Cathy, list, I was hoping to post sooner, but just got around to it; I'm sorry for the late contribution.
First of all, I find myself in agreement with Frederik's proposed view of the Kandinskys, namely that they form a part of Peirce's analysis of natural classes in the manuscript, and probably should have been included in the publication of the manuscript. Second, I noticed that on p.255, when enumerating the definitions of natural classes given from Ms. 725, Frederik writes for the third definition: "3) classes without an Area". Compare with p.239, where Frederik quotes the paragraph from Ms. 725: "In other words *cow* is a term which has an area; *red cow* has no area, except that area which every term has, namely that it excites a particular emotion in the mind." The third definition has to be a typo on Frederik's part; it should read "3) classes with an Area". Of course, Frederik goes on to argue that this way of defining natural classes is untenable, because artificial classes must have area too, on Frederik's view. I would like to discuss this problem of defining natural classification further below. But first, Cathy, you said above: "I think what the snippet shows is that it's worth bearing in mind that Peirce's paper on logical comprehension and extension was very early - 1867 - and here he is still working in a 'finitist' tradition in metaphysics and logic, which he manages to shake himself free of in his later synechism. Under synechism every real object has an infinite number of attributes, and every meaningful predicate or general term effectively has an infinite number of aspects, so a simple multiplication of B x D is pointless." Are you making a criticism of the position that Frederik defends in Chapter 9, arguing that his interpretation does not adequately take into account the influence of Peirce's synechism on later accounts of his theory of information? Consider p.236, where Frederik says: "In the geometrical metaphor adopted from Hamilton, Peirce consequently names this information concept 'Area': Breadth x Depth = Area = Information This formula is a formalization of the common sense intuition that if a sign says a lot of things about a lot of objects, it contains much information, but it does not yield to explicit quantification because of the issue of quantifying intensions (depth). A quarter of a century later, in the 'Kaina Stocheia' (1904), Peirce retains this theory: 'Besides the logical depth and breadth, I have proposed (in 1867) the terms *information* and *area* to denote the total fact (true or false) that in a given state of knowledge a sign embodies' (EP II, 305)." On my view, this means that a multiplication of B x D is anything but pointless. While it is true that Frederik goes on to say that area cannot be sufficient for identifying natural classes, this is not the same as saying that area definitions are "pointless". The definition of a natural class does not exhaustively identify a thing's attributes, but it does form the basis of further inquiry, wherein the information identified with the natural class can increase throughout the course of inquiring into that natural class; whereas this cannot really be true for an artificial class, which has its area decided by fiat, or so Frederik would have to aver. So the difference between a natural class and an artificial class is not that one has area and the other does not; rather it is that a natural class's area can change and increase over time, while an artificial class's area cannot. This means that breadth x depth = area = information is still very much at play and basic to Peirce's theory of logical quantity; in other words, the multiplication of B x D is not pointless, but still forms the basis of analyzing the meaning of a term (or proposition, or argument), as well as forms the basis of its synthesizing with new findings in continuing inquiry. It seems to me that you, Cathy, do recognize that a natural class is one into which we can continue to inquire and learn more about the class, but I find your analysis then gets confused in rejecting the idea of information as the product of breadth and depth; this formula is never really rejected by Peirce, and I don't find that Frederik rejects it either. It only becomes more nuanced and part of a more complex analysis over the years, or so I find. Now, having accepted it for the sake of argument above, I would actually like to take issue with Frederik's notion that the class *red cows*, or any artificial class, has an area. In OLEC, Peirce clearly states the following (see 6th paragraph, "The Conceptions of Quality, Relation, and Representation, applied to this Subject", available online at Arisbe; italics in original): "1st, The informed *breadth* of the symbol; 2d, The informed *depth* of the symbol; 3d, The sum of synthetical propositions in which the symbol is subject or predicate, or the *information* concerning the symbol. By breadth and depth, without an