Natural Kinds & Essences

 
We can ask a simple question about scientific theories. We accept


All ravens are black.


though not


Non-black things are non-ravens.


Why?


They are, after all, logically equivalent.


When we ‘count’ all non-black things and all non-ravens, what are we left with? We are left with black ravens. Thus we arrive back at ‘All ravens are black’. That is why they are equivalent. If something, or anything, is a non-black thing, it can’t be a raven. If anything is a non-raven, then, well, it can’t be a raven. A blue bird is not a raven. A banana (a non-raven) is not a raven.


J.S. Mill believed that the world contains (natural) kinds. We don't compose these kinds. They are there in the world. They are mind-independent. It seems to go against Mill’s empiricism to talk about mind-independence. Perhaps he wouldn’t have used the term ‘mind-independence’ in this context. Perhaps instead he would have talked about his "permanent possibility of sensation" in that if we were to observe a natural kind like a raven, we would observe x, y and z.


What binds a kind together? Its ‘common nature’.


Ravens and other species aren't the only natural kinds. Gold and water are also natural kinds. Though perhaps we should say that H2 O is a natural kind; if ‘water’ refers only to secondary properties or Locke’s ‘nominal essences’. Yes, "we do not create the kind water simply by our classifications" (192). However, we only get to water via our classifications. And if we only get to water via our classifications, then perhaps, in a sense, we do create that natural kind in that we only know it via our classifications and only observe it through our classifications.


Firstly, the ‘nominal essences’ of diamonds. We "pick out diamonds by means of their hardness and transparency" (192). Scientists have no time for these properties. They are not only ‘interest-relative’; but mind- and sense-dependent too. Science discovers what real essences are. Does that automatically mean that such properties will not be ‘interest-relative’ and ‘sense-dependent’? Not according to many philosophers; not least those of whom deny essence altogether.


What is the real essence of diamonds? It is carbon, the very same thing as charcoal.


How can we flesh out this essence of diamonds? By saying that the fact that diamonds are essentially carbon "is another instance of an a posteriori necessary truth" (192) It is necessary that diamonds are carbon. Alternatively, they are carbon at every possible at which they exist. The result of this is that a diamond could lose its "hardness, sheen and transparency – without ceasing to be what it is" (192). Perhaps a diamond wouldn't loose its essence if it lost these contingent’ properties; though but would it still be ‘what it is’? It depends on what it is. And if diamonds are only their essences, then this conclusion follows by definition. Could we still have a diamond without its sheen, transparency, hardness, etc., or would we just have a lump of charcoal? Certainly no layperson would recognise it as a diamond. Why is the layperson’s view of what a diamond is irrelevant? Why are sheen, hardness and transparency irrelevant? Is a lump of charcoal really a lump of diamond?


Natural kinds have become very fashionable in the last, say, fifty years (after a long time of anti-essentialism). Why was this so?


Firstly, "it suggests that science looks for necessary connections" (192). Does this mean necessary connections between natural kinds? Does it mean that that necessary connections between natural kinds are themselves natural kinds? Or does it mean that there are necessary connections between the properties which constitute natural kinds?


Is it really the case that "it is the task of science to discover’ these necessary connections"?


Essences increase the possibility of objectivity in science if we have both natural kinds and necessary connections. In addition, the interest in natural kinds and necessary connections helped "detach it from our observations and attach it to an objective order" (192). Is science really detached from our observations? We know that observations aren’t everything; though surely they account for something – perhaps for much!

Sortal Identity

 
You can't make any judgements about identity, or even self-identity, unless one uses a sortal concept. When someone asks: 


"Is Jack the same as John?"


We must reply:


"The same what? The same banister?" No? The same man? The same person? Yes. The same official? Perhaps not."


Formally, a can be the same F as b; though not the same G. For example, according to Christian doctrine, Christ is the same substance as God the Father; though not the same person. This is not unlike, then, the substance monism of Spinoza. In that case, the substance would be God, and a mode of that substance would be Christ.


This takes us to Leibniz’s law.


This doctrine can be seen to violate this law and transitivity. 


Is everything true of Christ, also true of God?


For example, God Himself was not crucified on the cross. And Christ didn't have the property omniscience (he had the property, after all, of being a man). If Christ is the same substance as God, then if Christ was crucified, then God was crucified.


David Wiggins had his own take on Peter Geach’s thesis:


"Whenever a is the same as b, there must be a sortal concept, under which a and b both fall, which defines their conditions of identity." (147)


So under which sortal concept do both Christ and God fall? Substance? Is substance a sortal concept?


