Games With Proper Names and Essences

“…if we are to entertain the possibility that a thing might not have had properties which in actual fact uniquely describe it or if a thing remains what it is through many vicissitudes but ceases to exist altogether through others, then there is a semantical role for genuine proper names which is different from the semantical role of singular descriptions.” - Ruth Barcan Marcus (1990)

What can we say about a thing being “what it is” without already presuming an essence of that thing? If we've already decided “what it is”, then this isn’t discovered a posteriori by finding out which properties remain “through many vicissitudes” and those that don’t. The prior stipulation of a thing’s essence will tell us which properties remain and which don’t. 

After all, certain properties may be essential at time t; though they don't remain over the entire existence of that thing. Similarly, certain properties may be deemed inessential/contingent despite the fact that they remain through many vicissitudes. A thing may remain the thing it is even though we've chosen different properties to characterise it with. In addition, my thing may “cease to exist” before your thing even if they're one and the same thing. In other words, my essence, E, of thing¹, may disappear; whereas your essence, E¹, of thing¹ may remain.

If a thing has different properties at another possible world, then why are we saying that it's the same thing? Again, it depends on a prior choice of essence to determine whether the thing in w¹ is the same thing as that thing in a-world.

Ruth Marcus talks about the “unique descriptions” of a thing.

i) Do the descriptions depend on (or come via) the essence?

       ii) Does the essence depend on (or come via) the descriptions?

In the first case, the descriptions would certainly come via a prior definition of the thing’s essence. In the second case, the essence would come via the descriptions of the thing. In the latter case, the essence wouldn't be known beforehand and therefore the descriptions would in fact determine the essence. If the descriptions come via the essence, then such descriptions would come via earlier descriptions which have already defined the essence of the thing.

In a sense we often have first- and second-order descriptions; rather than descriptions and essences. That is, the descriptions which determine essence would be first-order descriptions. The second-order descriptions, on the other hand, would depend on the first-order descriptions which have themselves become the essence of the thing. The second-order descriptions, of course, will be deemed contingent by the essentialist. However, his essentialist position would tacitly depend on a set of first-order descriptions being taken as the essence of the thing.

In theory this order could be reversed. The second-order descriptions could become first-order descriptions and therefore the essence of the thing. Likewise, first-order descriptions (or the essence of the thing) could become second-order descriptions to another person (or even to another essentialist).

In Marcus’s scheme, proper names refer to (or pick out) essences; or, as I’ve called them, first-order descriptions. Singular descriptive names, on the other hand, refer to (or pick out) second-order descriptions of the thing. Singular descriptive names are meant to refer to the contingent properties (or attributes) of a thing. Proper names, on the other hand, are meant to refer to (or pick out) the essence of the thing.

However, the essence of the thing is just another set of descriptions which have been given a first-order (or privileged) status. Thus if proper names are referring to (or picking out) an essence or first-order descriptions, then how come these descriptions aren't contained in the name as it is in itself? Such descriptions are in fact contained in proper names; though they're hidden descriptions only used in the context of the use of the proper name. It's indeed the case that such descriptive content of a proper name is oblique (or indirect) in the way it attaches itself to the referent. The proper name can't escape this problem.

We can now say that the content of singular descriptive names is explicit; whereas the descriptive content of a proper name is implicit. Of course different people rely on different descriptive contents to fix (or pick out) the referent. Thus it's hoped that a content-less proper name will refer directly to the referent without “empirical vicissitudes” (David Kaplan). However, just because the content of a proper name is implicit, that doesn’t mean that the proper name isn't reliant on descriptive content in order to fix (or pick out) the referent. Indeed, in a certain sense, the proper name is in a worse position than a singular descriptive name because we don’t know what the content is of other people’s uses of a proper name. We may not even be sure what descriptive content we rely on when we use a proper name ourselves. At least a singular descriptive name lays its cards on the table: we know the referent because we know the description which fixes (or picks out) the referent.

