Friday, 19 June 2015

Carnap on Linguistic Frameworks (or Conceptual Schemes)



According to Rudolph Carnap’s approach, x, y, and z can be variables of anything you want. Carnap might have simply said here that these are questions for the scientist or the ontologist. Quine, for example, let science (though not scientists) decide these matters.

If a priori or necessary truths are true simply via linguistic convention (in Carnap's scheme), then what’s the point of them? If they bear no relation to the world, the mind or a non-spatiotemporal realm (take your pick), what purpose do they serve? How do we get outside language or “schemes”? Do we even need to get outside language/convention? If not, why not?

Conventionalists may say that we have good reasons for adopting conventions. What are those reasons? And if they're reasons outside language and conventions, doesn’t the conventionalist stop being a conventionalist by adopting those reasons? I guess that realists would happily accept that we need conventions. No problem there. The realist can’t say anything without conventions; even if these conventions do indeed duplicate, in some way, the actual nature of the world.

As Karl Popper might have put it, if a conventionalist’s law becomes analytic and therefore unfalsifiable, then what’s the point of it? It may help you predict; though what if the predictions are incorrect or the laws postulate non-existents? If what's analytic becomes law-like in this respect, isn’t it a dangerous law in that it halts philosophical or scientific advancement?

It's true that conventions aren't forced on us by nature. (What would it mean to have a convention forced upon us?) Even realists would accept that nature doesn’t force itself on us. However, we have causal interactions with nature and these causal interactions impinge on us - even if they don’t force us to speak nature's very own language. Nothing forces the realist to say, “There are quarks and planets.” However, there are causal reasons for him to say what he says. If there are no restraints on the adoption of conventions, then anything goes and we have…well, relativism (if with lots of added logical symbols and fancy technical/scientific terms).

Why can’t the realist be a realist and still accept (with the conventionalist) that there's more than one description (or explanation) of a given “space-time point” (in Carnap's scheme), event or object? I don’t see why a realist must uphold a single “correct description” of a given space-time point. That, surely, isn't necessarily entailed by realism. (Think here of Husserl’s metaphysical “positions”.)

Again, of course conventions are freely chosen. I think that the realist can accept this. The "nature forcing itself on us” metaphor isn't very helpful in this debate. I don’t believe that, for example, realists were really horrified by Poincare's admission that contradictory scientific principles can be maintained. Why can't the realist accept Poincare’s position too? You could accept and still believe that your principle (or theory) is dis-confirmable in the future. The realist must accept and live with the alternative descriptions (or explanations) of the world even while accepting that, of course, some are correct and some are false. One can be a realist and say that “there is a way the world is” and still live with – many? – alternative descriptions (or explanations) of the world.

What being said here (if rather counter-intuitively) is that realists are conventionalists (in some ways, at least) and conventionalists are realists (in some ways, at least).

Carnap's Scheme

In theory T certain new terms are postulated (say, a, b, c…). Does a Carnapian need reasons for postulating a, b, c…? Is it the very nature of postulation that they're assumed without proof or even evidence? If they're postulated variables with objects, properties, classes, etc. as their extensions, then what is the Carnapian’s ontological position on these things? For example, what is to stop a Carnapian from saying that a’s reference or extension is a round square?

Does “anything go” if it's via stipulation? In addition, Carnapian analyticity makes it the case that what's analytic is analytic because the terms are so devised to be analytic (“by fiat”, as Quine put it). A priori analytic statements are true and analytic because they're constructed to be true and analytic. So didn't Carnap restrict the range of his own variables? Or would Carnap have said that his variables range over what scientists say they range over (as Quine did)? However, if philosophers accept everything that science (rather than a science or scientists) postulates, then why would science need philosophy at all (that's if it does need it)?

                             ************************************************

*) Carnap's "linguistic frameworks" approach can be found in various places. This piece is mainly based on the paper 'Empiricism, Semantics, and Ontology'; which was first published in 1950 and later found in Carnap's book Meaning and Necessity.