If Gordon Brown is both the Prime Minister and the husband of Mrs Brown, then both the Prime Minister and the husband of Mrs Brown fall under the concept person – they are both the same person.


Is person a sortal concept?


In the case of Gordon Brown, we have an abundance of sortal concepts under which he could fall (if he’s not careful): man, human being, animal, person, biped, earth-dweller, non-raven, etc. Are all these sortal concepts? Well, you can ‘count’ with all these concepts. You can count human beings and persons. You can even count, in theory, all non-ravens.


The non-raven sortal, if it is a sortal, doesn’t make much sense for the reasons given in Hempel’s paradox. However, we can ask which of these sortals is ‘basic’. Perhaps the most inclusive is the most basic. In that case, more things are human beings than are men. Women are not men. But, then, more things are animals than are human beings. Moreover, more things are non-ravens than are animals! Would that mean that Gordon Brown's being a non-raven is more basic or fundamental than his being an animal or a human being? How would we decide such an issue other than by saying that non-raven is a bogus sortal concept because of its infinite application?


Perhaps Aristotle has the solution.


In his ‘theory of being’ he attempted to find "the ultimate constituents of reality". The things which we "must identify if we are to identify anything" (147). Thus we surely don't require the concept [non-raven].


Isn’t the concept [thing], or [object], necessary in order to identify anything – or any thing? Isn't that a circular conclusion?


We don’t need the concept [animal] to identify anything at all. We don’t even need it to identify animals. We can identify animals as objects or things.


What concept, or constituent of reality, is basic or fundamental? Peter Strawson and Donald Davidson, for example, have said that things, objects or persons are fundamental (as well as 'events') – or ‘medium-sized dry objects’. This was an argument against ontological reductionism which cited particulars like sense-data as the fundamental constituents of reality. Or, on a metaphysical reading, simples or atoms as the fundamentals.


What about the sortals we can apply to ‘artificial kinds’? What about the sortal term ‘table’, as applied to tables?


Is table a the same table as table b?


S argues that table "sorts things relative to a human interest, and touches only superficially on the nature of things" (147). We can ask, here, why are human interests ‘superficial’ at all? They aren't superficial to, well, humans! Yes, human beings create tables for specific purposes. Does that make tables superficial? Again, not to us.


Even natural kinds can be seen ‘relative to human interests’.


For example, horses can be seen as good racers or nice pets. Is the sortal term ‘horse’ really that different? If one believes in God, then didn’t God create horses, at least through evolution? Aren’t horses relative to God’s ‘interests’? S describes the difference between ‘table’ and ‘horse’ thus:


"A horse’s history is determined by the laws of equine nature, and without
reference to human interests." (147)


Are science’s classifications unrelated to the interests of scientists and other human beings? Many philosophers argue that they are.


Our classifications can be wrong.


What about the laws of equine nature: are they relative to the interests of scientists? Perhaps not. Though we might have also have got the laws of equine nature wrong. Even if we have got them right, does that automatically mean that the ways in which these laws are determined, described, measured, classified and tested aren't relative to the interests of horse-scientists?


In any case, when we let George the horse fall under the sortal ‘horse’, we also "avail ourselves of a real criterion of identity; we also say what George fundamentally is" (147). Now we know how to identify George as George and as a horse. How does the sortal ‘horse’ in and of itself give us a criterion of identity? It's just a word or a concept. In order to flesh the concept out we would require descriptive information which would bring on board with it other sortal concepts. Though the word ‘horse’ itself wouldn't be a criterion of identity because it only tells us that a horse is a horse. It doesn’t tell us what a horse is. It doesn’t tell us why George is a horse. And so on. When we say that George is a horse, we are saying that this particular horse in front of us is, well, a horse.

Bertrand Russell on True Belief & Knowledge

 
According to Bertrand Russell (at least at one point in his career), not only is a belief not knowledge if it can't be substantiated with arguments, reasons or other beliefs, but it's not knowledge if it is derived from false beliefs which may have acted as reasons for the new belief.

So, in theory, I could derive the true belief that the earth isn't flat from the true belief that most swans are white. Clearly, in this case, there's no clear material connection between the two beliefs. If they weren't connected in some way by the subject, then such connections would have been either bogus or irrelevant – that is, not genuine connections.