Thus I think that the problem is that “fanatical mono-denotationalists” (Kaplan, 1969) are quite correct to point out the many problems with relying on definite descriptions. However, simply because there are such problems that doesn’t mean that proper names don’t rely on descriptive content. Perhaps what's at stake is a normative issue. That is, it should be the case that proper names have no descriptive (or conceptual) content. (Or it would be a good thing if this were the case.) However, we could create an important difference in degree - though not of kind - between proper names and a definite descriptive names in that the same content (or contents) is always part of a particular proper name; whereas singular definite descriptive terms are free to come and go as we see fit. In that case, we would need to decide which fixed contents to apply to proper names. 

What could decide the matter? On the surface it's easy to show a difference of degree.

For example, "the British Prime Minister” would be could descriptive content of the name "David Cameron". However, “the man who once went to Blackpool” wouldn't be a good descriptive content and for obvious reasons.

There are problems, of course.

What happens when David Cameron is no longer the Prime Minister of Great Britain? The name ‘David Cameron’ would then need different descriptive content. However, it depends on who's using the proper name ‘David Cameron’.

For example, the primary content of Mrs Cameron's uses of the name ‘David Cameron’ may not be “the Prime Minister of Great Britain”. Her primary descriptive content may be: “my husband who's also a great father”. Of course if singular descriptive terms remain true or accurate at all times, then such a term may actually become a proper name in time.

For example, the name ‘Jack the Ripper’ was once a descriptive phrase and is now used as a proper name. This is the case because Jack the Ripper will always be Jack the Ripper; whereas David Cameron won't always be the British Prime Minister. In addition, many people don't even know the real name of Jack the Ripper. In that sense, it was never a descriptive term for certain people.

There's one way of turning the descriptive phrase ‘the British Prime Minister” into a proper name and that's the following. We can use the tensed and descriptive phrase “the British Prime Minister during 2011”. That will always be true of David Cameron. Therefore it's possible (though very unlikely) that the British Prime Minister (David Cameron) will be one day known by the proper name 'The British Prime Minister of 2011’.

References

Kaplan, David. (1969) 'Quantifying In'.

Marcus, Ruth Barcan (1990) 'A Backward Look at Quine's Animadversions on Modalities'.

Four Brief Thoughts on Validity & Soundness

1) Modal Logic From the Beginning?

An argument is valid if “the truth of the premises guarantees the truth of the conclusion”.

So how does that actually work?

Regardless of the truth (or otherwise) of the premises and conclusion, what is the relation (in a valid argument) between premises and conclusion? Is it a necessary connection? Is it semantic? Is it syntactic? Or is it logical – full stop?

Moreover, what precisely is meant by the word “guarantee” (it doesn't seem like a word from logic)?

Similarly with the word “impossible” (as in “it's impossible for the premises to be true and the conclusion false”)? What does the modal word “impossible” mean in this context? Is it natural impossibility? Or, again, purely logical (i.e., syntactic)?

Similarly, how do we recognise the soundness and validity of arguments? Again, through semantic connections or through logical (syntactic) form alone? More interestingly, does the logical (syntactic) run entirely free of the semantic?

Modal logic is implied by propositional logic and predicate logic (or first-oder logic). That is, with words such as “necessarily” and “possible”, aren't we moving beyond propositional and predicate logic?

For example, if I say,

It couldn't be possible for the premises to be true and the conclusion false.

that introduces possibility. (Indeed even the world “couldn't” has modal import.)

Similarly,

If the premises are true, then necessarily the conclusion must be true.

That introduces necessity.

Finally, I can say:

It is impossible for the premises to be true and the conclusion to be false.

That, again, introduces possibility.

2) The Cogito and Implicit/Hidden Premises

Some arguments may only have one premise. Thus we move from that single premise to a conclusion.

This seems to be the case with Descartes' Cogito: “I think. Therefore I am.”

It follows, then, that in order for the argument to valid (if not true), the single premise may - or must - have hidden content. That's certainly the case with the Cogito.

The “I think” leads to the conclusion “Therefore I am” because that “I think” has implicit/hidden/co premises (or hidden content). So what is its hidden content?

