Showing posts with label function. Show all posts
Showing posts with label function. Show all posts

10 Jan 2017

Uexküll (4.6) Theoretical Biology, “Object and Implement”, summary

 

by Corry Shores

 

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[The following is summary. All boldface and bracketed commentary is my own. Proofreading is incomplete, so please forgive my typos. Page citations refer to the 1928 German edition first and to the 1926 English edition second. Note: German terms are repeatedly inserted to facilitate comparison with translations of other Uexküll texts.]

 

 

 

 

Summary of

 

Jakob von Uexküll

 

Theoretical Biology

[Theoretische Biologie]

 

Ch.4 Object and Living Organism

[Gegenstand und Lebewesen]

 

4.6 Object and Implement

[Objekt und Gegenstand]

 

 

 

Brief summary:

Physics sees things being ordered merely by causality. But biologists also recognize an additional ordering principle, namely, conformity to plan. “Objects” are things whose organizing relations are understood simply as causally governed and whose composition is explained merely on the properties of its constituent materials. But we call “implements” those things whose organizing relations are understood as fitting within a larger plan (or functional system) and whose essential properties are understood as those contributing to its functionality. The parts of an implement relate to the whole in a meaningful way, namely, in how they contribute to the implement’s functioning. If we do not know how the object conforms to a plan, that is, how it has a certain functionality that places it within a larger system of practical human activities, then we do not see how its parts relate meaningfully to the whole. A ladder for example, to those who never have seen one or have never had need for one, would simply appear as planks arranged with holes between them. But after learning its function and how it is used, they would realize that it is designed with certain essential features. The essential properties of an implement, that is, those properties that serve the implement’s function, are called “leading” properties. Those that do not serve the function are “accompanying” properties. The same thing can be used different ways, which will cause the leading properties to become accompanying and vice versa. For example, consider two properties of a concave piece of glass: it is rounded in shape, and it is transparent. When it is used as a window-pane, its transparency is the leading property and its concavity is its accompanying property. But when it is used as a saucer to hold liquid, its concavity is its leading property, and its transparency is its accompanying property. To complicate things further, implements have main functions and subsidiary functions, and accompanying properties can serve the subsidiary functions. So when the concave glass is used for a window-pane, its concavity serves the subsidiary function of making it hard to see what is going on inside the house. And when it is used as a saucer, its transparency serves the subsidiary function of helping us discern its liquid contents. There are still yet other accompanying properties which do not even serve subsidiary functions. These simply express properties of the materials composing the implement. For example, a wooden boat has planks that express features of the trees they came from, and these properties are completely inessential to any aspect of the functionality of the boat (for example the color of the wood, which is hidden under the paint.) There are no other properties of a implement than those that serve its functioning and those that do not.

 

 

 

 

Summary

 

§494

[Physics only recognizes causality as what orders things (which under this view we call “objects”), but biology recognizes a second organizing rule, namely, conformity with plan (Planmäßigkeit).]

 

Uexküll will distinguish physics and biology. Physics says that the things [Dinge] in nature only obey causality, and Uexküll’s term for causally ordered things is “objects [Objekte]” (83-84 / 103). Biology also acknowledges causality, but it says “there is a second, subjective rule whereby we systematise objects [Gegenstände]: this is conformity with plan [Planmäßigkeit], and it is necessary if the world-picture [Weltbildes] is to be complete” (84 / 103, bracketed insertions mine). [I am not sure, however, why this is considered a “subjective” rule.]

 

 

§495

[A piano hammer hitting the string and playing a note is a series of causally related events, but the note has its place in a melody, which is another series and which is not causally ordered.]

 

Uexküll illustrates with the example of a hammer in a piano striking a string. [The idea seems to be the following. We have a series of events organized by causality. The hammer hits the string, which causes a note to be played. But there is another sort of series. The note is one in a melody, so it is a part of another series which is non-causal. Perhaps it is something like final-cause (the note happens because the melody was moving toward that part where it is played), but I am not sure. Or perhaps it is like another layer of order. There is the causal layer of ordering relations, but the note occurs in a context where it is ordered according the parts of a melody. Or maybe simply we are to think that the way the notes are arranged in the melody is not a necessary succession, as it could have been otherwise, but in this case it was decided and “planned” in a sense. Let me quote.]

When the hammer strikes the string of a piano and a note sounds, that is a purely causal series. If this note belongs to a melody, it is interpolated in a sound-series, which also exhibits arrangement, but not of a causal kind.

(84 / 103)

 

 

§496

[When a carpenter builds a ladder, she does so through a series of causal events which result in the ladder. But this production is unlike normal causal relations between moving bodies as studied in physics. The thing produced has a certain meaningful arrangement of its parts that cannot be explained by causal relations.]

 

He gives another example. A carpenter is building a ladder. While it is being made, there is a causal chain of events. She chops the wood for the parts and assembles the ladder. [But suppose we are simply physicists looking at the interacting of objects, the carpenter and her materials. We see a causal series, but it is unlike other kinds of interactions between inert sorts of objects, like rocks colliding. Here the “causal” result is an object that has a certain meaning or sense to it. We cannot simply regard the ladder like it were any object whatever. It has a particular structure that would not arise just by causality alone. Instead, there is a meaningful relation between the parts that govern its structure.]

When the carpenter’s axe chops up the wood into planks and pegs, and when the drill bores through the planks and the hammer drives the pegs into the holes, these are all of them in causal succession. But the structure emerging from this process, the ladder, cannot be interpreted by causality; it can be understood only from a knowledge of the designed arrangement [planvollen Anordnung] of the rungs with relation to the main planks, and of all the parts to the whole.

(84 / 103, bracketed insertions mine)

 

 

§497

[When an object cannot be explained just by causality on account of the parts standing in a meaningful relation to the whole, we call it an “implement” (Gegenstand).]

 

Uexküll gives the name “implements” [“Gegenstände”] to such objects that cannot be explained simply by causality, “since in them the parts stand in the same relation to the whole as the individual sounds do to the melody” (84 / 103).

 

 

§498

[Mere objects have only the structural features provided by their constituent matter. Implements, however, have the additional planned structure governing the meaningful relations between the parts and the whole.]

 

He explains that the only structure an object has is what its constituent matter provides it with. Implements, however, have an additional structure that connects the parts to the whole in a meaningful way, in accordance with plan.

Both objects [Objekte] and implements [Gegenstände] consist of matter [Stoff]; but in the object [Objekt] there is no arrangement of the parts [Anordnung der Stoffteile] other than that which the structure of the substance [Stoffes] brings with it. In | the implement [Gegenstand], there is, in addition, a framework which connects up the parts into a whole that expresses plan [ein Gefüge, das die Teile zu einem planvollen Ganzen verbindet].

(84 / 103-104, bracketed insertions mine)

 

 

§499

[Objects and implements both have the same sorts of material properties, but implements have an organization that is recognizable to those who can see its meaning or plan.]

 

He then notes that both objects and implements have the same sorts of material properties. But to those who recognize the plan in the implement, they see an additional structure. This is like words in a foreign language. To those who do not know the language, it is a meaningless series of squiggles. But to those who do know the language, there is a meaningful arrangement of strokes forming linguistic symbols.

In outward appearance, objects [Objekte] and implements [Gegenstände] are indistinguishable from one another. The same local signs [Lokalzeichen] and content-signs [Inhaltszeichen], enclosed by the same schema, form them both; just as the words of a language present the same optical appearance to the man who knows the language as they do to the foreigner. But the one knows the laws determining the juxtaposition of the letters in the word, while the other, not having this guide, stares uncomprehendingly at the words of the foreign tongue. The one sees before him only various assemblages of letters; the other reads words.

(84 / 104, bracketed insertions mine)

 

 

§500

[Some inorganic objects are simply objects, because their parts can be rearranged in any which way without the whole changing, as for example a heap of sand. Physicists normally consider things in the inorganic world as not having design or plan.]