Wednesday, 17 June 2015

John Searle says “it's all syntax and no semantics”



i) Introduction
ii) In Reference to Reference
iii) Mental Content

This is a simple introduction to the philosopher John Searle's main argument against artificial intelligence (AI). This means that it doesn't come down either for or against that argument.

The main body of the Searle's argument is how he distinguishes syntax from syntax. Thus the well-known Chinese Room scenario is simply Searle's means of expressing what he sees as the vital distinction to be made between syntax and semantics when it comes to debates about computers and AI generally.

In Reference to Reference

One way in which John Searle puts his case is by reference to reference. That position is summed up simply when Searle (in his 'Minds, Brains, and Programs' of 1980) writes:

Whereas the English subsystem knows that 'hamburgers' refers to hamburgers, the Chinese subsystem knows only that 'squiggle squiggle' is followed by 'squoggle squoggle'.”

So whereas what Searle calls the “English subsystem” involves a complex reference-relation which involved entities in the world, mental states, knowledge of meanings, intentionality, consciousness, memory and other such things; the Chinese subsystem is only following rules. (The computer will have a memory; though a memory with none of the features talked about here.) That is, when the input 'squiggle squiggle' is fed in, the Chinese subsystem delivers (or computes) the answer 'squoggle squoggle'. This is really a simple case of the computer (or Chinese subsystem) following x with y. And that's simply the result of following a rule (or an algorithm). Again, knowledge of meanings, intentionality, consciousness, etc. aren't required in this simple case of following a rule/algorithm.

When its puts like this it seems that the computer/Chinese subsystem is a system which is of the same type as a thermometer; except that the system is more complex and it involves inscriptions and rules/algorithms. (Then again, a thermometer can be given a computational or mathematical explanation/description too!)

Margaret A. Boden (in her paper 'Escaping from the Chinese room' - 1986) offers a little more detail on what she calls the “causal semantics” of reference (whether beliefs or individual words/terms). She writes:

In a causal semantics, the meaning of a symbol (whether simple or complex) is to be sought by reference to its causal links with other phenomena.”

Above a beyond that, Boden does ask a couple of questions about this aspect of causal semantics. She writes:

The central questions are 'What causes the symbol to be built and/or activated?' and 'What happens as a result of it?' The answers will sometimes mention external objects and events to an observer, sometimes they will not.”

The first point to make here is that it's obvious that a computer (or even a man in a Chinese room) has no causal links to the things it's answering questions about. Of course it can be said that there are indirect causal links. Indeed some theories of causal reference (or semantics) have tackled these indirect (or circuitous) causal links.

For example, the data that's fed into a computer has causal links to external objects care-of the computer programmer. It's the programmer himself who has causal links (expressed in the data which is fed into the computer) to external objects or events. (This parallels Searle's “as if” intentionality.)

The final clause about sometimes not mentioning external objects is possibly a reference to some of the problems found with causal semantics. Such problems include that of a reference-relation to a non-existent entity or to an event which occurred in the past. There are various solutions to these problems. However, I don't think they are relevant to the issue under discussion because some of these causal accounts of reference to non-existent entities still supply us with causal explanations.

Mental Content

Searle also argues for his position in terms of mental content; though reference itself will involve mental content.

The usual way that other people have put Searle's position is by saying it's a case of syntax vs. semantics. Though Searle expresses pretty much the same thing here in terms of form vs. mental content. This is how Searle himself puts it:

... the program is purely formal, but the intentional states are not in that way formal. They are defined in terms of their content, not their form.”

That's the technical terms “form” and “content” out of the way. What, exactly, does Searle mean by them? He continues:

The belief that it is raining, for example, is not defined as a certain formal shape. But as a certain mental content with conditions of satisfaction, a direction of fit and the like. Indeed the belief as such hasn't even got a formal shape in this syntactic sense, since one and the same belief can be given an indefinite number of different syntactic expressions in different linguistic systems.”

Here we find two technical terms/phrases which were (as far as I know) coined by Searle himself. In fact they're more or less two ways of saying the same thing: viz., “conditions of satisfaction” and “direction of fit”.