It's this: “Anything that thinks, must exist.” Then it can be said that “I think. Therefore I am” is effectively a tautology in that the “I think” itself contains the notion of the speaker's (or thinker's) necessary existence. In other words, existence is implied in the premise - “I think”. Thus:

i) I, a living and existing being, think.

ii) Therefore I am.

Or the implicit premise can be even more detailed or broad. Thus:

i) If a thing thinks,
ii) then it must exist.iii) I think.
iv) Therefore I am.

Thus we have two conditionals (or one conditional within another conditional). Thus:

i) If a thing thinks,

ii) then it must exist.

and then:

i) I think.

ii) Therefore I exist.

There are other examples of a one-premise argument.

For example,

i) The world is flat.

ii) Therefore the world is not mountainous.

Or:

i) Jim is a gay.

ii) Therefore, Jim's not heterosexual.

This is because, again, there are implicit premises involved. Thus in the following

I) Jim is a bachelor.

ii) Therefore Jim's an unmarried man.

the implicit premise is:

No bachelor can also be married.

Similarly with 'gay' and 'heterosexual', as well as with 'flat' and 'mountainous'.

Whereas 'bachelor' and 'unmarried man' can be deemed synonyms, that's not the case with 'flat' and 'mountainous'. In this case we have antonyms rather than synonyms. However, it isn't really the case the 'mountainous' is the antonym of 'flat'. A more accurate antonym of 'flat' would be, say, 'bumpy'. Or, more logically, the purest antonym of 'flat' is, in fact, 'not flat' (except, of course, that antonyms don't usually simply negate the source of the antonym).

3) Validity Without Soundness

An invalid argument can have a true conclusion.

To put it simply: if the conclusion doesn't follow from the premises, then it doesn't matter if it's true or false because, well, it doesn't follow from the premises.

That argument itself works as a conditional. Thus:

i) If a conclusion doesn't follow from the premises of an argument,

ii) then it doesn't matter – logically - if the conclusion is either true or false.

If a conclusion genuinely follows from false premises, then the conclusion can come out false. Again, that would only be the case if the logical moves from the premises to the conclusion are valid. In other words, in this scenario falsity is passed on from premises to conclusion.

What about the case in which the premises are true yet the argument is invalid? In that case, false premises can lead to a true conclusion if the argument is invalid because any conclusion (as already stated) can follow an invalid argument.

The obvious point to make is that because content (or even truth) is unimportant when it comes to recognising a logical form, you can create bizarre arguments which are nevertheless valid (though not sound).

For example,

All corbetts are bricks.

All bricks can solve equations.

Therefore all corbetts can solve equations.

The importance of this lack of a connection between premises and conclusion (or between validity and soundness) can be shown with the example of a true conclusion which follows an invalid argument. Or, more likely, one may not immediately believe that the conclusion is true because of the invalid argument. Thus one may look for a flaw in the argument which led to it. However, even if the argument is invalid, the conclusion can still be true.

4) Either/Or Arguments

The following argument is valid because it's impossible for the premises to be true and the conclusion to be false:

i) Either Corbett eats Cornflakes or he eats Ready Brek.

ii) Corbett doesn't eat Cornflakes.

iii) Therefore Corbett eats Ready Brek.

Of course the obvious question is: Why is this an either/or case? Couldn't Corbett eat neither Cornflakes nor Ready Brek? Sure. However, that would be a factual matter and not the concern of logic. Corbett may eat neither Cornflakes nor any other cereal. Again, that would be irrelevant from a logical point of view. What matters here isn't content or fact, but logical form. More precisely, it's the relation between a disjunctive premise (as in “...or...”) , a premise which is a existential negation (“... does not...”) and a conclusion (“Therefore...).

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A → B

“The words ‘to imply’ in the English language mean the same as ‘to contain’ or ‘to involve’…[note the] confusion of implication with the consequence relation.”

— Rudolf Carnap (1937), The Logical Syntax of Language.

[Note: this is an essay in the philosophy of logic, rather than in (pure) logic.]

Does the Symbolism A → B Always Have a Semantics?

If the symbol A has no meaning (or intension), then how can it imply or entail B? If A is just an inscription (or is self-referential — i.e., an autonym), then what connection could it have to B?