 

Of course even for the biologist many objects are simply objects. In these cases, the parts can be “interchanged in every direction without the whole being in any way affected”, like a heap of sand. They become implements only when used by humans. Physicists will acknowledge that human artifacts have a plan, but there they do not recognize any conformity with plan among inorganic things.

Undoubtedly to the biologist of the present day many things [Dinge] around him appear to be objects [Objekte] pure and simple — such, for instance, as a heap of sand, or the water in a vessel. In both instances, the parts can be interchanged in every direction without the whole being in any way affected. We shall admit, therefore, even from the biological standpoint, that there are objects without design [planlose Objekte], or mere heapings together of matter, in which at the present day we are unable to discover conformity with plan [keine Planmäßigkeit]. The whole of inorganic nature [Natur] is usually looked on as consisting of objects [Objekten] governed by causality alone. Inorganic objects [Objekte] are at present treated as substances [Stoffe] held together by a schema, and forming designed implements [planvolle Gegenstände] only when they are used for the products of human beings. The plan [Plan] in such implements [Gegenstände] is exclusively a human one; matter [Stoff] is merely the medium employed in their construction. Even the physicists cannot deny that there is a plan [Plan] in human products, but they refuse to admit any other kind of conformity with plan [Planmäßigkeit] in the things [Dingen] of the inorganic world [Welt].

(84-85 / 104, bracketed insertions mine)

 

 

§501

[However, the ancient Greeks saw everything in the world as having plan.]

 

[So the physicist recognizes that a very limited number of things in the world have design or plan, and those are the things made by humans.] Humans did not always see the world as being fundamentally without design. The ancient Greeks saw everything as having design.

Men did not always think in this way. According to the Greek view, nothing in the world was without design [Planloses]. The entire inorganic world seemed to them as much a work of art | as the organic. Sun, moon, planets and the heaven of the fixed stars united in a vast work of art expressing plan [planmäßigen Kunstwerk], in which every substance [Stoff] occupied its appointed place. The water flowed on the earth and gave life to it, just as the blood does in the body. There was no such thing as dead matter [toten Stoff].

(85 / 104-105, bracketed insertions mine)

 

 

 

§502

[Ancient Greek water jars, for example, seem like a faithful reflection of the water it holds. This is because they recognized a larger plan of nature governing the shapes water takes, and their vessels reflect that plan rather than imposing human purposes onto the water.]

 

We notice for example that ancient Greek water jars “represent as completely as possible a clothing of the water itself” (85 / 105). [Perhaps he is referring to the water-droplet sort of shape they often have. I am not sure how this illustrates his point. Maybe the idea is that today our water vessels are designed simply for human practical interests, but the ancient Greeks saw water itself as having a certain planned form that should be reflected in its vessel. Thus the human artifact is coherent with the larger plan of Nature of the cosmos.] He notes how this is like the way that rhizopod shells are shaped; “thus we get the impression that, in those old Grecian jars, the water created for itself the only envelope that would exactly fit it, and that this was subsequently made use of by man. In their perfection, these ancient vessels are true forms of Nature in art” (85 / 105).

This must be obvious to any naturalist who passes through the museum at Athens, and looks critically at the ancient water-jars, which differ so essentially from our own water-vessels. While our own, when they are good, reproduce in every detail of their form man’s preoccupation with his own affairs, in the ancient jars these signs recede into the background, and the vessels come to represent as completely as possible a clothing of the water itself.

 

They are strikingly reminiscent of certain rhizopod shells, with which the fluid protoplasm of these wonderful organisms invests itself. And thus we get the impression that, in those old Grecian jars, the water created for itself the only envelope that would exactly fit it, and that this was subsequently made use of by man. In their perfection, these ancient vessels are true forms of Nature in art.

(85 / 105, paragraphs are one in the German edition)

 

 

§503

[In light of the ancient Greek view, perhaps biologists should also see both the organic and inorganic as conforming to plan.]

 

So the Greeks see both the organic and inorganic worlds as conforming to plan. Biologists just see the organic as conforming to plan, while physicists see nothing (except human tools) as conforming to plan. Uexküll, noting the Greek view, wonders if biologists ceded too much to the physicists (85 / 105).

 

 

§504

[But given that the properties of inorganic materials are precisely conducive to life, we might wonder if in fact the inorganic is not designed according to plan as well.]

 

[Uexküll’s next point I think is that there is still reason to wonder if the inorganic world is governed by plan. He exemplifies this with the idea that were the physical properties of water slightly different, life may not be able to survive. I am not sure I get the reasoning, because I would think that one could argue were the properties of water different, life would have evolved differently to adapt to it. Let me quote.]

There are a number of facts that can be used in support of this view. It is certainly no proof of the lack of plan in Nature that water is heaviest at 4° C., for this prevents the inland lakes from being frozen up, and so animal life is preserved. Neither does the formation of snow-flakes suggest that there is no plan [Planlosigkeit], for if in winter the water poured down on | us in the form of icicles like so many winged arrows, the life of every creature would be imperilled.

(85 / 105-106, bracketed insertion mine)

 

 

§505

[For now, however, it will prove more fruitful to develop the argument that the organic world conforms to plan.]

 

[I think his next point is that we will not try to argue for the plannedness of the inorganic world, because it will prove more fruitful to continue developing the argument that the organic world conforms to plan.]

For the moment, however, it is not advisable to lead the attack in this direction, for the defence offers us more important strategic positions.

(85 / 106)

 

 

§506

[Even physicists acknowledge that human artifacts conform to plan, because they are designed, created, and used with a sense of how they fit within a system of practical uses, and thus they have particular features that give them their place in that system.]

 

Even physicists acknowledge that human products and tools have a design and thus conform to plan. The reasoning for this is that had we no knowledge of plan for them, we would be unable to create them or to use them. [So here plan is understood as fitting within a system of practical operations. Things are designed so that they fit within that system, and they are used in such a way that they appropriately serve those practical purposes.]

The design expressed in our human products and tools [Planmäßigkeit unserer menschlichen Erzeugnisse und Gebrauchsdinge] is incontestable, and it is not denied even by the physicists that these are invariably to be reckoned as implements [Gegenständen], for without knowledge of plan [Planmäßigkeit] in them we could neither create nor use them.

(86 / 106, bracketed insertions mine)

 

 

§507

[An African native, upon first seeing a ladder, initially only saw a mere object with its own particular structure. Only after learning how to use it did he realize that it had a meaningful structure that related to its functionality.]

 

Uexküll illustrates with an experience he had with a young African native who lived in the interior of Africa but traveled with Uexküll to the coast. The native was unable to climb small ladders, because he did not know what the object was [presumably never having need of one nor having coincidental experience of one before.] But the native of course saw the object and its given structure, namely, an arrangement of planks such that there are large holes set throughout it. But after he learned how to use it, he did so expertly. [The object then made a transition from a mere object without a plan to one with a plan.]

An instance that I experienced myself brought the truth of this assertion home to me with peculiar force. A clever young negro, whom I took with me as my “boy” from the interior of Africa to the coast, was unable to climb up a short ladder placed before him, because he did not know what sort of a thing it was. “I see nothing but planks and holes,” he said. After someone else had demonstrated ladder-climbing to him, he could at once imitate him, for he was a superb climber. The ladder was not shrouded in mist; it stood right there in front of him; he could see it and touch it; and yet for him it was not an implement [Gegenstand], but an object without plan [planloses Objekt], of which he could make no use.

(86 / 106, bracketed insertions mine)

 

 

§508

[Since the functionality is what determines the meaningful relation between parts and whole in an implement, we can speak of its functionality instead of its plan.]

 

The example shows us that the rule of action governing the ladder’s use is what converts it in our minds from a “confused medley of sticks and holes” into a ladder. Thus it is the thing’s function which tells us the meaningful arrangement of the parts into its whole. Without knowing the function, we cannot recognize the thing’s design. This means that instead of referring to the implement’s plan, we can also speak of its “functionality”.