adjective, I shall hereafter mean the informed breadth and depth. It is plain that the breadth and depth of a symbol, so far as they are *not* essential, measure the *information* concerning it, that is, the synthetical propositions of which it is subject or predicate. This follows directly from the definitions of breadth, depth, and information. Hence it follows:-- 1st, That, as long as the information remains constant, the greater the breadth, the less the depth; 2d, That every increase of information is accompanied by an increase in depth or breadth, independent of the other quantity; 3d, That, when there is no information, there is either no depth or no breadth, and conversely. These are the true and obvious relations of breadth and depth. They will be naturally suggested if we term the information the *area*, and write-- Breadth x Depth = Area." What we find here is that information has to do with the sum of *synthetical propositions*. Artificial classes, being the kind of classes into which we cannot actually inquire, and thus not learn any facts about, obviously do not involve synthetical propositions. In the case of red cows, anything which can be said of red cows can be applied to red or cows; there are no unique facts to be learned about concerning red cows. The class red cows will have essential breadth, and essential depth, but can never be informed, and consequently, having no informed breadth and no informed depth, has no area. What I have just said is my answer to Frederik's statement given on p.255: "It is hard to see why Red Cows should not have an Area in the simple *b *x* d* sense defined in the OLEC." I hope I have shown that it is not quite so hard to see after all, when one looks closely at how *b* x *d* is defined in the OLEC. I should point out that I don't think the above point affects any of Frederik's other conclusions. It will still be true, after all, that what separates natural classes from artificial classes is that a natural class cannot be understood merely through its given definition (which we might assume to be the essential breadth and essential depth of the term)--diagrammatic experimentation involving theorematic reasoning still has an important role to play in inquiry. I am a little confused though why, on p.255, Frederik asserts that in "the brief paragraph preceding the graphical experiments of Ms. 725, Peirce proposes no less than three different definitions of natural classes, two of them negative...2) classes which have more properties than their definition.." I have re-read the entire passage several times, but I cannot find Peirce giving this definition in any part of it, namely that natural classes are classes which have more properties than their definition. The closest thing I've seen in the one paragraph which mentions the other two definitions, is where Peirce mentions that a natural class like cows "cannot be defined as the common extent of two or more classes such that nothing can be universally predicated of the former which is not predicable of one or other of the latter." But clearly this is not the second definition that Frederik mentions, namely that of having more properties than the definition. Could someone help me out here? I'm clueless on this one. On a separate topic, I notice that Frederik appears to accept the idea of the a priori, mentioning it on p.254 and p.255: "...completely brackets any possible explanations, empirical or a priori (by statistical, causal, or ontological necessities, respectively), for the reason behind the co-occurrence of certain Ps and not of others. In the real world, such co-occurrences will of course have explanations both in [the] form of empirical laws...and a priori regularities (determining the dependence of colour on space, or of obligations on promises, for instance.)". Frederik seems to me to assume Peirce shares the same view, that we can investigate into the a priori. Perhaps I have missed something, but I thought that Peirce rejected any philosophical project involving the notion of the a priori? That sounds more like Kant, maybe Husserl (of whose work I don't know much), and in pragmatist circles, like C.I. Lewis's conceptual pragmatism. The point about the dependence of color on space, I seem to recall, is hinted at in "On a New List of Categories", but I'm not sure Peirce's aim there is to claim that it is an a priori dependence. In any case, in his later phenomenological turn he has turned away from any kind of a priori approach, holding phenomenology to consist in the analysis of experience in general, not as what makes experience possible, but what most basic, fundamental, general characteristics are actually found in any experience (or at least most of experience). Thus phenomenology is no task of a priori inquiry, but is aposteriori from the outset. I would like to know other's thoughts on this topic, if anyone is interested to comment. Sincerely, Franklin On Wed, Mar 11, 2015 at 3:20 PM, Catherine Legg <cl...