On one reading, A implies B (or B is a consequence of A) because B “contains” (or “involves”) something that’s already also “in” A. This is the standard Kantian view of conceptual analyticity. B, on the other hand, can be a consequence of A without it containing (or involving) something that’s common to A.

What exactly does it mean to say that “B is contained within A”? The American philosopher W.V.O. Quine accused Immanuel Kant of speaking at a metaphorical level when he used the word “containment”. However, what non-metaphorical way of describing what’s at issue here have we got left? If A is simply an inscription (or syntactic form), then of course it can’t contain B — it can’t contain anything except itself.

Symbol A will require semantic content if it’s to to imply B. In that case, it all depends on what the symbol A stands for. Does it stand for a concept, sentence, statement/proposition, fact or state of affairs? All these possibilities have content. (Arguably “content” is a problematic term when it comes to facts or states of affairs.)

For example, if the symbol A stands for the concept [politician], then what content will it have? We can say that contained within the concept [politician] are the macro-concepts [human being], [person], etc; as well as the micro-concepts [professional], [Member of Parliament], etc.

In a certain sense, it’s quite arbitrary to categorise certain concepts as micro-concepts and others as macro-concepts because it all depends on context. However, we can say that in one (or this) context we can categorise the concept [politician] as a micro-concept.

There’s a simple way to decide what’s what. We can ask this question:

Is it necessary for a politician to be a person or a human being?

The answer is (admittedly dismissing contemporary artificial intelligence and aliens) yes.

Then we can ask this question:

Is it necessary for a human being or person to be a politician?

The answer is no.

Thus, in this simple sense, the macro-concepts encompass the micro-concepts. Of course there are also yet higher levels of concept.

Take the concept [animal]. This includes the concepts [human being] and [person]. And there are yet higher-order concepts than that: e.g., [living thing]. This could go on until we reach the concepts [object], [thing], [entity], [a spatiotemporal part] and so on.

If A is taken to be a concept, then it may well have a large amount of content. Thus it could imply all sorts of things. Indeed it’s a strange thing to take A as simply standing for a single concept. (It’s hard to make sense of a concept all on its own.) Thus we need to fill in the dots ourselves.

On the other hand, if the symbol A stands for a sentence, then things become a little clearer and not as broad-ranging. (Usually, however, we have the symbols p and q for sentences or statements.) The sentence may (or will) of course include concepts; though concepts within a sentential framework will probably be more finely delineated and circumscribed. Something will be said about the concepts contained and they’ll also be contextualised.

To state that “the concept [politician] implies the concepts [human being] and [person]” sounds strange. In a sense, the bare concept [politician] isn’t actually saying or implying anything. Thus the idea of containment must be taken more literally in the case of concepts standing for A than if A stands for a statement (or a sentence).

How would B, therefore, be a consequence of A if the relation between A and B weren’t that of conceptual containment? In nature, B can be caused by A without sharing anything at all with A. Perhaps B can also be deduced from A without sharing anything with A. If this is so, then how would that deduction actually come about?

Note:

There are various kinds of conditional in philosophy, mathematics and logic. Among them are the following:

(1) Material conditional = This is found in propositional calculus and in mathematics.
(2) Conditional probability = The probability of an event B given that another event A has occurred.
(3) Causal conditional = If X then Y — where X is a/the cause of Y.
(4) Conditional proof = In logic this is a proof that asserts a conditional, and proves that the antecedent leads to the consequent.
(5) Strict conditional = In philosophy and logic there we often have symbols for propositions (such as p → q); rather than the symbolism A → B. In this case, despite the p’s and q’s rather than A’s and B’s, it’s still not always entirely clear whether state of affairs (or facts) are being discussed or propositions (or statements).
(6) Relevance conditional = In relevance logic there’s a demand that the consequent be “relevant” to the antecedent — or vice versa.

[I can be found on Twitter here.]

A Miniature: Panpsychism & Monism

What is the argument for panpsychism? Is it this? -

1. Since there is consciousness in the complex parts of the world, and
2. the complex is only a sum of simple parts, it must follow that
3. there must also be consciousness in the simple parts of the world.