From this example, we recognise what it is that binds the parts into a whole. The fixed rule of the action of climbing at once brought order into the confused medley of sticks and holes, and formed the ladder. It is only the knowledge of the rule of action pertaining to its “function” [“Funktion”] that arranges the parts into the whole. If we do not know the function, which establishes fixed relations, we cannot know the design [Planmäßigkeit], and we do not recognise the significance of the implement [Bedeutung des Gegenstandes]. Accordingly, instead of the plan [Planmäßigkeit] expressed by an implement [Gegenstandes], we may speak of its “functionality” [“Funktionsmäßigkeit”].

(86 / 106, bracketed insertions mine)

 

 

§509

[The fact that we recognize implements on the basis of their use is reflected in the fact that the name for many tools indicates their use (saw, hammer, etc.).]

 

[Uexküll’s next point seems to be that we often name tools in accordance with their use (rather than their other properties). We might think of our own examples, like ‘hammer’, ‘drill’, ‘saw’, ‘rake’, and so on. This reinforces his point that we recognize an implement on the basis of its use.]

On closer consideration, it will be clear to everyone that by the word with which, for our mutual understanding, we | describe the implement [Gegenstand], we make allusion to its “functionality” [“Funktionsmäßigkeit”]. A bench [Stuhl], for instance, may be called a “settle” [Sitzgelegenheit]; and in the word “steps” [Steige] for “stairs” [Treppe] the function [Funktion] is clearly expressed.

(86 / 106-107, bracketed insertions mine)

 

 

 

§510

[Children often refer to objects simply by the uses they have, and thus they live in a world of implements.]

 

Children often refer to objects simply by the uses they have or the activities the objects partake in. Only adults strip the function from objects and think of them as a sum of properties and capacities. Thus “the child’s world [Welt] is still entirely built up of implements [Gegenständen], and that the object [Objekt] is a creation only of later reflection” (86 / 107, bracketed insertions mine)

 

 

 

§511

[The importance of relating properties to functions in all things is seen especially in cases where an implement is invented or when a mere object is converted into an implement.]

 

[Perhaps an important idea here is that the child refers to many natural things (and not just human artifacts), like the clouds and stones, in terms of their function or activity. He then concludes that it is fundamentally important to consider the relation between a thing’s properties to its functions. I am not sure why, however, because it was not yet explained why the child’s approach is better. In other words, while it is obvious why an implement should be explained in terms of how its properties serve its functions, why is it best to do this with all things? His next point is that the best examples for this sort of description are with new implements or with the conversion of an object into an implement. Here, in order to understand how the object becomes an implement, we of course should understand which properties are responsible for its use and how those properties contribute to that use.]

Accordingly, for the understanding of all things [Dinge], it is of fundamental importance to take exact account of the relations of properties to functions [Funktion]. The most instructive examples in this direction are those in which a new implement [Gegenstand] arises, or an object [Objekt] is transformed into an implement [Gegenstand].

(87 / 107, bracketed insertions mine)

 

 

§512

[A boy selecting stones for skipping does so on the basis only of those properties that have bearing on their skippability, and taking no heed of their other “inessential” properties.]

 

Uexküll then uses an example to show that the only properties of a thing that are considered for its classification are the ones that lend to the use we have for it. In this case, a boy selects stones for skipping over water not on the basis of their smell, color, taste, etc., which have no bearing on how they skip over water (and thus they are considered “inessential”). Rather, he selects them on the basis of their being hard, flat, circular, and having a certain weight, all of which do determine their suitability for skipping. This also means that when we refer to the “nature” of an implement, we really mean its function.

When a boy collects “skipping-stones,” which he wants to send dancing across the surface of a lake, there arises out of the general implement [Gegenstand] “stone” (whose function [Funktion] in general is to be thrown) a particular implement [Gegenstand], the properties of which group themselves round the special function [Funktion] of “skipping.” The skipping-stone is hard, flat, circular and of a certain weight. These are the properties required for this special function [Funktion]; the other properties it possesses, over and above these, — such as colour, smell, taste and resonance, — are “inessential” [“unwesentlich”], and are not determined by the function [Funktion]. It follows from this that, by the much misused word “nature” [“Wesen”] of an implement [Gegenstandes], we always mean its function [Funktion].

(87 / 107, bracketed insertions mine)

 

 

 

§513

[“Leading” properties (leitenden Eigenschaften) are those essential ones that lend to the functioning, while those that simply express the (inessential) properties of the implement’s constituent materials are “accompanying” properties (begleitenden Eigenschaften).]

 

Uexküll will now introduce some terminology based on this distinction he has made between properties based on functions. Those properties that lend to the function of the thing are called “leading” properties. Those that do not contribute to the functioning but rather simply express the material of the implement are called “accompanying” properties.

I shall call leading [leitenden] properties those which are necessary and “essential” [“wesentlichen”]; those others which depend only on the character of the substance [Natur des Stoffes], I shall call accompanying [begleitenden] properties.

(87 / 107, bracketed insertions mine)

 

 

§514

[Some implements have more than one function and in themselves are mere objects.]

 

Uexküll notes that in all languages, there are words that have more than one meaning, depending on the context in which they are used. Likewise, certain things have more than one function. Thus, they have no fixed function, and understood simply by themselves, are not implements but mere objects (87 / 108).

 

 

§515

[For example, a concave piece of glass is a mere object. But when placed in a window frame it becomes an implement, namely, a window pane; and when it is placed on a table, it becomes a different implement, a saucer.]

 

Uexküll then gives an example of an implement with two uses, which understood on its own, is simply an object. He has us consider the mere object, which is a “circular, concave piece of glass”. Were he to set it into a window frame, it would become the implement, a window pane. Were he instead to place it on a table and fill it with water, it becomes the implement, a saucer.

So long as I hold in my hand a circular, concave piece of glass, it is merely an object [Objekt]. If I set it in a window-frame, it becomes a window-pane; if I put it on the table, it becomes a saucer, which I can fill with water. In both cases, the object [Objekt] has become an implement [Gegenstand].

(87 / 108, bracketed insertions mine)

 

 

§516

[When function changes, so too do the leading and accompanying properties change. The transparency and concavity of the glass have inverted statuses for the two uses.]

 

We can see then that with changes of function, there are changes in leading and accompanying properties [as often a different function would call for different properties lending to that function.] So when the concave piece of glass is used as a window-pane, it is its transparency that serves as the leading function, and its concavity is the accompanying property. However, as a saucer, the concavity is the leading property while the transparency is accompanying.

It must be borne in mind that the leading and accompanying properties change with the change of function. In the case of the window-pane, the transparency is the leading property, and the concavity the accompanying. In the case of the saucer, the reverse is true — the concavity is the chief property and transparency is the accompanying. Function acts like a magnet, which attracts towards it now some qualities and now others.

(87 / 108)

 

 

§517

[Accompanying properties can also serve a subsidiary function, like how the transparency of a drinking glass does not serve its main function of holding liquids but rather does serve the subsidiary function of revealing the contents.]

 

[Uexküll then introduces a notion of subsidiary function. The idea seems to be that leading properties always serve the main function of the implement, but accompanying properties may serve other functions related to the main function. In his example, the transparency of a drinking glass does not serve its function of holding the drink inside, but it can serve the function of indicating the contents, which the transparency makes visible.]

Now it appears that the accompanying properties are frequently used by subsidiary functions [Nebenfunktionen], and so enter with them into a framework of the implement [Gefüge des Gegenstandes]. Thus transparency becomes a subsidiary function [Nebenfunktion] of drinking-vessels, the contents of which we wish to test by the eye. In the same way, concavity becomes the subsidiary function [Nebenfunktionen] of certain window-panes, which by reflections on the convex side ward off the gaze of the inquisitive.

(87-88 / 108, bracketed insertions mine)

 

 

§518

[An implement’s subsidiary functions can easily convert into main functions when it is used in a different way.]

 

[I do not quite grasp the next point so well. He gives us an example of where subsidiary functions transform into main functions. We think of a “portable engine” transforming into a locomotive. I am not sure what the subsidiary function of the portable engine is. I can only think of its main function, to provide mechanical motion, and I would think that remains its main function when operating in a locomotive. Perhaps its portability begins as its main function and its ability to produce motion is subsidiary, but when used in a locomotive, its portability becomes subsidiary and its ability to produce motion becomes its main function. I will quote so you can see for yourself.]

