971)

Do Logic and Existence Go Together?

It's said by some (or most) logicians that “logic must handle every possible state of affairs” and hence that it “can't imply the existence of anything” (Dale Jacquette). That almost sounds like a non sequitur. Yes, logic must handle “every possible state of affairs”. Nonetheless, how does it follow from this statement that logic can't imply the existence of anything? Why can't logic be able to handle every state of affairs and imply the existence of something (or one thing)?

Is it because if logic is applicable to everything, then implying the existence of something would pollute its ability to handle all states of affairs (note the jungle of quantifiers here)? Or is is it that the case that something (or these things) would somehow make logic contingent (or empirical) in nature? Nonetheless, implying (or allowing) the existence of something that's contingent (or empirical) isn't the same as arguing that logic itself is contingent (or empirical). Logic can still be applied to the the contingent (or empirical) even if isn't itself contingent (or empirical).

Does it mean, instead, that if logic implies the existence of anything (or even something) that it would somehow depend on that something? And, if logic did imply the existence of anything, then its logical purity would somehow be sullied?

In that sense, quantificational logic (or first-order logic) is far from being pure. Quantifiers in logic have existential import (or have ontological commitment). That is, a quantificational proposition is about the existence (or non-existence) of something (or of many things). Even free logic accepts abstract objects of various kinds. It can also be said that logical statements about self-identity have existential import. That is, the proposition (x) (x = x) has existential implications. And, more obviously, so too does, (∃y) (y = y).

It seems to follow from the acceptance of quantificational logic that an empty universe is excluded – nay, it's logically impossible. However, do these facts about quantificational logic necessarily apply to the more generic “logic” we began discussing? Perhaps quantificational logic is actually a deviant logic!

Lewis Carroll's Premises Paradox

The British writer, mathematician and logician Charles Lutwidge Dodgson (which was Lewis Carroll’s real name) worked in the fields of geometry, matrix algebra, mathematical logic and linear algebra. Dodgson was also an influential logician. (He introduced the Method of Trees; which was the earliest use of a truth tree.) For some time Dodgson was Mathematical Lecturer at Christ Church, Oxford University.

And, of course, Dodgson (under the name Lewis Carroll) also wrote Alice in Wonderland, Alice Through the Looking Glass and many other books and poems.

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Lewis Carroll (I’ll use Dodgson’s better-known pen name from now on) formulated his premises paradox in 1895. (The argument was advanced in Carroll’s paper ‘What the Tortoise Said to Achilles’; which was published by the journal Mind.) This paradox refers to the possibility of infinite premises being required in order to reach a single conclusion.

Firstly, two or more premises are usually linked to a conclusion in a logical argument.

So how are they linked?

Now that can be a question of the philosophical nature of the link between premises and conclusion: whether it’s an example of entailment (or logical consequence), implication (or material implication) or whatnot. However, that wasn’t the point that Lewis Carroll was making. He was making a purely logical (not a philosophy-of-logic) point.

To put this simply: in order to justify (or explain) how any given premises are related to a conclusion (or how the premises entail or imply the conclusion), then a further premise will need to be brought into the argument in order to do so. Moreover, another premise will be required in order to tell us (or show us) how (or why) it’s the case that if the premises are true, then the conclusion must follow and also be true.

Now that added explanation (or justification) will itself be a premise within the argument.

Of course the same problem will repeat itself.

Just as we brought in a premise to link two, three or more premises to a conclusion: now we have to say how this new premise is itself linked to those previous premises. Or, alternatively, we’ll need to know how all the premises (when taken together) are linked to the conclusion.

A solution has been offered to this logical paradox.

That solution is simply to say that no added premises are needed in the first place. That is, the link between the premises and the conclusion doesn’t need to be explained (or justified) by a further premise.

So why is that?

The (or one) answer is to say that the premises and conclusion are simply linked by a rule of inference. That rule itself explains (or shows) the relation between the premises and the conclusion. Nonetheless, that sounds (at least at a prima facie level) like a cop-out. To simply say that premises are linked to a conclusion by a rule of inference doesn’t appear to be saying anything… much. Surely that rule -again! — will need to be explained by a further premise.