Conditions of satisfaction seems to be a phrase which belongs to a theory of reference in that in order for a word or a belief (in Searle's example) to have a reference to something outside the head (or beyond the page), it must have conditions of satisfaction. There must be something in the world (a condition) which satisfies the belief (or word). In Searle's example, the belief that it is raining has the condition of satisfaction if and only if it is indeed raining. (This appears to be similar to a Tarskian T sentence in which the sentence is simply disquoted to provide its truth conditions.)

As for “direction of fit”, this seems to be a theory within (mental) intentionality in that a belief (or a word) must have directedness (or an “intentional relation” to) something outside the head and in the world. However, the phrase “direction of fit” seems equally suitable to a theory of reference in that a reference-relation itself will require a direction of fit.

It certainly seems true that a belief itself couldn't possibly have a “formal shape”; at least not until it's given a formal shape when expressed in words or symbols. As mental content only, it has no formal shape or syntax. Indeed it can be said that no example of mental content could have a formal shape. (Except in the indirect sense that beliefs refer to things which have shapes or that mental images can be said to have shapes or at least be about – or representations of – shapes.)

I've just mentioned that non-formal beliefs or mental content generally can indeed be given formal shape when expressed in words or symbols. Searle himself says that

the same belief can be given an indefinite number of different syntactic expressions in different linguistic systems”.

That means that belief P can become, for example, S1, S2, S3... Sn when it's expressed. S1, S2, S3... Sn are the syntactic expressions of P. In all these cases, P remains the same; whereas S will differ syntactically. In other words, the belief that it is raining can become “It is raining”, Il pleut, 「雨が降っれます」or be given an artificial expression in some kind of computer code. The belief it is raining can even be expressed in Morse code; providing we have a translation manual and we know the translation.











Saturday, 13 June 2015

Kurt Kurzweil's Systemhood Argument vs. Searle's Chinese Room Argument


“‘When we hear it said that wireless valves think,’ [Sir Geoffrey] Jefferson said, ‘we may despair of language.’ But no cybernetician had said the valves thought, no more than anyone would say that the nerve-cells thought. Here lay the confusion. It was the system as a whole that ‘thought’, in Alan’s [Turing] view…” — Andrew Hodges (from his book Alan Turing: the Enigma).


In his rewarding book, How to Create a Mind, Ray Kurzweil tackles John Searle’s Chinese room argument.

It’s a great book; though I do find its philosophical sections somewhat naïve. And that’s despite the book’s abundance of scientific and technical detail; as well as Kurzweil’s imaginative capabilities. Of course there’s no reason why a “world-renowned inventor, thinker and futurist” should also be an accomplished philosopher. That said, there’s also a danger of philosophers criticising him for not being so. 

Kurzweil says, for example, that all his critics tend to know about Watson (an “artificially intelligent computer system capable of answering questions posed in natural language”) is that it’s a computer in a machine. He also says that some commentators don’t “acknowledge or respond to arguments I actually make”. He adds:

“I cannot say that Allen and similar critics would necessarily have been convinced by the argument I made in that book [The Singularity is Near], but at least he and others could have responded to what I actually wrote.” 

The problem is that, in the case of John Searle’s Chinese room argument, the same can be said about Ray Kurzweil case against that. Sure, you wouldn’t expect a full-frontal and elongated response to Searle in a popular science book like How to Create a Mind. Having said that, there is a great deal of detail and some complexity — at least when it comes to other issues and subjects — to be found in this book.

The Argument

Ray Kurzweil’s argument against Searle is extremely basic. He simply makes a distinction between Searle’s man-in-the-Chinese-room and that man’s rulebook. Basically, the man on his own doesn’t understand Chinese. However, the man and the rulebook, when taken together, do understand Chinese.

So instead of talking about a man and his rulebook, let’s talk about the central processing unit (CPU) of a computer and its “rulebook” (or set of algorithms). After all, this is all about human and computer minds.