The transformation of such subsidiary functions [Nebenfunktion] into main functions [Hauptfunktion] may easily take place under our very eyes; | as an example, we have only to consider how a portable engine [Lokomobile] becomes transformed into a locomotive [Lokomotive].

(88 / 108-109, bracketed insertions mine)

 

 

 

§519

[The properties that do not serve either the main or subsidiary functions can be changed without damaging the implement, and they are often simply properties of the materials making up the implement.]

 

[Uexküll’s next point seems to be the following. An implement has both a main function and subsidiary functions. The properties of the thing can be said to serve either function. But there are still some properties which serve neither function. We can alter them without damaging the implement (because the implement is defined by its function, and switching them will not change its function. We might think for example of the skipping stones. If we changed their taste, it would not make them any less of a skipping stone.) These fully inessential properties belong only to the material making it up. So were we to destroy the implement (such that its constituent material remains but it no longer serves its function), then we will still have these fully inessential properties. (If we break the skipping stone into powder, it is no longer a skipping stone. But it will still have the same odor presumably.)]

The great majority of our tools [Gebrauchsgegenstände], machines [Maschinen] and apparatus [Apparate], show the following structure:— there is a “main function” [“Hauptfunktion”], to which a greater or less number of “subsidiary functions” [“Nebenfunktionen”] are attached. However fully the framework [Gefüges] be analysed, there is always some residue of accompanying properties [begleitende Eigenschaften] that do not enter into it [Gefüge], but can be interchanged without damage to the implement [Gegenstand]. For the most part, they belong to an implement [Gegenstand] that has been destroyed in order to form a new one, or to the substance [Stoff] from which the implement [Gegenstand] was made.

(88 / 109, bracketed insertions mine)

 

 

§520

[Inessential properties belong to the implement’s constituent material but not to the defining structural elements of the implement itself. For example, boats made of wood exhibit properties of the trees they are made from, but some of these tree properties are not essential to the boat (as defined by its function), like the trees’ color and smell.]

 

For example, boats made of wood exhibit properties of the trees from which the boards were derived, but these tree properties are inessential to the boat. [I am not sure which properties of the tree these could be, other than for example the smell and color of the wood perhaps. I am also not sure what he means by “do not belong unconditionally to the framework” in the passages: “all those of our implements [Gegenstände] which are prepared from metals or other substances [Stoffen] are laden with properties which do not belong unconditionally to the framework of the implement [Gefüge des Gegenstandes], but are conditioned by the structure of the substance [Struktur des Stoffes] alone.” Maybe the idea is simply that such properties are to be explained on the basis of the structure of their constituent matter but not additionally as being part of the functional composition of the implement itself. That is a guess, so please consult the quotation:]

A boat, for instance, always shows certain properties of the tree from which the boards were procured, properties which are inessential [unwesentlich] to the boat as such. In like manner, all those of our implements [Gegenstände] which are prepared from metals or other substances [Stoffen] are laden with properties which do not belong unconditionally to the framework of the implement [Gefüge des Gegenstandes], but are conditioned by the structure of the substance [Struktur des Stoffes] alone.

(88 / 109, bracketed insertions mine)

 

 

§521

[Thus all implements posses properties that are extraneous to its functionality.]

 

Thus “To all our implements [Gegenständen] something extraneous is attached, pertaining to the material [Material] only, and not entering into the framework [Gefüge] of the functions [Funktionen] and subsidiary functions [Nebenfunktionen]” (88 / 109, bracketed insertions mine).

 

 

§522

[An implement has both a main function, often produced through many smaller component mechanisms, and subsidiary functions.]

 

[Uexküll then describes the way functionality is expressed in the implement’s framework. An implement has a main function, which is often derived through the participation of many component functions, like in complex machines, and it also has subsidiary functions. He uses the example of an automobile to illustrate. The main function is constituted by all the internal mechanisms that give the car its primary functionality. It also has subsidiary functions which are expressed in the “body” of the car. But I am not sure what is meant by that. Is he referring to extra things like the comfort from the upholstery, or does he mean other mechanisms like windshield wipers which actually aid the main function of driving? Or does he mean something like the car could operate without the outer body, but it is included to improve the overall functioning and usefulness of the car? Let me quote so you can see:]

The framework [Gefüge] itself displays everywhere the same principle, i.e. a main function [Hauptfunktion], achieved often through the agency of a multitude of part-functions [Teilfunktionen] (one has only to think of how many functions [Funktionen] must be exercised before an automobile gets going), and a large number of subsidiary functions [Nebenfunktionen] (which are expressed in the “body” of the car).

(88 / 109, bracketed insertions mine)

 

 

§523

[Implements only have these two sorts of properties (material and functional), but living creatures have properties that cannot be explained in these terms.]

 

Uexküll’s final point is that there two sorts of properties, those of the material and those serving the functionality, are the only two sorts of properties an implement has. [He then seems to suggest that living creatures, however, do have properties that cannot be explained either as belonging to their material or to their functionality. (This is something he will discuss more in the next section).]

In all cases, the properties of an implement [Gegenstandes] can be analysed into the properties of the material [Materials] and those of the functional framework [funktionellen Gefüges], without anything being left over. There is never anything unexplainable attaching to our implements [Gegenständen], such as makes the study of the living organism at once so difficult and so fascinating.

(88 / 109, bracketed insertions mine)

 

 

 

 

 

Works cited (in this order):

 

Uexküll, Jakob von. 1928. Theoretische Biologie, 2. gänzlich neu bearbeitete Auflage. Berlin: Springer.

 

Uexküll, Jakob von. 1926. Theoretical Biology. Translated by Doris Livingston MacKinnon. London: Kegan Paul, Trench, Trubner & Co. / New York: Harcourt, Brace & Company. PDF available at:

http://www.archive.org/details/theoreticalbiolo00uexk

 

 

.

10 Aug 2016

Priest (1.2) One. ‘Frege and the Unity of the Proposition,’ summary


by Corry Shores

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Summary of


Graham Priest


One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness


Part 1: Unity


Ch.1: Gluons and their Wicked Ways


1.2 Frege and the Unity of the Proposition



Brief summary:

Frege’s theory of meaning on the one hand accounts for the unity of a proposition while on the other hand makes it impossible for there to be such unity when making statements about concepts and their important structures. A concept has the same structure as a function. This means there are two elements involved. {1} There is an unsaturated function part, in which there is a ‘gap’ or variable where the argument can go. And when a specific argument is put in that open place, then the concept has {2} an object. For example, ‘is unsaturated’ is a concept, and it has a gap (at the beginning) where we could place one or another  particular concept (which is something that structurally speaking is unsaturated) so that it takes ‘is unsaturated’ as its predicate. However, this structure does not allow such an expression about concepts to be made, despite the fact that the theory requires we do so and also despite the fact that our intuition tells us we should be able to do so. Were we to use a name for concepts, like ‘a concept is unsaturated’, then we have a false sentence. For, the name ‘a concept’ is not unsaturated, because it itself, as the name taking that predicate, is an object and not a concept. It is in this way that Frege has a problem of unity with regard to his notions of concept and proposition.




Summary


Priest notes that in philosophy, it is not always obvious if the problems we choose to deal with are really profound of if they are merely silly (Priest 5). He then says that one way we can determine that a problem is the profound kind is by seeing “how some important philosophical projects have run aground on the matter” (6). Priest will look at one such case, namely, Frege’s view on meaning and, in particular his account of the unity of the proposition” (6).