It can also be argued that saying that premises are linked to a conclusion by an inference rule is itself a further premise.

Yet that’s unless that rule of inference somehow works without any justification or explanation.

In other words, it’s not a justification: it’s just a rule. It’s something that “can be shown but not said” (to use Wittgenstein’s much-quoted phrase); just as the nature of the logical constants can’t be said, only shown.

Does the Mind-as-Computer-Programme Idea Support Mind-Body Dualism?

“Yes, I am a confirmed "dualist" at this point in my journey, i.e., I understand my mind to be separate from my body/brain, analogous to the way an application program and its data are separate from the computing infrastructure they depend on.” - Chasw

Does believing your mind to be separate from your body/brain automatically mean you're a dualist? That would depend on what the word 'separate' means. The mind simply being (fundamentally) different from the body wouldn't commit anyone to dualism.

Dualism is a commitment to the idea that mind and brain are fundamentally different ontological categories or 'substances'. That creates the problem of mind-body interaction. If mind and brain (body) were fundamentally different, then how could brain-to-mind and mind-to-brain interactions be explained?

Dualists are also committed to minds being separable from brains, not just being separate and different. I don't think the 

mind = programme/data 

and the 

brain = hardware

comparison works here because, after all, even programmes and data are physical. Programmes and data depend on physical syntactic devices which encode data/info and which themselves rely on physical processes to implement that data (as well as to send that data, electronically, around the hardware/infrastructure). The programme-hardware/mind-brain analogy works only to show us that the same programme can be instantiated in different kinds of hardware: from brains to computers to coke machines. In itself, it's not an argument for dualism; which is specifically about the mind being of a different substance/category than the brain. When it comes to computer programmes and their different hardware juxtapositions, there are no such deep ontological problems as there are for mind-brain/body dualism.

The Cartesian Circle

Rene Descartes' basic position can be summarized in the following manner:

 

i) I can only know (or be certain) as to whether or not some statement or proposition (p) is true if I already know (am certain of) that God exists and is not a deceiver.

 

ii) I can only know (or be certain) that (i) God exists and is not a deceiver if I already know (am certain of) that every proposition I clearly and distinctly perceive is true.

 

That encapsulates the "Cartesian circle".

In other words, i) depends on ii) and ii) depends on i). Neither i) nor ii) can get off the ground without the prior existence of i) or ii). Or, in other words, i) can't get off the ground without ii) and ii) can't get off the ground without i). It seems to follow, then, that neither can get off the ground.

 

In more detail, one would need to ask why Descartes has already assumed God's existence, let alone the fact that He's not a deceiver. It could be said that written into God's nature and existence, as it were, is the fact that He can't be a deceiver. But since Cartesian Doubt is supposed to begin at rock bottom, Descartes could hardly have assumed any of these things.

 

In terms of ii), we would need to know what Descartes mean by 'clear' and 'distinct'. How does clarity and distinctness guarantee truth? How did he know that he clearly and distinctly perceived certain propositions? And what did he mean by “perceive” here? (He wasn't talking here about external objects such as trees or chairs.)

 

Descartes, or at least philosophers defending Descartes, have said that metaphysical or logical certainly isn't required at the beginning of Cartesian Doubt. Or, more correctly, metaphysical or logical certainty isn't required to take one to the existence of God. Instead only psychological certainty is required: presumably to take you to God and be certain about the aforesaid propositions.

 

From psychological certainly you can reach metaphysical or logical certainty about both God's existence and the truth of clear and distinct propositions. This, of course, leaves out entirely what the nature of this psychological certainty is and whether or not it's meaty enough to take us to both God's existence and nature and the truth of these propositions.

 

It also leaves out the Cartesian circle: why talk about taking oneself to God's existence at all when God hasn't been proven in the first place? Surely even the assumption of God's existence can't be accepted in Cartesian Doubt. Yet here we are assuming God's existence in the very process of arguing about psychological certainly taking us to the existence of God. That means that God's existence is assumed not only before metaphysical certainty: it's also assumed before psychological certainty (whatever that is).

