Paul Churchland on Non-Propositional Animal Thought?

Patricia and Paul Churchland

The philosopher Peter Geach hinted at the possibility of non-linguistic concepts when he wrote that the “ability to express a judgement in words thus presupposes a number of capacities previously acquired” [1958]. This is reminiscent of Paul Churchland's position. Churchland says, in greater detail, that

“how to formulate, manipulate, and store a rich fabric of propositional attitudes is itself something that is learned…” [1981]

Again, elsewhere in the same paper:

“…language use is something that is learned, by a brain already capable of vigorous cognitive activity…language use appears as an extremely peripheral activity, as a species-specific mode of social interaction which is mastered thanks to the versatility and power of a more basic mode of activity. Why accept, then, a theory of activity that models its elements on the elements of human language?

The first quote above (from Churchland) would be given an immediate reply by a follower of Jerry Fodor. He'd say that the formulation, manipulation and storage of “a rich fabric of propositional attitudes” can be accounted for by something linguistic or at least something language-like: the language of thought. Thus we don’t escape from language here. Indeed, with more relevance to the issue of animals' non-linguistic concepts, Fodor says that the cognitive activity of animals could also be “linguaformal”.

Although Churchland may accept that the LOT could account for our learning (in the first place) how to “formulate, manipulate, and store a rich fabric of propositional attitudes”, his answer is that our learning to manipulate propositional attitudes is actually based on non-linguistic brain phenomena. To him, it's a question of the following:

“…a set or configuration on complex states…figurative ‘solids’ within a four- or five-dimensional phase space. The laws of the theory govern the interaction [“formulation”?], motion, and transformation [“manipulation”?] of these ‘solid’ states within that space…”

The point of bringing in Churchland is that - and we needn't accept his whole conceptual scheme - if he supplies us with possibilities/actualities of non-linguistic “cognitive activity”, then clearly this can be co-opted to show the same for non-linguistic concepts. (It’s a shame that Churchland himself doesn’t tackle concepts here.)

Fodor muddies the water by claiming that animal “cognitive activity” may also be “linguaformal”. The problem is that Fodor’s use of the word lingua (in what appears to be, inferentially, his acceptance of an animal Language of Thought) may be a use of a word that's so vague (vis-à-vis animal, not human, LOT) that it doesn’t satisfy any of the usual criteria for being a language.

Like Churchland, however, Fodor doesn’t say much about animals and non-linguistic concepts.

Now take Churchland’s reference to non-linguistic “representations” which can also be co-opted (to some extent) in order to talk about non-linguistic concepts. Here's Churchland talking about representations:

“Any competent golfer has a detailed representation [concept] (perhaps in his cerebellum…) of a gold swing. It is a motor representation [concept]…The same golfer will also have a discursive representation of a gold swing (perhaps in his language cortex…)...” [1989]

And later:

“A creature competent to make reliable colour discriminations has there developed a representation of the range of familiar colours, a representation that appears to consist in a specific configuration of weighted synaptic connections…This recognition depends upon the creature possessing a prior representation…This distributed representation is not remotely propositional or discursive…It…makes possible…discrimination, recognition, imagination…”

In a strong sense, what's been said above makes sense from an evolutionary perspective. At the level of species there must be a cognitive continuum between animal and human thought. On the scale of individuals, there's also a continuum between what can be called proto-thought and linguistic thought/verbal expression.

In the above, Churchland provides some of the scientific and philosophical details for such an argument; although, again, he doesn't tackle the subject of animal thought explicitly.

References

Churchland, Paul. (1981) ‘Eliminative Materialism and the Propositional Attitudes’
- (1989) ‘Knowing Qualia: A Reply to Jackson’
Geach, Peter. (1958) Mental Acts: Their Content and Their Objects
Fodor, Gerry. (1987) 'Why There Still Has to Be a Language of Thought'
 

My Dog Believes that x is F

According to Fred Dretske, concepts can be very rudimentary indeed. He writes:

“One can…see armadillos without seeing that they are armadillos, but perhaps one must…see that they are (say) animals of some sort…in seeing an object [one must] see that it is an object of some sort. To be aware of a thing is at least to be aware that it is…how shall we say it?…a thing. Something or other.” [Dretske, 1993]

In the above, Dretske is getting down to bottom-line quasi-Kantian concepts. Dretske appears to argue that animals don’t even have such basic concepts. My position is that if we insist on seeing concepts as exclusively sentential or linguistic (in any vague sense), then we will, by definition, exclude animals from concept-use. I think that such a position is both arbitrary and unnecessary.