[Priest will have us consider the sentence ‘Sortes homo est’. I am not familiar with this formulation, but I would think it is the classic logic sentence, ‘Socrates is a man’ or ‘Socrates is mortal’. At this webpage it is stated that ‘Sortes’ was a contracted form of ‘Socrates’, as used in Medieval logic. Now let us recall from “On Sense and Reference” Frege’s notions of sense and reference. Here we learned that both names (signs, terms, etc.) and whole sentences can have both reference and sense: {a} the reference of a sign is the specific object(s) it designates; {b} the sense of a sign is its mode of presentation (the contextual elements of how it is to be grasped. The same object can be cognized using different cognizable contents); {c} the reference of a sentence is its truth value; and, {d} the sense of a sentence is its thought (that which is cognized when it is conceptualized, usually taking the structure of predication). The thought or sense of ‘Sortes homo est’, when articulated as a proposition, is that Socrates is a person. Now recall from “Function and Concept” how Frege distinguished two parts of a function (and a predicate proposition can be understood as a function). A function can be understood as having a variable part and a non-variable part. So he has us consider a function that when its variable part is assigned values gives us:

‘2∙13 + 1,’
‘2∙23 + 2,’
‘2∙43 + 4,’

These stand for the values 3, 18, and 132, respectively. As we can see, there is a part that varies consistently. We can think of these and all the other possible variations of the above form as being a structure with a gap in it, and that gap is filled by specific arguments.

‘2∙(   )3 +(   )’

We can also think of those gaps as letter variables.

‘2∙x3 + x

(See Frege, “Function and Concept”, pp.21-24)

When the argument is not specified, and there is a variable or ‘gap’ placeholder of some kind, then it is unsaturated, in Frege’s terminology. But when the specific argument is supplied into the structure, then the function is saturated. It might not be obvious then how Frege’s notion of function applies to predications like ‘Socrates is a human’. It works like the following. In this example, the unsaturated function is the predicate “... is a human”. The argument place then can take any name, but depending on which name, the whole sentence will be true or false. So when it is a name of an animal, for example, then the sentence is false. Priest will divide the sentence into two parts, namely, the noun-phrase ‘Sortes’ (s) and the verb phrase ‘homo est’ (h). Frege does not give a name for the senses for each part of the function, so Priest supplies them as ‘object-senses’ and ‘concept-senses’. Priest’s philosophical concern is that on the one hand, there is a real structural unity to the proposition, perhaps because it constitutes a singular thought, but I am not sure. However, despite that unity, Frege insists that there is a fundamental internal difference. (In fact, recall that Frege even says that the argument “does not belong with the function, but goes together with the function to make up a complete whole; for the function by itself must be called incomplete, in need of supplementation, or ‘unsaturated’ ” (Frege, “Function and Concept”, p.24).  As Priest explains, for Frege, the radical difference between concepts (and concept-senses) and objects (and object senses) is that concepts (and concept senses) are unsaturated, meaning that they are radically incomplete. However objects (and object senses) do not have such a gap in them. Priest then raises a problem. We are saying that ‘homo est’, as a concept, has a gap in it, because it is unsaturated. This means more specifically that its sense has a gap in it. (We might for example try to conceive this concept ‘... is a human’. It in a way has conceptual content, but something is missing from that concept, namely, that which is being said to be human.) Now I am not sure I have Priest’s point right here, but he seems to be saying that the problem is that since ‘homo est’ has a sense with a gap in it, we can make the following formulation: The sense of ‘homo est’ has a “gap” in it.  And this is problematic, because on the one hand we are saying that the sense of ‘homo est’ is unsaturated, but the noun-phrase ‘the sense of “homo est” ’ is an object (which would seem to be nothing other than the sense of ‘homo est’), which means it is saturated (that it does not have a gap). So it would seem that ‘the sense of “homo est”’ has a sense which is both an unsaturated sense and a saturated sense. But Frege makes it clear that an expression cannot be both a concept and an object. Let me quote as I did not render his insight well enough.]

Consider the sentence ‘Sortes homo est’. The sentence is constituted by a noun-phrase, ‘Sortes’, and a verb phrase, ‘homo est’. According to Frege, the sentence has a sense. This is the proposition (thought) that it expresses: that Socrates is a person. The proposition is composed out of the senses of its two components, the sense of ‘Sortes’ (s), and the sense of ‘Homo est’ (h). But the proposition is not a plurality, a congeries of its two parts, s and h. Somehow these cooperate to form a unity. How?


For Frege, names (including definite descriptions) refer to objects, and predicates refer to concepts. He has no special names for the senses of the two grammatical categories, so let us just call them object-senses and concept-senses. Frege’s answer was that concepts and concept-senses are radically different from objects and object-senses. Unlike objects and object-senses, they are “unsaturated”, radically incomplete. The sense of ‘homo est’ has a “gap” in it, which is plugged by the sense of ‘Sortes’ to produce a single thing. Note the form of words here:

(*) The sense of ‘homo est’ has a “gap” in it.

The notions of being unsaturated, of having a gap, and so on, are of course metaphorical. This is not in itself a problem: literal explanation may well give out somewhere. What is a problem is that concept-senses are supposed to be unsaturated. But, the expression ‘the sense of “homo est” ’ is a noun phrase, and so refers to an object(-sense); and these, according to Frege, are not unsaturated.

(Priest 6)


[Priest will explain that Frege’s solution is to emphasize that the sense of ‘homo est’ is saturated. Priest further develops his critical examination of this problem in Frege in Priest’s Beyond the Limits of Thought, section 12.1 and section 12.2. The point Priest makes there is that in order for Frege to express his theory of meaning, he needs this notion of the concept having this form of the function where there is an open place for an argument to be placed. This allows for predicates to take objects, which is the main way of expressing propositional sense. And, since the concept (which is defined by this open structure) is something we need to describe and characterize in this theory of meaning, we need to predicate the notion of concept. However, that very same conceptual structure which is essential to what it is as a meaning-expressing entity is also what prevents it from expressing any meaning about concepts themselves. For, there is no way to predicate a concept (as nothing but a concept) by means of another concept. Priest mentioned a variety of ways to try to do so, and none of them are ultimately successful. The first is to use a name for the concept and put it in the argument place of a predicate that says something about concepts. This is what we saw happening above with the example. So we might say, “‘A concept’ is unsaturated”. But here, the expression for concept is an object, and thus is saturated, and therefore the expression is false. For, the predicate does not hold for the object that it predicates. But we need this expression of the unsaturatedness of the concept to be true. Another strategy is to articulate the expression of the concept in such a way that it maintains its unsaturated form. So we might write: ‘Is a concept is unsaturated’. This could be deemed true. However, it does not seem to make much literal sense. It would make more sense if we put quotes around the expression in the argument place, as “‘Is a concept’ is unsaturated”. But then we have the same problem as with the first proposed solution, where the sentence becomes false. ‘Is a concept’, when it takes that position in the sentence, is saturated, and thus the sentence is false. The third main solution Priest explored was to use higher-order quantification. This approach involves us using a variable in place of the concept that we want to predicate. This way it might somehow serve both as a predicate (in that it could be filled-in secondarily by other predicates) and as an object (as it takes the argument place of another predicate) in certain sorts of formulations. But this strategy fails for a number of reasons. The main problem is that in order to say what we have in mind, we need the concept and the other concept it falls under (is predicated by) to both be of the same order, so by making one at a higher order, we have not resolved the issue. I return now to the present Priest text. Here Priest refers to the defense of his theory that Frege gives in On Concept and Object, where he deals with an example involving the concept horse. Here Frege was dealing with an objection (by someone named Kerry) that had been leveled against Frege’s notion of concept. Kerry argues (contrary to Frege) that there is not an absolute distinction between the content of the concept and concept-object, for, an expression can be dually both a concept and a concept-object. Frege clarifies that the concept belongs to the predicate of a sentence and the concept-object to the subject of the sentence. On this matter, Frege wrote:

There are, indeed, cases that seem to support his view. I myself have indicated (in Grundlagen, §53, ad fin.) that a concept may fall under a higher concept – which, however, must not be confused with one concept’s being subordinate to another. Kerry does not appeal to this; instead, he gives the following example: ‘the concept “horse” is a concept easily attained,’ and thinks that the concept ‘horse’ is an object, in fact one of the objects that fall under the concept ‘concept easily attained.’ Quite so; the three words ‘the concept “horse” ’ do designate an object, but on that very account they do not designate a concept, as I am using the word. This is in full accord with the criterion I gave – that the singular definite article always indicates an object, whereas the indefinite article accompanies a concept-word.