@waikato.ac.nz> wrote: > Ben that is a fascinating snippet! Thank you. > > I think what the snippet shows is that it's worth bearing in mind that > Peirce's paper on logical comprehension and extension was very early - 1867 > - and here he is still working in a 'finitist' tradition in metaphysics and > logic, which he manages to shake himself free of in his later > synechism. Under synechism every real object has an infinite number of > attributes, and every meaningful predicate or general term effectively has > an infinite number of aspects, so a simple multiplication of B x D is > pointless. > > And now for what I think is the answer to the question I posed: > > *QUESTION: How does Peirce attempt to draw the distinction, in the two > cases Frederik catalogues?* > > The examples Peirce gives of a natural and artificial class are* cows*, > and *red cows* respectively. > > I think what he thinks distinguishes the two is that the latter, being > arbitrarily defined, has no further properties than those already > enumerated in the definition. So all we can say about the class of red cows > is that they are cows and they are red. > > Whereas the natural class can be inquired into further indefinitely. The > class of cows all share - a certain DNA, certain feeding habits, certain > reproductive strategies, etc. Now I suppose one might argue that the class > of red cows has all those properties too, because the red cows are cows. > But I guess the key point is that there is no EXTRA determination being > given by the redness. Whereas if we said, all *Jersey* cows, the > Jerseyness would have certain further characteristics which can be studied, > and thus this is a natural class. > > So with the drawings, I think Peirce is trying to make it that case > that certain of the repeatable drawing features covary with certain other > of the features, and not with others, in ways such that we can capture the > minimal structure necessary for us to be able to group the features > together into 'artificial' and 'natural' classes. So the artificial ones > are those where features A and B go together in a series of cases, but no > other features are shared there. The natural ones are ones where features A > and B go together and in those cases are accompanied by further features C > and D. > > All this reminds me of a passage I was writing in a paper but then took > out before publication. It is trying to give a minimal definition of > *scholastic realism*, and arguing that it is not ruled out by fiat as > certain Humean picture in philosophy suggests. I reproduce it below in > case anyone is interested. > > And here ends my postings on Chapter 9! > Cheers, Cathy > > Hume’s maxim [i.e. 'there are no necessary connections between distinct > existences', 'the only contraries and existence and non-existence' - CL] , > and associated Modal Combinatorialism, can be usefully summed up as a > *syntactic > approach to modality*. To argue this, let us frame the issue in maximally > general terms. Consider a world consisting of 4 ‘idea / objects’ (*a*, *b*, > *c* and *d*) – which may combine to make larger states of affairs. > Imagine that these idea / objects are all *distinguishable*. Then > according to Hume they must be *separable*. Let us now imagine a toy > universe in which the only contraries are existence and non-existence. In > such a universe ontologically there may exist - and epistemologically we > may imagine - all possible ‘combinations’ of the objects (just one simple > two-way combination is illustrated for purposes of simplicity, represented > by the names of our objects appearing to the left or right of each other): > > *aa ab ac ad ba bb bc bd ca cb cc cd da db dc dd…* > > Let us now imagine a toy universe in which Modal Combinatorialism is > false. This just means that not all combinations are realisable. Here is > just one example: > > *aa ab ad ba bb bd ca cb cc cd da db dd…* > > This toy universe is missing *ac*, *bc* and *dc*, (for some reason, let > us imagine it is to do with the nature of *c*). An intelligent mind > inspecting the world above might think to summarise the combinations > missing from it in a simple statement – something like, ‘*c* can never > come last in combination, unless with another *c*’. This statement is > obviously a rudimentary law, or universal. > Our point is now merely that the second scenario is not incoherent. > It is not analytically false to conceive extra-logical constraints on the > happy combination of any conceivable object with any other conceivable > object (bearing in mind that of course these objects will have *natures*). > Mathematics...rules out such combinations regularly: for example, the > combination of 2 × 3 with 3 × *x*, for any *x *other than 2. Hume’s Modal > Combinatorialism is therefore a way of killing off a kind of realism about > universals without being honest about it. >
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