This may be why logicians say that "from a true premise anything can be derived". That is, unless we require a material or relevant derivation from the true premise.

A true and materially connected belief for "The earth is not flat" may be "The horizon shows us that the earth is not flat’" Here, of course, there is a material and relevant connection with initial true belief.

Similarly, it's quite possible to deduce a true belief from a false belief. In this case, even if the false belief is somehow materially connected to the true belief, one still can't acceptably deduce a true belief from a false belief.

So, for example, we may derive from ‘Fish can fly’ the true belief that ‘Fish generally have scales’. Here there seems to be some kind of material connection in that both beliefs are about fish. But that isn't enough in this case.

For a start, they are about different aspects of fish. So, in that sense, there is still no genuine material connection. Also, we must repeat that one can't derive a true belief from a false belief.

In all these examples, it's clear that in order to gain knowledge, certain logical principles have to be adhered to. These principles guarantee knowledge.

For example, if the premises are true, then all correct inferences from these true premises must result in true conclusions. These true conclusions, then, would be examples of knowledge within a logical context. Of course the premises and conclusions must have material content and not just be examples of formal logic. That is, the premises must themselves be the conclusions of previous empirical investigation.

To have knowledge, according to the above, seems to mean that some kind of cognitive work has been done in order to reach a belief that is true. That is, Russell’s man is correct to believe that the then Prime Minister’s last name begins with B. However, this is because he thinks that the then Prime Minister was Balfour. In that sense, he was wrong. But he was, after all, only articulating a belief about the first letter of the Prime Minister’s last name. Though if he thought that Balfour is the Prime Minister, and the actual Prime Minister was Bannerman, then he clearly hadn't done any cognitive work to establish the first letter of the last name of the then Prime Minister. His true belief, therefore, was based on false knowledge. That is, he came to that belief for false reasons. Therefore he had no true knowledge.

To put this another way: Russell’s man had no justification for believing what he believed, even though what he believed is true. In a sense, his belief, though true, was based on pure guesswork. Knowledge, on the other hand, requires reasons for believing what one believes.

Though what if he did have reasons? He might have had the wrong reasons for believing his true belief. He might have thought, for example, that it was about time that a Prime Minister’s last name began with ‘B’. After all, up until then, no Prime Minister’s last name had begun with ‘B’. So, on his probabilistic reasoning, it was very likely that the Prime Minister’s last name would begin with ‘B’.

This kind of reasons is of course ridiculous. However, ridiculous or not, he might still have offered us reasons for believing what he believed. The problem is that they were simply bad reasons for believing what he believed. The problem now is: what would constitute, in this case, good reasons for believing what he believed about the then Prime Minister’s last name? This is, of course, another issue.

Does the above amount to saying that a belief can't be true, or can't be true knowledge, if it is believed for the wrong reasons? Similarly, a true belief may not be knowledge if it is produced by the wrong method:

"… a true belief cannot be called knowledge when it is deduced by a fallacious process of reasoning, even if the premises from which it is deduced are true. If I know that all Greeks are men and that Socrates was a man, and I infer that Socrates was a Greek, I cannot be said to know that Socrates was a Greek, because, although my premises and my conclusion are true, the conclusion does not follow from the premises." (131-2, Problems of Philosophy)

Are we to say that nothing is knowledge except what is validly deduced from true premises?

So it's not just false premises or prior beliefs that we need to watch out for; but also fallacious processes of reasoning. That is, there is more to reasoning that true premises and true conclusions. We could go from ‘Most birds fly’ to ‘Snow is white’; though clearly this would not instantiate a correct process of reasoning. However, is relying on the star charts or clairvoyance an example of correct reasoning simply because we take the premises to be true and the conclusion to be true? Russell's own example of faulty reasoning starts off with true premises and ends up with a true conclusion. However, no correct method of inference is used in this example: therefore the conclusion isn't an example of knowledge.

According to David Lewis, we can have examples of knowledge that don't depend on true beliefs, true premises or correct methods of inference. Sometimes we just know something and we don’t know why. For example, when we may have arrived at that piece of knowledge by justificatory reasoning in the past. Now, however, we have completely forgotten these cognitive processes; though we still, nevertheless, have knowledge.

Also, according to Lewis, we may have knowledge even though we haven't eliminated all possibilities of not-P, where P is our piece of knowledge. Lewis simply claims that it's impossible to eliminate all examples of not-P. Primarily because we are simply not aware of all examples of not-P. We couldn't be aware of all examples of not-P. In addition, some examples of not-P must be simply disregarded if we are to get the epistemic ball rolling.