(Frege, On Concept and Object, 45)

Priest will quote the passage where Frege asks the reader just to understand what he really means, even though his theory does not allow him to say it properly. Priest says that this does not resolve the issue of the proposition supposedly being something unified but in cases of predicating concepts it cannot be unified.]

Frege was well aware of the matter. His solution was simply to reiterate the claim that the sense of ‘homo est’ is indeed saturated. But he was aware that this put him in a difficult situation. He says in the infamous concept horse passage:2 |

I admit that there is a quite peculiar obstacle in the way of an understanding with my reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thoughts; I mention an object when what I intend is a concept[-sense]. I fully realize that in such cases I was relying on the reader who would be ready to meet me half-way—who does not begrudge me a pinch of salt.

But Frege underestimated (or understates) the problem. If he is right in his insistence that the description refers to an object, this undercuts his whole explanation of the unity of the proposition. Merely reflect for a moment on (*). This is now simply false. We seem forced into the view that concept-senses are objects, even though they cannot be.

[Footnote 2 (quoting): Geach and Black (1952), p. 54. Frege actually addresses the matter for reference (bedeutung) rather than sense (sinn). However, he takes matters to be similar for sense. For our purposes, they are not. Frege takes a concept to be a function which applies to an object to form a truth value. Now, whatever a truth value is, the object is not part of it. (In the same way, the referent of ‘John’ is not a part of the referent of ‘the father of John’.) Of course, there is a very good question about how one is to understand the relationship between an object and a concept (property) which applies to it. This is the question of how to understand instantiation; we will come to it in due course. Note that if Frege had taken the referent of a sentence, more naturally, to be a state of affairs (either existent or nonexistent), of which the object and the concept are a part, the situation concerning reference would be exactly the same.]

(Priest 6-7)



And since concepts have the form of functions, the same problem arises in the context of functions. [Priest first notes that in Fregean semantics, both the senses and the referents of predicates are functions. I am not exactly sure I know what is meant. Suppose we have an unsaturated predicate. Its sense I guess is the thought involved in the concept expressed in that predicate. So the sense of ‘is a horse’ might be something like the notion of horseness, or something like that. The reference I would think is the set of all things that would make the predicate true. But I am not sure. Perhaps we can think of there being a function that assigns to the predicate the sense that belongs to it and also a function that assigns to the predicate its reference, being the set of items in its extensions. Now suppose instead we are speaking of a saturated predicate, like “Phar Lap is a horse.” Here the sense is the thought of Phar Lap being a horse, or having horseness, and the reference is the truth value. We can again perhaps think of there being a function that assigns to the sentence its sense and reference. At any rate, Priest has us consider the unsaturated predicate ‘the father of’. It refers to a function that “maps each person to their father (and each non-person to something else), and has a corresponding sense”. I do not know what is meant by “and each non-person to something else”. Does he mean simply each animal is assigned its male parent? Or does he mean that things which do not have fathers are assigned something else altogether? But I would not know what. Or would things without obvious fathers be assigned something like whatever is responsible for how they came about? At any rate, the sense of this function has a sense that Priest calls the ‘function-sense’. He gives the example, ‘the father of Frege’. This refers to a singular person, Frege’s father. He says further that its sense is an object-sense, a unitary thing. As I understand, here the function sense is the object, Frege’s dad. Then Priest explains the problem here, but I do not follow it very well. He says that the reason ‘the father of Frege’ has the sense of Frege’s dad is because there was a gap in ‘father of (x)’, and since ‘Frege’ filled that gap, it received the sense of Frege’s dad. (Something that I find a little confusing here is that if Frege’s dad is the sense of the function ‘father of Frege’, then what is the reference? I would think that the reference is Frege’s dad, and the sense is something more conceptual, or is something like Frege’s idea of the mode of presentation of Frege’s dad. For, Frege’s dad could have been presented as the husband of Frege’s mother, for example.) The part that I do not follow is the next sentence which says that ‘the father of’ is according to Frege’s criterion an object(-sense). I do not know what criterion would make it an object. Let me quote.]

It is not just the unity of propositions which generates this situation for Frege. In Fregean semantics, both the senses and referents of predicates are functions, and the same problem arises for normal cases of functional application. Thus, for Frege, ‘the father of ’ refers to the function that maps each person to their father (and each non-person to something else), and has a corresponding sense. Call this a function-sense. So ‘the father of Frege’ refers to Herr Frege sr., and its sense is an object-sense — a unitary thing. It has this because the sense of ‘Frege’ fills the gap in the sense of ‘father of ’. But the sense of ‘father of ’, according to Frege’s criterion, is an object(-sense), and so it does not have a gap at all. The situation is exactly the same.

(Priest 7)


[Priest then summarizes the problem. It is cast in a light that is a shade different from Beyond the Limits of  Thought. There the problem was more a matter of expressibility, but here it seems more to be an issue of unity. To explain the unity of the proposition, Frege has the structure of the concept-senses, by which a predicate is completed by some function. As such, concept-senses cannot be objects. For, objects are completed or closed structures, but concepts are open or incompleted ones, as they can take one or another or no particular argument. However, as we have seen, concept-senses are objects (since we need to place them into the argument place, and our intuition tells us we should be able to predicate them). Priest says that this is not merely a problem with meaning but rather is a deeper issue regarding how “parts cooperate to form a unity of any kind”. Priest in the following section will go into this problem in more detail.]

Frege’s problem, then, is this. If concept-senses and function-senses are to play their role in accounting for the unity of complexes, they cannot be objects. But they are. One might avoid Frege’s problem simply by rejecting his account of meaning. The situation in which Frege finds himself is, however, but an example of a much deeper problem which cannot be avoided in this way. At root, the problem is not about meaning at all. It is about how parts cooperate to form a unity of any kind. Let me spell this out.

(7)



From:


Priest, Graham. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University, 2014.


Or if otherwise noted:

Frege, Gottlob. “On Sense and Reference”. Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Oxford: Basil Blackwell, 1960, second edition (1952 first edition), pp.56-78.


Frege, Gottlob. “Function and Concept.” Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. pp. 21–41. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).


.

9 Aug 2016

Priest (12.2) Beyond the Limits of Thought, “The Concept Horse”, summary

 

by Corry Shores

 

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[The following is summary. Boldface and bracketed commentary are my own. You will probably encounter typos and other distracting errors, because proofreading is incomplete. I apologize in advance.]

 

 

 

 

Graham Priest

 

Beyond the Limits of Thought

 

Part 4 Language and Its Limits

 

Ch.12 The Unity of Thought

 

12.2 The Concept Horse

 

 

 

Brief summary:

Frege’s theory of meaning is based in part on concepts being structured like functions, where there is a concept part (the predicate) and an argument part (what is being predicated). The argument part is structurally distinct from the concept part. The concept itself has a gap that is either filled or not filled by some argument. This creates a problem for Frege, because this basic structure for concepts prevents him from saying anything meaningful about concepts. There are two basic attempts one can make using this structure in order to say something about concepts, and both attempts fail. The first attempt uses a name for the concept, as in, “‘The concept horse’ is a concept.” Here the concept is “...is a concept”. It can take one or another argument, in this case, it takes the argument ‘the concept horse’ which is a name referring to that concept itself (which would have to have the function structure that all concepts share). This strategy fails, because the predicate “... is a concept” would only be true if it is predicated to a concept. But in this case, it is predicated to a name, and since names are not concepts, “‘the concept horse’ is a concept” would be false under Frege’s theory, even though we intended it to be true. And in fact, similar sorts of expressions would need to be true in order to actually describe the properties of concepts as they are under this theory. The other attempt is to keep the function structure by placing a predicate in the argument place. This would give us “is a horse is a concept”, which is nonsensical, because we cannot conceptualize how ‘is a horse’ can fit be the subject of such a sentence (and it does not work to put quotes around it as in ‘is a horse’ is a concept”, because then it is a name and not a concept).  Michael Dummett proposed as a solution that we use second-order quantification, which will allow us to use a variable in place of a concept. This way it might somehow serve both as a predicate and as an object in certain sorts of formulations. But this strategy fails for a number of reasons. The main problem is that in order to say what we have in mind, we need the concept and the other concept it falls under (is predicated by) to both be of the same order, so by making one at a higher order, we have not resolved the issue. Thus Frege’s notion of the concept is fundamentally inexpressible within his theory of meaning, which is based on that very same notion of the concept.