Here is Dretske making a distinction between awareness of facts and awareness of things:

“Consciousness of facts implies a deployment of concepts. If S is aware that x is F, then S has the concept F and uses (applies) it [to x]… awareness of things (x) requires no fact-awareness (that x is F, for any F) of those things…there is no reasonably specific property F which is such that an awareness of a thing which is F requires fact-awareness that it is F.”

Perhaps all the above amounts to is that an animal (or  animals) hasn’t got our own concept of x (e.g., [human]). However, it may have its own. The concept, say, [human] may be dependent on sentential constructions; whereas an animal’s concept [C] may be based on (or partly made-up of) mental images [see Brian Loar, 1990].

How can an animal be aware of a thing (x) without having concepts which help it differentiate or individuate that thing? How can it be aware of x without the application of concepts to x? Doesn’t individuation and the application of concepts also entail (or at least imply) Dretske’s “fact-awareness”?

Of course “that P” isn't,  strictly speaking, applicable to animals if it's seen exclusively as a linguistic formulation (or a strict logical schema). Though need concepts and factual awareness be linguistic (or sentential) in form? Indeed couldn’t there be a non-linguistic version of  - or alternative to - that P? Can we really distinguish “awareness of things” from “awareness of facts”? Perhaps things are, in a sense, bundled facts; or at least they are determined or delineated factually or conceptually.

My parents’ dog is called Joe. He's aware of a thing, Paul Murphy, by being aware (non-linguistically) that P. (i.e., that x, in front of him, is Paul Murphy.) Of course he doesn’t know me as 'Paul Murphy'.

Dretske almost seems to be saying that unless one knows that P (or a non-formal, though linguistic, version of it), then one has no “fact-awareness”. This is reminiscent of Descartes’ exclusion of animals from rationality and even thought because they didn’t speak French; or, more fairly, because they didn’t speak any human language. This is Descartes himself on that subject:

“…it has never yet been observed that any animal has arrived as such a degree of perfection as to make use of a true language; that is to say, as to be able to indicate to us by the voice…anything which could be referred to thought alone, rather than to a movement of mere nature; for the word is the sole sign and the only certain mark of the presence of thought…” - Letter to Henry More (1649)

Dretske himself claims as much when he says that the

“cat can smell, and thus be aware of, burning toast as well as the cook, but only the cook will be aware that the toast is burning”.

Yes, that last clause is indeed correct. Who would doubt it? The cat won't sub-vocally think to itself “the toast is burning”. Though it may have its own concept [B] for burning, its own concept [T] for toast, and even its own molecular concept  [BT] for burning toast.

The implication also is that the cat is aware that the toast is burning; though not “fact-aware” that the toast is burning. Of course the cat isn’t aware that the toast is burning in the sense of thinking “the toast is burning” in English, French or in any language (even its own). However, it might be fact-aware of something.

That can be explained in this way.

The cat isn’t aware that “the toast is burning”; though it is aware that the toast is burning. We can say that it's aware of the truth-condition (i.e., burning toast); though not that truth-condition's expression in a natural language (i.e., "the toast is burning").

Despite all the above, Dretske himself says (at the beginning of his paper) that he doesn’t “know about animals”. He may not know about animals in the plural; though he seems to know about the cat in his own example.

If mental-image-based concepts can “pick out a kind” (Loar, 1990), then perhaps some animals can't only pick out an x. They may also believe that x is F (or that P). In a sense, an animal needs to think that x is F in order to distinguish x from, say, y. Of course the belief that x is F isn't sentential, linguistic or even formal or quasi-linguistic. Why should it be? Why is it necessary to believing x is F that it's a (as it were) linguistic by-product?

Take Joe again.

I'm x to Joe. I'm an individuated object to him. That much, surely, must be uncontroversial. How does Joe individuate and differentiate me from, say, y (say, another person or even an inanimate table)? It must do so by believing that x is F (or x, not y, is F). That is, it believes that the object in front of it is Paul Murphy. However, Joe is also applying a concept [P] to a reoccurrence of x. The concept [P] is being applied to x. Therefore, to Joe, x is F.

The concept [P], or [Paul Murphy], may be an agglomeration of atomic concepts: [a certain smell,] [certain clothes], [a certain voice], etc., as well as - perhaps more importantly - a concept-image (i.e., a mental image used as the basis for a concept).

Thus x is F (for Joe the dog) means that it applies (or has already applied) the image-concept [I], plus various atomic concepts (including smells, dress, etc.) to x. x, in this case, is a re-occurrence of the object my family - though not the dog - calls 'Paul Murphy'. Therefore the variable x isn't identical to the dog-concept of x. The concept [P] is applied - or belong - to object x. For Joe, therefore, x is (indeed) F.