Firstly, Kurzweil says that “the man in this thought experiment is comparable only to the central processing unit (CPU) of a computer”. However, “but the CPU is only part of the structure”. In Searle’s Chinese room, “it is the man with his rulebook that constitutes the whole system”.

Again, “the system does have an understanding of Chinese”; though the man on his own doesn’t.

The immediate reaction to this is how bringing two things (a man and a rulebook) together can, in and of itself, bring about a system’s understanding of Chinese. Why is a system of two or more parts automatically in a better position than a system with only one part? (That’s if a system can ever have only one part.) How and why does multiplicity and (as it were) systemhood bring about understanding? It can be said that the problem of (genuine) understanding has simply been replicated. It may indeed be the case that the addition of a rulebook to either a man or a CPU brings about true understanding; it’s just that Kurzweil doesn’t really say why it does so.

John Searle is of course aware of what’s called the “system reply”. Nonetheless, he doesn’t really talk about the same system as Kurzweil. Instead of a man and a rulebook (or a CPU and a set of algorithms), Searle (in his paper ‘Minds, brains, and programs’) writes:

“Suppose we put a computer inside a robot…. the computer would actually operate the robot in such a way that the robot does something very much like perceiving, walking, moving about…. The robot would, for example, have a television camera attached to it that enabled it to ‘see’.”

As I said, this system isn’t the same as Kurzweil’s: its more complex and has more parts. Thus, on Kurzweil’s own reasoning, it should stand more of a chance of being a mind (or even person) than a computer’s CPU and its set of algorithms.

Searle then talks about putting himself in the robot instead of a computer. However, neither scenario works for Searle. It’s still a case that all Searle-in-the-robot is doing is “manipulating formal symbols”. Indeed Searle-in-the-robot is simply

“the robot’s homunculus, [he] doesn’t know what’s going on. [He doesn’t] understand anything except the rules for symbol manipulation”.

Again, how does systemhood alone deliver understanding?

Ned Block on Systemhood

The American philosopher Ned Block, on the other hand, offers us a system which is very similar to Kurzweil’s. He too is impressed with the systemhood argument. In his ‘The Mind as Software in the Brain’ he states that

“we cannot reason from ‘Bill does not understand Chinese’ to ‘The system of which Bill is a part does not understand Chinese’…”.

Block continues: 

“[T]he whole system — man + programme + board + paper + input and output doors — does understand Chinese, even though the man who is acting as the CPU does not.”

Block adds one more point to the above. He writes:

“I argued above that the CPU is just one of many components. If the whole system understands Chinese, that should not lead us to expect the CPU to understand Chinese.”

Again, how does systemhood — automatically or even indirectly — generate understanding? Block hardly offers an argument other than complexity or that the addition of parts to a system may (or does) bring about understanding. Indeed he goes so far as to say that his own system could (or even does) have what he calls “thoughts”. He tells us that

“Searle uses the fact that you are not aware of the Chinese system’s thoughts as an argument that it has no thoughts. But this is an invalid argument. Real cases of multiple personalities are often cases in which one personality is unaware of the others”.

One part of Ned Block’s argument does seem to be correct. It doesn’t appear to be the case that 

if Searle-in-the-system doesn’t know the thoughts of the entire system, 
then consequently the system must have no thoughts either. 

Nonetheless, the question still remains as to how mere systemhood brings about understanding. It doesn’t matter if the CPU or Searle-in-the-system does — or does not — know what the entire system is thinking (or understanding) if mere systemhood can’t bring about thoughts (or understanding) in the first place. In other words, Searle-in-the-system (or the CPU) may in principle be unable to know if the system as a whole has thoughts or understands things — and yet at the same time it’s still the case that it doesn’t actually have thoughts or understand things.

Kurzweil’s Computer-Behaviourism?

Kurzweil says something that assumes much in its simplicity. He writes:

“That system [of a man and his rulebook] does have an understanding of Chinese; otherwise it would not be capable of convincingly answering questions in Chinese, which would violate Searle’s assumption for this thought experiment.”