 

Summary

 

[Recall some of the important points from the previous section 12.1. We saw that Frege created a way of understanding propositions under the form of a function, where there is the functional part that operates on the argument part. The concept is to be understood as belonging to the function or predicate, and the object is a variable part that can be placed into the argument position of a function or predicate. And we learned that although another concept (another function or predicate) can be found in an argument place, that does not mean for Frege that the same thing can be both a concept and an object. Instead, such a concept in an argument place is to be understood as having its own structure of concept and object. In other words, the distinction is absolute and not relative to its functioning under a certain perspective.]

As is clear, concepts and objects are quite different kinds of thing, and must be so, since concepts perform a quite different kind of function in the composition of thought.

(Priest 199)

 

But, Priest notes, the fact that concepts and objects are very different kinds of things (as “concepts perform a different function in the composition of thought”) leads to a profound problem for Frege. Since a concept is very different from an object, it cannot be named using a noun-phrase like objects can. However, it does appear that we actually can refer to concepts using noun-phrases. Frege insists however that the appearances are deceiving. Whenever we use a noun phrase to name a concept, we are actually thereby not designating a concept.

But this poses a nasty problem for Frege. For since concepts are not objects, they cannot be named, that is, referred to, by a noun-phrase. But it would appear to be clear that we can refer to a concept with a noun phrase; for example, to use Frege’s notorious example (due to Kerry): the | concept horse. Frege is well aware of the problem. His solution to it is to insist, quite consistently, that, despite appearances, such phrases do not refer to concepts. As he puts it (p. 45):

the three words ‘the concept “horse”’ ... designate an object; but on that account they do not designate a concept as I am using that word.

(299-200, bracketed text mine. Here and in following instances, Priest’s parenthetical text citations are for the Geach Frege text, listed at the end of this post.)

 

The problem is not just in trying to explain how the appearances are deceiving. There is another even more profound problem as well that is related to this. [I might not express this idea right. It seems to be the following, but I am not sure. We begin with Frege’s notion that the noun phrase, “the concept horse” is an object and not a concept. Now, we say that an object falls under a concept. So if we have the concept “... has four legs” then we can say that a horse falls under this concept. But if we literally write “falls under”, then we are using falling under as the concept, that is, as the predicate. It seems to me that it is a two-place predicate, where we have as one argument some object in question, and we have as the other argument some concept (predicate) in question. So the concept of the whole structure is ‘falls under’. Let us take as the first argument the famous race horse Phar Lap, as in Priest’s example. And we will say that the second argument is ‘is a horse’. Now, Priest writes, “For example, consider the claim that Phar Lap falls under the concept horse. Falling under is a relationship between an object and a concept. Hence, this statement is false”. I am not certain I follow, but perhaps Priest is saying that Par Lap, the horse, cannot be said to fall under the concept horse, when ‘the concept horse’ is regarded as an object and not as a predicate. So perhaps we might write for this example: “Phar Lap falls under ‘the concept horse’.” This would make it clear that it is false, because the only thing an object can fall under is a concept and not an object like ‘the concept horse’. But I am not sure. (If I am following this right) Priest then acknowledges that we can still express what we really mean to say in that sentence in a way that preserves its truth, namely, we can simply say, “Phar Lap is a horse”. But we cannot find a correct way to say what we mean when we write, “the concept horse was considered by Frege”. I am not sure, but perhaps we should say that this is a false sentence as it is written here, but I am not sure why. Maybe it is because what was considered by Frege was a concept and not an object. I also am not sure why it cannot be written in a correct way. I suppose it is because any effort to do so would involve making the concept be an object. Conceptually speaking, we might think that the concept here is: the concept horse falls under the concept of things considered by Frege. Perhaps the problem is that in order for us to know that we are talking about the concept horse and not some horse itself, we need to specify that it is a concept, but by doing so, we have transformed it into an object. I probably have all of this wrong, so let me quote.]

This raises a more serious problem, however. If ‘the concept horse’ does not refer to a concept, a number of claims about concepts would appear to be problematic. For example, consider the claim that Phar Lap falls under the concept horse. Falling under is a relationship between an object and a concept. Hence, this statement is false. On this and similar occasions, what one would normally want to express by this sentence might be expressed in other ways. For example, one can say simply: Phar Lap is a horse. But on other occasions this is impossible. For example, there is no similar paraphrase of: the concept horse was considered by Frege.

(Priest 200)

 

[Recall the notion of definite descriptions from Priest’s Logic: A Short Introduction, chapter 4 and from Nolt’s Logics section 6.3. Nolt noted that sentences with definite descriptions, like “The present King of France is bald” has a structure that is more complicated than the normal subject-predicate relation. We are saying that there is at least one thing that is the King of France, that it is the only thing that is the king of France, and that thing is bald. Priest might be saying that “the concept horse” is a definite description. But he adds that the use of definite descriptions is not the source of the problem. Rather the problem is with the predicate “is a concept”. I am not sure if Priest is saying that our sentence is something like “ ‘the concept horse’ is a concept”, or if he is saying that the noun-phrase ‘the concept horse’ is to be understood as containing a concept and object. Kerry gave the example sentence, “the concept “horse” is a concept easily attained’” (Frege, “On Concept and Object”, p.45). So maybe Priest is saying that the predicate “is a concept” is found in the grammatical subject of that sentence, and the concept of the whole sentence is “is a concept easily attained”. At any rate, in cases like these, the phrase ‘is a concept’ needs to apply to concepts. However, since it is a predicate, it must apply to objects. The final point I may not follow well. He says that if we join the predicate ‘is a concept’ to a phrase that refers to a concept, we obtain non-sense. Priest gives the example, “is a horse is a concept”. I guess here “is a horse” refers to a concept. His point might be that we have no way to express this idea under Frege’s restrictions. If we formulate the sentence with a noun phrase, then we have a sentence that makes sense, but we are missing the idea, because we have expressed a concept as an object, thereby stripping it of its essential structure or basic mode of self-presentation. However, if we instead try to formulate the sentence by placing in it a grammatical structure that expresses a concept (namely, a predicate structure), then we have expressed the concept correctly, but we have created a non-sense sentence. Let me quote, as I might have this wrong.]

Actually, the problem is not so much with the use of a definite description, as with the predicate ‘is a concept’ itself, which allows us to form the description. To say what it needs to say, it must apply to concepts; yet, like all (first-order) predicates, it must apply to objects; if we join it to a phrase that refers to a concept, nonsense results, for example: is a horse is a concept.