Even language-users may use (or have) such non-linguistic (or non-sentential) concepts. Either that, or non-linguistic mental phenomena may be the basis of linguistic concepts.

x is F is conceptual . It needn't be based - or reliant - upon other sentential formulations such as “You know Tony sometimes lies?” or “That guy is a dissembler”. However, the concept (or belief) needn't be purely abstract either. There’s nothing more real (to me) than my mental images of Tony and also of Tony lying. However, lying itself, admittedly, is necessarily linguistic. Thus Joe (or any animal) can't think that Tony (or anyone or anything else for that matter) is a liar. Lying comes with language use (though not deception – animals practice deception).

Thus I’m not saying anything in the above that's very surprising. There are some human concepts that animals not only don’t have; but which they could never have. And not just beliefs/concepts such as “4 + 4 = 8”: far more mundane and basic ones too.

What of a semi-complex beliefs/concepts such as [forests are full of trees]?

My dog-translation of the verbal locution “forests are full of trees” wouldn’t of course be an exact translation in the way “I love you” can be precisely translated into French. So what? Animals aren’t fellow human beings like the French. A dog’s version of “forests are full of trees” may come close (if only in a few respects) to our concept or belief. In any case, why would we require (or need) an exact equivalent (or translation) anyway? I don’t need one to argue my case. The point is that the dog’s version (or alternative) would still be conceptual. It would also be (by inference) a belief. It could even be (in a sense) an example (or version) of a predicate attached to a noun. Of course we'd need non-linguistic interpretations or equivalents of predicates and nouns. That’s not a problem: we have them in philosophy. The predicate “are full of trees” could become some kind of property or attribute of the subject-term “forests”. The noun “forest” could become some kind of non-linguistic subject (or object). Indeed Frege (for one) believed that predicates are concepts; just as others think that concepts are universals.

Now we’ve reached bedrock.

Thought Before Language?

Something (or some things) must come before our linguistic expressions: both as a species and as individuals. Our linguistic expressions didn’t occur ex nihilo. 

Here’s Paul Churchland making related points:

“…language use is something that is learned, by a brain already capable of vigorous cognitive activity; language use is acquired as only one among a great variety of learned manipulative skills; and it is mastered by a brain that evolution has shaped for a great many functions, language using being only the very latest and perhaps the least of them. Against the background of these facts, language use appears as an extremely peripheral activity, as a species-specific mode of social interaction which is mastered thanks to the versatility and power of a more basic mode of activity. Why accept, then, a theory of cognitive activity that models its elements on the elements of human language?” [1981]

I believe that certain animals have beliefs and concepts even though I also believe that language and language-based concepts utterly shape human thought and experience.

Joe’s x is F could be even more abstract. It could be x (Paul Murphy) is a F (human being). I needn't stress again that F (i.e., the dog-concept [H]) needn't be our concept [human being]? Though Joe may have some concept (or concepts) of a human being or of what we call human beings. It may notice that we only have two legs; that we don’t sniff each other’s backsides; and that we smell a certain way (i.e., unlike him). Even these atomic concepts of the molecular concept [human being] would need to be “translated” into dog-concepts.

Joe “picks out a kind”[Loar, 1990] - the kind human beings call human beings. More correctly, Joe picks out a particular (say, Jim) and sees that he belongs to the kind we call (though it doesn’t) human beings. At no stage of the game am I saying that Joe’s x is F is anything like our x is F. It's structural; though not linguistic or sentential. It may even have a similar structure in some broad sense.

In any case, how close must Joe’s x is F be to our x is F? More relevantly, why do we demand an exact parallel with our x is F in order to allow attributions of concepts and beliefs to dogs and other animals?

Many 18th-century Europeans didn’t think that central-African tribesmen had rationality (or even concepts, etc.) simply because they didn’t speak English or French and were a different colour. (Think here of the earlier Descartes quote.) Of course 18th century central-African tribesmen were far more intellectually advanced than any animal; though my point still hold. The Europeans demanded exactitude from the tribesmen in order to ascribe rationality or even thought to them. Thus it’s no wonder that some contemporary philosophers are looking for exact equivalences between themselves and other animals in order to allow animals the privilege of having or using concepts and beliefs. It is (dare I say) a kind of chauvinism similar in spirit to that which the functionalists (of mind) detected in the 1960s when they argued  that minds (qua minds) needn't share our (human) neurobiology.

Finally, I hope the reader doesn't get the wrong impression from all the above. I don’t think that animals are as clever as human beings... not even dolphins or apes. And I don’t want to say (here) whether or not these conclusions will have any impact on other issues related to animals, let alone on the issue of animal rights.

My claim is very simple: some animals do have concepts and beliefs.

References

Churchland, Paul. (1981) 'Eliminative materialism and the propositional attitudes'.

Dretske, Fred. (1993) 'Conscious Experience'.
Loar, Brian. (1990) 'Phenomenal States'.

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...).

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

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.]