For example, I believe that ‘snow is white’. But is it possible that my sensory receptors have inverted the colours I receive from the world due to a brain damage of some kind? Similarly, and more fashionably, I could be a ‘brain in a vat’ who is being fed sensory distortions care-of a mad scientist. Though I think that Lewis may see here that the brain in a vat hypothesis must be ignored ‘(proper ignoring’) simply because there is no known way of disproving that possibility. (Putnam does claim, however, that it is possible to prove that we aren't brains in a vat.)

There are similar sceptical stratagems that, according to certain epistemologists, we can't disprove. And in many cases, the reality of the sceptical challenge is essentially indistinguishable from the non-occurrence of the sceptical possibility.

Bertrand Russell himself gave the example of the earth being created five minutes ago with all its examples of fossils and remains exactly as they would be if the earth had been had it been around for billions of years. Though because the differences between the sceptical possibility and the present actuality are zero, it's simply counter-productive to take these sceptical challenges seriously. Again, if not-P were taken seriously, we couldn't get going in any epistemic process. Not only is there a possible infinite amount of not-Ps, but some not-Ps are deemed, by some, to be basically nonsensical.

Richard Rorty on Analytic Philosophy’s a Priori

What is it, precisely, that Richard Rorty thinks analytic philosophy is trying to achieve?

Let us take the ‘linguistic turn’ for starters. The aim of philosophers at that period (according to Rorty)

"was to mark off a space for a priori knowledge into which neither sociology nor history nor art nor natural science could intrude". (EHO)

Basically, Rorty believed that philosophers were trying to find "a space" for themselves. They wanted their own playground. That's why they needed a priori knowledge: that is, non-empirical knowledge. The things which only needed a philosopher’s brain and nothing more than a good armchair.

This was part of a long tradition.

Take Kant.

Before the linguistic turn, Kant had formulated his own "transcendental standpoint". In Kant’s case, it was the mind which provided us with the a priori limits of experience. Then it was meaning – or language – which provided all that is a priori. If language or meaning can offer us with the a priori, is that the same thing as claiming that the mind does too?

Donald Davidson also spoke out against this a priori notion of language or/and meaning. He wrote that we

"must give up the idea of a clearly defined shared structure which language users master and then apply to cases." (‘A Nice Derangement of Epitaphs’).

What can language as a "clearly defined shared structure" possibly mean? It sounds as if Davidson thought that philosophers are treating language - or a language - as some kind of quasi-object or entity. Thus such philosophers were reifying language it as if it is there – as a given – before people actually used it. That is, as something with necessary structures which are out of people’s control.

Surely, then, it must follow that the invariability of language’s givens must flow from the invariants of minds. Where else could language - or a language - come from? If we can ‘master’ language, then it must already be there. This is saying more than the fact that language is passed on from adults to children. In a sense, it's passed onto adults; who themselves pass it on. 

We can imagine the logical constants being, well, constant - as some kind of given. Perhaps certain inferential relations between propositions too. Though it's still hard to understand - without examples - what certain philosophers mean by the word ‘language’.

Logicism

Frege's prime purpose for writing his well-known and important Foundations of Arithmetic was to show us that mathematics is really analytic; as well as to disprove Kant’s view that it is synthetic a priori. In that, Frege was at one with Hume. This analyticity of mathematics, according to Frege, could only be proved and shown by reducing mathematics to the elementary laws of logic – hence ‘logicism’.


Frege took these logical laws to be more basic than any truths and laws in mathematics because they "must be accepted if there is to be reasoning at all" (385). It can be said, therefore, that Frege’s position on the logical laws is not unlike Aristotle’s on his ‘laws of thought’ which are required in all reasoning, even reasonings which deny their truth or dispute their fundamental nature.


Interestingly enough, Leibniz was basically a proto-logicist. He provides these proofs that arithmetical statements can be expressed logically:


2 = df. 1+1
4 = df. 1+1+1+1
Therefore:
2+2 = df. 1+1+1+1 = 4


As can be seen, however, Leibniz still uses numbers in his ‘logical’ reductions of numbers and arithmetical statements. In a sense, every reductionist logical definition only uses the number 1, along with the equality sign and other operators.


However, surely 4 + 2 = 6 is more illuminating than 1+1+1+1+1+1 = 6 because that too could become 1+1+1+1+1+1 = 1+1+1+1+1+1 and so on.