What Kurzweil seems to be arguing is that if the system answers the questions, then, almost (or literally!) by definition, it must understand the questions. Full stop. This is a kind of behaviourist answer to the problem: 

If the system behaves “as if” it understands (i.e., by answering the questions), 
then it does understand. 

So it’s not even a question of behaving as if it understands. If the system answers the questions, then it does understand. That’s because if it didn’t understand, it couldn’t answer the questions!

Searle is of course aware of this behaviourist (or at least quasi-behaviourist) position. Basically, the problem of computer minds replicates the problem of human “other minds” (as in the Problem of Other Minds). As Searle himself puts it:

“‘How do you know that other people understand Chinese or anything else? Only by their behaviour. Now the computer can pass the behavioural tests as well as they can (in principle), so if you are going to attribute cognition to other people, you must in principle also attribute it to computers.’”

As I said, this raises all of Searle’s questions about true understanding — or, in his terms, meaning, intentionality and reference. To put Searle’s point in very basic terms: the system could answer the questions without understanding the questions. Though since Kurzweil is arguing that the very act of answering the questions quite literally constitutes understanding; then, by definition, Searle is wrong. Nothing, according to Kurzweil, is missing from this story.

So forget the man and his rulebook, let’s talk about the CPU and its rulebook (or set of algorithms) instead: 

If the CPU and the rulebook answer the questions, 
then the whole system understands the questions. 

If it’s definitionally the case that answering the questions means understanding the questions, then Kurzweil is correct in his argument against Searle. Nonetheless, Searle knows that this is the argument and he’s argued against it for decades. There’s something left out of (or wrong about) Kurzweil’s position. So what’s wrong with it?

Kurzweil himself is aware — if in a rudimentary form — of what Searle will say in response. Writing of Searle’s position, Kurzweil says that

“he states that Watson is only manipulating symbols and does not understand the meaning of those symbols”. 

It does indeed seem obviously the case that this is just an example of “manipulating symbols” and not one of true understanding. Having said that, that obviousness (or acquired obviously) is probably largely a result of reading Searle and other philosophers on this subject. If you have read more workers in artificial intelligence than philosophers on this subject, then it may seem to you that what Kurzweil argues is obviously the case.

So let’s forget intuition or obviousness.

Does a thermometer understand heat because it reacts to it in the same way each time? What I mean by this is that a thermometer is given a “question” (heat) and provides an “answer” (the rising or falling mercury). Sure, this understanding is non-propositional and doesn’t involve words or even symbols. But if Kurzweil himself sees these things in terms of the brain alone (i.e., its physical nature and output — not in terms of meaning or sentences), then why should that matter to him? In other words, if we can judge a computer squarely in terms of its output or behaviour (e.g., answering questions), then can’t we judge the thermometer in the same way? According to Kurzweil, if the computer answers questions then, by definition, it understands. Thus if the thermometer responds in the right way to different levels of heat, then it too understands. Thus sentences and their meanings are no more important to computers than they are to thermometers.





Tuesday, 9 June 2015

Names & Essences: Ruth Marcus on Quine’s Kripke



Saul Kripke claims that the statement

Aristotle might not have been a philosopher.”

isn't necessarily false because at other possible worlds Aristotle might have been born in an environment that banned any kind of philosophy. Kripke, on the other hand, takes the statement

Aristotle might not have been Aristotle.”

to be necessarily false at every possible world because Aristotle at all worlds would have been Aristotle (even if not a philosopher). This is the case because our name ‘Aristotle’ is what Kripke calls a ‘rigid designator’. Rigid designators designate the same individual at all possible worlds at which that individual exists. Thus the statement ‘Aristotle might not have been Aristotle’ is false – necessarily false. Kripke still uses the past tense in his example. That is, “Aristotle might not have been a philosopher” is true at some possible worlds because at these worlds Aristotle might have been born (as we have said) in a world which banned or didn't even have philosophy. Though “Aristotle might not have been Aristotle” is false because at every possible world at which Aristotle exists he would have been born as, well, Aristotle.