Premises i and ii seem intuitively true. However, is iii a correct conclusion to premises i and ii? Is it, in fact, true?

There is indeed “consciousness in the complex parts of the world”. For instance, in the brains of human beings (if ‘in’ is the correct word here). And many people agree that consciousness is a result of some level of complexity.

How complex must something be in order to bring about consciousness? Human beings, for example, have billions of neurons in their brains. Ants have, say, tens - or hundreds - of thousands of neurons in their brains. Is this enough to bring about consciousness? Or is there more to this story than simply counting how many neurons a creature has?

If a creature had trillions of neurons, would it be ultra-conscious (or have ultra-consciousness)? And need that complexity only be the complexity of neurons and other aspects of the human brain?

What if we connected a thousand computers up together and programmed them to work as one? If that could be done, then would that large-scale and complex integration automatically bring about consciousness? Alternatively, is it an a priori truth that something simple (like an earthworm or even a pencil) can’t be conscious?

As for premise ii). Yes, it would seem to be the case that “the complex is only a sum of simple parts”. (Indeed the complex must be a sum of simple parts otherwise it wouldn’t be, well, complex.) However, what about the word “only” - as in “only the sum”? Perhaps there's more to a complex machine, creature or thing than simply the addition of simple parts to one another in order to create a complex whole. Perhaps something emerges from the addition of simple parts. Is a nation state, for example, only the sum of its parts? Is a class or set only the sum of its members? Is mind or consciousness only the sum of the parts of the brain (as well as, perhaps, other physical things)?

Was Wittgenstein a Language-games Relativist?

In very simple terms, the philosopher Ludwig Wittgenstein (1889–1951) was concerned with whether concepts are useful or not.

At first glance, Wittgenstein’s position on the introduction of new concepts into different (what he called) language-games (or Sprachspiel) seems very pragmatist or even instrumentalist in nature. (See ‘Wittgenstein and Pragmatism’ and ‘Wittgensteinian instrumentalism’.)

So one may now ask how can such concepts be useful if the entities they refer to don’t in fact exist or have any reality. In other words, doesn’t the usefulness of such concepts depend on — or presuppose — the existence or reality of what it is they refer to? (Wittgenstein specifically wrote about Sigmund Freud’s “subconscious thoughts” and Georg Cantor’s “different infinities”.)

So does “use” rely — or depend — on reality?

[It can be seen in the quote above — from Philosophical Grammar — that Wittgenstein never believed that this issue was only about “use”.]

Isn’t it the case that, say, the concepts ROUND SQUARE and FLAT NUMBER aren’t much use if the entities they refer to don’t exist or aren’t real?

[The word “refer” as just been used. It’s usually words or terms which are said to refer, rather than concepts. Concepts are said to have extensions instead.]

Take the possible worlds of analytic philosophers.

Possible worlds may not be real, However, they have proved to be useful and fruitful when it comes to formalising and clarifying our modal notions. Thus the concepts PHILOSOPHICAL DONKEY and GOLDEN MOUNTAIN may prove useful in some respects. That said, these two examples aren’t exactly equivalent to the concepts ROUND SQUARE and FLAT NUMBER. That’s primarily because there are mountains, there is gold, there are donkeys and there is the phenomenon of being philosophical. And gold and mountain can be juxtaposed without contradiction. So too with donkey and being philosophical. However, roundness and squareness, as well as flatness and number, can’t likewise be juxtaposed.

The American philosopher W.V.O. Quine’s position on (abstract) numbers wasn’t so distant from Wittgenstein’s position on the introduction of new concepts. Quine basically believed that numbers have instrumental use value. Quine also believed that it’s dishonest to deny the existence or reality of numbers when during one’s practice (i.e., in mathematics and physics) one effectively assumes that they do in fact exist or are real. (See ‘Quine–Putnam indispensability’.)

So is it the case that because numbers have instrumental value, then they must also exist or be real?

Why use the concept (to use Wittgenstein’s own example) SUBCONSCIOUS THOUGHTS (or plain SUBCONCIOUS) in our grammar if there are no such things as subconscious thoughts? What possible use could such a concept have if that usage doesn’t depend on the reality or existence of subconscious thoughts?