In one sense Leibniz is also committed to a proto-extensionalist logic in which numerals can be substituted within an arithmetical statement if the substitutions have the same extension – the same number – as its extension.


However, Leibniz’s reduction does not function as correct classical logic because it misses out the brackets needed in his:


2+2 = df. 1+1+1+1


It should be this:


2+2 = df. (1+1) + (1+1)


In other words, without brackets we don't recognise the logical scope of the original arithmetical operators in their statements. That is, 2 = df. (1+1), not 2 = df. 1+1. Similarly, 2 + 2 = df. (1+1) + (1+1), not the initial 2+2 = df. 1+1+1+1.


S puts it this way: "What entitles us to drop the brackets and convert (1+1) + (1+1) into (1+1+1+1)?" (386). The operation + enables us to add 2 + 2, so 1+1+1+1 isn't allowable because it is 2 that is added to 2, not 1 + 1 that is added to 1 + 1. Not only that: these brackets show us the scope of the arithmetical ‘2’ in terms of the operator of addition. So if Leibniz reduces it to 1 + 1+ 1 + 1 only by illicitly or tacitly using a mathematical operator in his ‘reduction’. And if he has done that, then he has not reduced arithmetic or mathematics to logic at all (just as a Tarskian meta-language cannot use terms from the object-language).


Other Reductions


Dedekind, at the end of the 19th century, reduced the basic notions of arithmetic (rational, real and complex numbers) to the theory of natural numbers, if not to logic itself. Of course we need to know what natural numbers are, and how they differ from rational, real and complex numbers.


Peano too reduced arithmetic to a set of axioms. Peano’s ‘postulates’, of course, are far better known than anything offered by Frege or Dedekind, for example. What are Peano’s postulates or axioms? These:


i) 0 is a number.
ii) Every number has at least one and at most one successor which is a number.
iii) 0 is not the successor of any number.
iv) No two numbers have the same successor.
v) Whatever is true of 0, and is also true of the successor of any number when it is true of that number, is true of all numbers.


It can be seen that Peano’s postulates are intuitively acceptable and also very simple in nature. Presumably he said that ‘0 is a number’ because other mathematicians and philosophers didn't actually think this.


In terms of postulate number ii). If every number has one successor, then this by definition seems to create or accept an infinite class of numbers. In addition, if the number 0 is not itself a successor of a number, then Peano must have rejected negative numbers like -1 and -44 and so on. They must have come later, as it were.


However, postulate v) seems to be incorrect. It says that whatever "is true of 0… must be true of all numbers". But postulate iii) has already claimed that "0 is not the successor of any number". Not being a successor, then, is a property of 0, so how can ‘all numbers’ have the same properties as 0? More correctly, how can the statement "whatever is true of 0… is true of all numbers" be true? If not true, then correct according to its other fellow axioms, specifically axiom three.


The last axiom just stated, interestingly enough, is the ‘ell-known axiom of mathematical induction. In other words, we have a strange juxtaposition of induction and a mathematical axiom. This is especially interesting because many philosophers and logicians say that the so-called ‘logical law of induction’ is not a genuine logical law at all, primarily because it deals with probabilities and not necessities and also, for example, because induction is a psychological phenomenon; at least according to Wittgenstein.


Anyway, the fifth axiom is inductive in nature because it "enables us to prove theorems about all the numbers by considering only three of them" (386). In other words, what is said to be the case in three of Peano’s axioms can be used inductively to show why the other two axioms are true, and also true about the nature of all numbers. So the axioms themselves, when taken separately, are themselves a micro-deductive or inductive system in that it has two ‘meta’-axioms, from which two lower axioms, as it were, can be deductively derived. And when we have all Peano’s postulates together, then we can again derive things; though this time theorems, not more axioms. Indeed not only can the axioms engender theorems and also two more axioms, but what is said or stated in them about numbers provides the basis of a mathematical system in which pure numerical axioms can be used to derive more numerical theorems from them (just as logical premises engender conclusions).


According to Peano’s postulates, all of arithmetic can be derived from them.


Are his postulates logical in nature?


In terms of logicism, the logicist seeks to define the three primitive terms – ‘number’, ‘successor’ and ‘0’ – and show that the postulates can be derived by logic from the definitions. So, in that sense, Peano carried on the programme begun by Frege a few decades earlier.


How were the primitive terms shown by Peano and the logicists to be explainable in terms of logic and logical terms?