The rigid designator ‘Aristotle’ still applies to Aristotle at every possible world. It does so because it's not a ‘description’, like our ‘is a philosopher’. Thus, in essentialist terms, ‘Aristotle’ doesn't pick out Aristotle descriptively or conceptually, but essentially. And if ‘Aristotle’ picks out at all, it only does so because it picks out Aristotle’s essence. This essence can't be anything to do with any of our descriptions of Aristotle – not even “is a philosopher”. Instead ‘Aristotle’ picks out or designates the object Aristotle. Not only that: because descriptions have been banished from the reference-relation ‘Aristotle’ must only refer to Aristotle’s essence; as Quine, in Ruth Marcus [1990], argues. Thus the Kripkean position on proper names entails a parallel commitment to essences.

According to this analysis, when Marcus says that Quine mistakenly fuses or conflates rigid designators with essences, she's wrong. According to Quine, the Kripkean theory is a commitment to the idea that rigid designators pick out essences. According to Marcus, on the other hand, Quine believes that Kripkean proper names are themselves essences (as it were). Perhaps, however, what Quine meant wasn't that proper names are themselves essences but that they entail, on Kripke’s theory, a necessary commitment to essences. Indeed surely Quine can’t have believed that proper names are taken by Kripke to be essences. A name, in and of itself, couldn't be an essence or an essential property of a person or object, not even according to Quine (or anyone!). However, the way that Marcus puts it, Quine’s position does seem strange. According to Marcus,

for Quine, the trouble… came down to essentialism… [it] suggested to him that objects have their proper names necessarily [1990]”.

Instead of believing, on Kripke’s reading, that

  1. Objects have their proper names necessarily.

Quine meant:

  1. Kripkean proper names (or the belief in them) entail that they necessarily designate the essences of the objects named by them.
It's not, then, Quine’s belief that an object has its proper name necessarily. Again, how could Quine think this? On a de re reading, to call an object’s name essential is to speak nonsense. Perhaps, however, on a de dicto reading we can say that there's a semantic relation between names and their objects in which that relation is necessary (or essential). And that's what Kripke, of course, thinks. Though Quine doesn't believe that objects have their proper names necessarily. This would mean that Quine might have confused the de re with a de dicto reading of Kripke. That is, instead of objects having essences in the ontological sense of properties, he applies the same de re to the names of objects. That is, objects essentially (not necessarily) and literally have their names, as it were, ‘in’ them or ‘attached’ to them. Perhaps, however, it's not Quine who made this mistake; but Marcus. She has read Quine as mistaking a de re reading of Kripke with a de dicto reading. Perhaps Marcus means all this when she says that Quine believes that Kripke argues that “objects have their proper names necessarily” [1990]. So what she means is that Quine believes that objects have their proper names essentially.

Kripke himself makes a de re/de dicto distinction in this way:

de dicto = the relation between proper names (or the use of them) is that they name their objects necessarily.

de re = objects have their properties essentially.

Quine could accept the fact that Kripke evidently makes this distinction. That proper names can't be essential to objects; but that they are involved in the necessary relation named as de dicto above. Quine accepts these Kripkean distinctions. He may think that Kripke himself misuses the distinction between the de re and the de dicto above. He doesn't confuse or conflate them; though he does fuse, and therefore misuse, them. Thus:

Proper names designate their objects necessarily for all name-users. They aren't the essences of the named objects.

Because of this distinction Kripke also believes, Quine thinks, that proper names designate the essences of the objects they name. Kripke does believe this. He does so because, as we've already shown, Kripke argues that “Aristotle might not have been a philosopher” is true because of his aforementioned modal arguments. He believes that “Aristotle might not have been Aristotle” is false precisely because the name ‘Aristotle’ designates Aristotle’s essence, not the contingent properties specified by descriptions or concepts. Thus there's a strong logical relation and connection set up between

  1. Names and the naming-relation are necessary and constitute the necessity of the reference-relation.
and

  1. The relation between named object and name/namer in the reference-relation is necessary. The name and the naming process pick out only their named object’s essence, not its contingent properties specified and picked out by contingent descriptions and concepts.
Thus Quine doesn't believe that