 

Nonetheless, philosophers have defined what metaphysical certainty is. This is one definition:

 

A proposition P is metaphysically certain if and only if there is no other proposition R that is a reason for doubting P.

Firstly, this definition is completely psychological in nature. The Cartesian wouldn't deny that. What I mean by that is that there could be a proposition R (or even many propositions) that would give S reasons to doubt P if he were aware of them. However, S isn't aware of them. In addition, R could be a logical reason to doubt P even though S doesn't take R as a logical reason to doubt P. Nonetheless, taken non-psychologically, R is logically a contradiction of P which S may not be aware of at all.

 

Indeed, in the post-Cartesian world, the very locution “metaphysically certain” has a strange psychological ring to it. Some philosophers or metaphysicians would ask: What has certainty (psychological or otherwise) got to do with metaphysical reality? In addition, R could contradict P without having any metaphysical reality as such; just as contradictions can be formulated in logical systems from symbols or formula which don't have any (metaphysical or empirical) content.

 

However, none of that is strictly relevant if all we're talking about is the Cartesian's move from psychological certainty to metaphysical certainty because that metaphysical certainty can be deemed to be just as psychological as the prior psychological certainty. That is, the metaphysical certainty that is derived from the psychological certainty is done so in an equally psychological manner – in what other manner could it be derived?

 

In an case, most of that is a sidetrack.

The Cartesian move is that, yes, we begin with only psychological certainty as to various clear and distinct propositions. The first thing we do with these psychologically certain propositions is prove that God exists. Then, with God's help, as it were, they become metaphysically certain as well. The question here, however, is that even if we accept psychological certainty, how is it, exactly, that such certainty “proves” God's existence? After all, psychological certainty alone can't prove God's existence or anything else for that matter. Only valid and true arguments can do that.

Then the Cartesian seems to move in another circle within the general Cartesian Circle. By proving God's existence from psychologically certain and therefore true propositions, we're giving a reason, apparently, for doubting all possible reasons for doubting those very propositions which prove God's existence. The propositions which took us to God are then blessed by God and therefore become certain. Thus:

 

God + psychological certainty = metaphysical certainty.

This could be seen as a virtuous, rather than a vicious, circle. Certain propositions lead us to God and God leads us the those very same propositions. And that, surely, is a classic case of the Cartesian Circle. I simply can't see how anyone has broken out of this very vicious Cartesian Circle. All that's has happened is we've expressed and codified it, not solved it.

Perhaps it all hinges on how psychologically certain propositions (if that's what they truly are) somehow “prove” God's existence. Clearly, simple psychological certainty of one or a hundred propositions can't prove anything, as I said. It all depends on what these propositions are. It also depends on whether or not these propositions assume the existence of God as well as the ability of God's existence to somehow give metaphysical legitimacy to the prior psychologically-certain propositions.

 

Another part of this Cartesian Circle is that reasons for doubting P also have to be certain. That is, not-P, or R, also has to be clearly and distinctly perceived. Clearly, if not-P is clearly and distinctly perceived to be true, then P is false, according to the Cartesian. This seems to imply that not-P or R is not clearly and distinctly perceived to be true. Therefore P must be true. Again, all this depends on what P is and what not-P (or R) is. In addition, the Cartesian requires more than one P and must defend itself against more than one not-P: there will be many not-Ps.

 

Of course one not-P is that God is a deceiver. Can I clearly and distinctly perceive that God is a deceiver? Not according to the Cartesian. (Really? Even if I'm an atheist?) That can't be true: there are many reasons for doubting clear and distinct propositions. One reason is their very existence as adumbrated by Descartes himself. Another thing we can doubt is that psychological certainty leads to metaphysical certainty, God's existence or anywhere else (as I have said).

 

Again, the Cartesian only accepts any not-P if it is certain. Alternatively, the Cartesian must be certain that not-not-P is certain (or -–P). Here again, and not surprisingly, it's all about psychological certainty, even if that can lead us to all sorts of other things. And, again, the only not-P that Descartes appears to consider is that God is a deceiver.