[Unconscious or non-conscious mental activities shouldn’t be confused with Freud’s and other theorists’ subconscious thoughts.]

Of course we can now debate the concept EXISTENCE itself; which has been used — or hinted at — a couple of times above. However, that’s doesn’t seem to be the point that Wittgenstein was making. In his view, we could introduce just about any concept into our grammar if we deem it useful to do so.

In a sense Wittgenstein was absolutely right.

The concept SUBCONSCIOUS THOUGHTS no doubt does have its uses. In other words, that concept explains many mental and behavioural phenomena.

For example, why does subject S behave in such a self-contradictory manner? It can be supposed that he does so because his subconscious thoughts are having some kind of effect on his conscious mental life and behaviour…

… Yet is it actually the case that S has such subconscious thoughts?

After all, there may be many other explanations of S’s behaviour which don’t include references to subconscious thoughts or to the subconscious generally.

Perhaps Wittgenstein might have responded: Then why not introduce new concepts into your grammar instead?

The only thing that matters, according to this reading of Wittgenstein, is whether or not these new concepts work within the overall domain of our grammar (or within a particular language-game).

Additionally, if old concepts no longer work, then get rid of them.

Some will argue, however, that certain old concepts didn’t work precisely because they had no basis in reality (e.g., PHLOGISTON, ETHER, etc.). That said, the characters and events in works of fiction aren’t actual or real; though they nevertheless prove to be (if in a loose sense) useful. They’re useful in that they display to readers, say, general kinds of situation and general kinds of character. That said, fictional events and characters are often (or always) parasitical on events and characters in the real (or actual) world. Thus such works of fiction work precisely because they indirectly refer (in the minds of the readers) to existents. Indeed even the most extreme works of fictional irrealism must depend on these kinds of indirect reference otherwise their readers wouldn’t relate to the works or even be able to make sense of them.

If we return to Wittgenstein’s general thesis.

Wouldn’t such a fast-and-loose attitude to concept-formation result in a multiplicity of contradictory concepts?

Relativism, Rules and Laws

If practices, customs, “forms of life” (see Wittgenstein’s position here) or language-games are truly autonomous, then perhaps the notion of conceptual contradiction doesn’t really have much purchase. That’s primarily because it presumes the existence of a correct (or true) language-game (or even a meta-practice) which somehow stands above all other language-games to pass its supreme judgement on them.

So if we take Wittgenstein’s (possible) position to its extreme limit, then any group can formulate any concept it wishes. That is, there will be no meta-language-game (or meta-practice) to tell them what concepts they can or can’t formulate. Thus everything everybody says would make sense in the context of the language-game it’s embedded in.

Again, Wittgenstein’s position automatically rules out any meta-language (or meta-language-game) which would try to make sense of the conceptual flux and chaos around it. Thus we would simply need to accept that it’s literally the case that anything goes. And that would primarily be because each individual language-game would be formulating its own rules.

In any case and according to the late Wittgenstein, such rules aren’t (as Ray Monk puts Wittgenstein’s early position) “fixed by immutable laws of logical form”. They are, instead, fixed by custom, practice or forms of life. Therefore, on this reading, rules couldn’t possibly be laws (certainly not “immutable laws”). That’s because laws are (usually) deemed to be universally applicable — i.e., applicable across the board. The rules of a language-game, on the other hand, may only apply to two individual (as it were) players.

Rules are therefore simply contingent conveniences instigated to serve the particular purpose at hand. Indeed they can be disregarded (or amended) according to new situations or purposes.

In may even be the case that — at least some — laws are laws even though they simply and only abide by arbitrary and contingent rules which are themselves custom- or practice-relative. Thus on this reading such laws are custom-built entities which have often (or usually) come to be seen as belonging to something beyond the station of mere rules. In other words, at least some laws are taken to be universal. However, such laws may be no more universal than poached eggs or flared trousers.

Main Reference

Wittgenstein, Ludwig, Philosophical Investigations (1945–1949).

[I can be found on Twitter here.]