Objects have their proper names necessarily.

which is what Marcus argues. Kripke may think that they have them essentially, even if he isn’t aware of this. He may think names are essential, Quine may argue that this is because he thinks them necessary, in the way specified as de dicto above. And this fusion, unknown or known to Kripke, is neither the result of Quine or Kripke’s conflation and misuse of the de re/de dicto distinction; but the (unintended) fusion of the two. And this fusion of the de dicto ‘necessarily’ with the de re ‘essential’ is a philosophical misuse, on a Quinian reading. That is, Kripke inadvertently (or not) begins with the de dicto

  1. The reference-relation between proper names (or their use) and their objects is that they name their objects necessarily.
and ends with the de re

  1. Objects have their names essentially.
which is what Marcus thinks Quine believes. But although Kripke never states ii) above, Quine believes it (of Kripke!), if implicitly, because he does believe that Kripkean proper names must be seen to only pick out the essences of named objects. And one can only believe this if one also believes that

Objects have their names essentially.

which is an unintended (or intended) consequence of believing that the reference-relation of designating is a necessary one. Thus proper names are necessary in this de dicto sense and they only designate the essences of named objects. Again, this may be Quine’s conclusion. Therefore his reading (right or wrong) of Kripke’s position because Kripke set up a necessary relation between

The necessary reference-relation or naming process

and the fact that

Proper names pick out or designate only the essences of named objects.

Kripke did so, as we've seen, because he fused, not confused, the de dicto reference- or naming-relation and the idea that named objects have essences, which is a de re idea. The de dicto relation requires de re essentialism. The necessary naming-relation is necessary if and only if it designates or picks out the essences of named objects. The de dicto relation is only necessary because of the essential properties of named objects. If named objects didn't have essences, then the reference-relation couldn't be necessary because it only has this modal property due to the relation set up between proper names and the essences of named objects. That relation would only be contingent, Kripke believes, if names picked out conceptual or descriptive properties (which he in fact believes). Conversely, if named objects don't have essences, then there could never be a necessary reference-relation between them and their names. Indeed there would only be a contingent relation between named objects without essences and their descriptions or conceptual predicates (which is what Kripke believes).

Thus Marcus is incorrect to think that only Quine himself believes that proper names must be the essential properties of named objects in Kripke’s scheme. She would be correct, on the other hand, to also add that Quine only put it this way (if he did put it this way) because he believes that Kripke himself fused de dicto necessity with de re essentialism. If Marcus believes that Quine thinks the former, then it is she herself who confuses the necessary de dicto with the essential de re; at least in the case of her reading of Quine. However, as we've said, Kripke didn't so much as confuse the de re with the de dicto but fuse them because of the necessary relation set up between proper names and their named objects. We can conclude that if Kripke, implicitly or explicitly, accepts the necessary relation between the de dicto and the de re, then we can argue that, in a sense, de re essentialism (which is vital to Kripke’s project) owes much of it power and point due to the necessary relation between objects (or the essences of objects) with the de dicto naming process. That is, de re essences could never be specified or even talked about as being ‘mind-independent’ because all acceptances of de re essences would depend upon - and be determined by - the necessary de dicto relation between proper names and essences. Though Kripkean proper names are only supposed to designate essences (not contingent properties), there would still be a necessary relation between proper names and essences. That, in turn, means that any talk of mind-independent essences would be illegitimate because every essence would be a named essence set up by the de dicto necessary relation between proper name and the named object. Thus every spoken-about essence could never be classed as a ‘mind-independent essence’ because it would be a named essence, set up by the necessary de dicto naming-relation – even if that relation is indeed necessary and named objects are deemed to have essences.

