Hi Franklin, Sorry for taking so long to reply. Thanks for setting me straight on Peirce still using the idea of breadth x depth later on in his career. I have to say though that I don't understand how such a metric might work in the later semiotic, just because it seems to me that the result of such a 'sum' will *always* be an infinity of an extremely high order, so any comparisons seem moot. As Peirce notes, propositions can't be counted. Even an artifically generated term such as 'red' and 'cow' will still partake of the surprisingness of 'cow' and 'red' taken on their own.
Best regards, Cathy On Mon, Mar 30, 2015 at 10:06 PM, Franklin Ransom < [email protected]> wrote: > 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 <[email protected]> > 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. >> > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to [email protected] with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm > . > > > > > >
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