If my Quine is correct (i.e., that Kripke needed to fuse the de dicto with the de re), then Marcus is wrong to say that Quine’s Kripke is a misreading. If she's correct, then Quine does hold the strange position that proper names are the necessary properties of Kripkean named objects. Therefore Quine wouldn't argue that Kripke fuses the de re with the de dicto in thinking that (though he may still believe this). This doesn't mean, however, that Kripke doesn't fuse the de re with the de dicto, only that Marcus’s belief about Quine’s Kripke is correct. However, I do believe that Kripke may have fused the two. I also believe that Quine thinks this too; despite Marcus’s position on what Quine argues (if he does say, or mean, such things).

I don't know if Marcus misread Quine’s position. And I don't know if she herself conflates or simply fuses the de dicto with the de re because of her reading of Quine’s Kripke. If she thinks what she thinks about Quine’s Kripke, as we have interpreted it, then she wouldn't say what she says about it. Perhaps this also means that Marcus too either confuses the de re/de dicto distinction, or she actually fuses it (as (my) Quine’s Kripke does). Because we've already said that Quine couldn’t think that Kripkean proper names are ‘necessary’ (therefore essential on this reading) properties of named objects. If Quine doesn't think this, then it may be that Marcus didn't only confuse the de re with the de dicto (and vice versa), but, like Quine’s Kripke, she fused them too. However, as we've argued, Kripke’s fusion of the de dicto with the de re doesn't automatically mean that he also confused them. Perhaps such a fusion could only have come about because of some other confusion on Kripke’s part. That confusion might have been the result of the implicit or explicit fusion of the de dicto with the de re.

Finally, Kripke may knowingly fuse the two; yet he may not accept our other conclusion about such a fusion: that it goes against the point and power of the de re classification and disallows any talk about the mind-independent essences of named objects.

References and Further Reading

Kripke, S – (1971) ‘Identity and necessity’, in Identity and Individuation, New York, ed. M. Munitz
Marcus, R. B – (1990) ‘A Backward Look at Quine’s Animadversions on Modalities’, in Perspectives on Quine, eds. R. B. Barrett and R. F. Gibson, Oxford: Blackwell Publishers, pp.230-43
Quine, W. V. O. – (1966) The Ways of Paradox and Other Essays, Random House

Friday, 5 June 2015

Bertrand Russell’s Paradox


What is the primary feature of Bertrand Russell’s Paradox? It's one of self-reference. Thus it's like the Liar Paradox in which a sentence (or speaker) speaks about itself (or himself). With Russell’s Paradox, it's a case of a set (or a class) referring to itself or including itself as a member of itself.

What about sets that contain themselves as members? Consider this set:

Set X = the set of all the sets I've written about today

Today I've written about the set of all the things owned by Paul Murphy, the set of all writing implements, the set of arseheads, among others. All these are subsets of the set of all the sets I have written about today. But, in that case, I've also written about the set of all I've written about today – today. Thus this set will be a set (or a subset) of itself. That is, the set of the sets I've written about today will be a member of the set of all the sets I've written about today.

Let’s call my previous sets S, H, B and L. We also have Set X – the set of all the sets I've written about today. Now take another set:

Set Z = the set of all sets that don’t contain themselves as elements

Well, Set S, the set of all things that are owned by Paul Murphy, isn't itself owned by Paul Murphy - so it's not a member of itself. Neither are sets H, B and L. Set X, the set of all sets I've written about today, is a member of itself because it too is a set I've written about today.

What about Set Z above: the set of all sets that don’t contain themselves as elements/members? The question is:

Is Set Z an element of itself?

If Set Z isn't an element of itself, then it's a member of the set of all sets that aren't members of themselves. If it is an element of itself, then it can’t be a member of itself. Though if it isn’t a set that doesn’t contain itself as a member, then it is indeed a member of the set of all sets that don’t contain themselves as elements (of itself).

That means that if it is, it isn’t. And if it isn’t, it is. Or, alternatively, Set Z above both is and is not a member of itself. This is a contradiction.

This is the same problem that we have with the Liar Paradox. If everything the Liar says is false, then what he's saying must be false. He's saying that what he's saying is false. Therefore what he is saying must be true. Though if what the liar is saying is true, then it must be false. (Because everything he says is false.) Thus what he says is both true and false. This is, again, a contradiction.