(200)

 

[Priest then notes the problematic ramifications of this situation. Frege’s theory of meaning is based on his notion of a concept. This means that in order to explain his theory, he needs to discuss concepts in a way that is true to what they are, at least as what they are according to the theory. But as we just saw, there is no proper way to do so. Priest then gives some examples it seems of a particular ways that Frege would be unable to express basic ideas of the theory. Suppose that one idea in the theory is that all concept-words denote concepts, or in other words, that “for every concept-word there is a concept that it denotes”. But, as we saw, we here have a predicate, “... is a concept”. Since it is a predicate, it is filled-out by an object and not a concept. Since there are no concepts that can take this predicate, that statement is false. But we needed it to be true. The next example I do not understand. The claim is “that concepts are unsaturated”. For some reason, this will be contradicted. That contradiction arises because “Anything that satisfies ‘is a concept’ is an object, and so saturated.” I think the idea might be the following. Concepts are said to be unsaturated because they can take any number of arguments, and only when one is provided is it saturated. Another way we looked at this is by distinguishing the saturated from the unsaturated parts. The function part is unsaturated, and the argument is the saturated part. Priest might be saying that because some particular concept can take the argument place of ‘... is a concept’, that means that concepts are saturated (as they do the saturating). But we stated at first that they are unsaturated. I am not sure however if that is what Priest is saying. The third example involves Frege’s claim that “a concept is a function whose value is always a truth value”. (Here the important point seems to be about the concept being a function and not about its value). But as we saw, a concept can be an argument, and thus it is not always a function. Priest then ends this paragraph by writing, “To
say what he needs to say, Frege needs a predicate that applies to concepts, and this is just what he cannot have.” I am not certain, but I think he is saying that we need to be able to predicate concepts in such a way that we designate them as being concepts. However, any attempt to do so only at best designates them as being objects of concepts (rather than being concepts in their own right) or in other words as being arguments to functions (and thus not as functions themselves.) Restating: the core notion of Frege’s theory of meaning, namely, the concept-structure, cannot itself be expressed in the theory, because there is no expressive structure allowed in his system that can to do justice to the meaning of a concept (especially with regard to its important structural limitation, namely, that it can never be both a concept and an object).]

The ramifications of this are clear. Frege needs to be able to talk about concepts in order to express his own theory. Yet he cannot do so (meaningfully) by his own theory. For example, consider the claim that all concept-words denote concepts, i.e., for every concept-word there is a concept that it denotes. Whatever satisfies ‘is a concept’ is an object. Hence this is false. Or consider the claim that concepts are unsaturated. Anything that satisfies ‘is a concept’ is an object, and so saturated. One more example, amongst many, from Frege’s own words: he says (p. 30) ‘a concept is a function whose value is always a truth value’. Whatever satisfies ‘is a concept’ is an object, and so not a function. To say what he needs to say, Frege needs a predicate that applies to concepts, and this is just what he cannot have.

(Priest 200)

 

Priest then notes Frege’s admission of this problem.

We see that the effect of Frege’s view is to put much, including his own theory, beyond the limit of the expressible. Frege recognises this, and is obviously embarrassed by it (p. 54):7 |

I admit that there is a quite peculiar obstacle in the way of an understanding with my reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thought: I mention an object when what I intend is a concept. I fully realize that in such cases I was relying on the reader who would be ready to meet me half-way – who does not begrudge a pinch of salt.

But he was not embarrassed enough. It is one thing for mystics, such as, perhaps, Cusanus, to hold views that they also hold to be ineffable; it is quite another for a man of science, such as Frege was.

(Priest 200-201, bracketed text mine)

[Footnote 7: See also the last paragraph on p. 55.]

[Additional quotation, from Frege p.55:

It may make it easier to come to an understanding if the reader compares my work Function [sic] und Begriff. For over the question what it is that is called a function in Analysis, we come up against the same obstacle; and on thorough investigation it will be found that the obstacle is essential, and founded on the nature of our language; that we cannot avoid a certain inappropriateness of linguistic expression; and that there is nothing for it but to realize this and always take it into account. (Frege 55)]

 

Priest then notes one of Frege’s solutions to the problem that he proposed later on. He proposes that instead of merely stating the concept that we place it within a ‘what’ clause. [The idea seems to be that the ‘what’ serves to point us to the conceptual content of the concept, while still using a name for it. Let me quote.]

In a later and, at the time, unpublished, essay (c1892) Frege comes back to the issue and offers a solution to it. He suggests that we may refer to a concept with a ‘what’ clause, as in ‘what “is a horse” stands for’. The point of such clauses is that they can themselves be used predicatively. Consider, for example, the sentence: Frege is what I am, a philosopher-logician. In this way, we can say, for example, Phar Lap is what ‘is a horse’ stands for.

(Priest 201)

 

[The important point here seems to be that the what-clauses are used predicatively, meaning it seems that they themselves are structurally speaking predicates, and they take some object. So in the example “Phar Lap is what ‘is a horse’ stands for,” here the predicate is, “... is what ‘is a horse’ stands for,” and the object is Par Lap. Priest’s next point might be that were it really the case that the what-clause is a predicate, then we still have the same problem we saw before.]

The construction does strain the ear somewhat. But in any case, the trick cannot do the required job. For if a what-clause must be construed predicatively then the claim, for example, ‘what “is a horse” stands for was considered by Frege’ is nonsense. Ditto the claim: ‘what “is a horse” stands for is not an object’, etc. And so we cannot paraphrase away all the things we need to say.

(Priest 201)

 

Priest also notes that this solution does not address the more basic problem with expressing the notion of concept in his system, which is namely that he needs predicates to apply to concepts, but the theory prevents him from doing so. Priest then notes Dummett’s solution. Dummett says that ‘is a concept’ is more of a pseudo-expression, and we should not try to use it. Instead, we should use a second-order predicate, for example, a quantifier phrase, that can be combined with a first order predicate to make a proper sentence. [I do not follow this solution very well. It seems to be the following, but I will be sure to quote for your interpretation. First recall what Nolt said about higher-order logic, in section 14.1 of Logics. Let us begin by considering first-order logic. Here we have quantifiers that range over variables that stand for individuals. But in second-order logic, we can have variables that range over predicates rather than variables. Nolt gave the following example of an argument that can be expressed using second-order predicate variables. In this example, we will have constants for individuals, and the variable X for predicates: “Al is a frog. Beth is a frog. Therefore, Al and Beth have something in common.” Nolt said that we can write this symbolically as: ‘Fa, Fb ⊢ ∃X(Xa & Xb)’. So in this case, we have the predicate, ‘... is a frog’. Then we make the inference that both individuals share one same unspecified predicate, here written in English as ‘share something in common.’ But we can think of that also as being, ‘share some predicate’. This is symbolized with the X, and that variable is ranged over by the existential quantifier. Let us return now to Priest, Frege, and Dummett. Again, I cannot offer an interpretation that I am confident in. But let us try to work through the ideas. Dummett’s proposal seems to be that we first craft a second-order formula that could be understood as meaning that a concept is unsaturated. So in English we would write first, “Everything either is ... or is not ...’, with the ‘...’ being the ‘gap’ for some predicate. It would be written symbolically as: ∀y(Xy∨¬Xy). So it seems already that we have made the predicate be variable. Apparently Dummett suggests that we try then, on the basis of this formula, to construct other formula that can express Frege’s notion of the concept. Priest says that for the notion that every concept is unsaturated, using Dummett’s formulation, we would write, ∀X(∀y(Xy∨¬Xy) → X is unsaturated). The idea here might be that we are saying for any given predicate (i.e., concept), it can be said for every term that it either belongs to that predicate or it does not. So perhaps what is expressed here is maybe something like the following. If we can say that any given predicate (or concept) either predicates some given term or it does not, then we are saying that a term can either be said to saturate it or not. But, this means that on its own, it is not itself saturated. For, its saturation is something that can be under variance, as some supplied argument might hold for it and others not, and possibly many might hold for it. That is probably not right, but I am not sure how else to understand the reasoning behind that formula. Priest says that this formula can be written more simply as ∀X(X is unsaturated). How then might this possibly avoid the problem Frege encountered? Perhaps the idea here is that just by using first-order logic, we cannot predicate a concept and say for example that ‘the concept horse is unsaturated’. However, perhaps we can render the concept into a variable, and quantify over it using a higher-order quantifier. So we might say, ‘any concept is unsaturated.’ Here, what is taking the argument place is a variable for a predicate and not a name for a predicate. Priest then says that “This raises the question of the intelligibility of second-order quantification in the present context”. But I am not sure why, and he sets that matter aside anyway. Maybe it has something to do with the fact that what we say about concepts we would want to apply to concepts on all orders, and maybe further we cannot do so this way. But that cannot be right. At any rate, his point is that “we still have the problem of the predicate ‘is unsaturated’, which is an ordinary first-order predicate; and so this sentence is nonsense”. I am not sure what is meant here. The issue might be that ‘is unsaturated’ is a first-order predicate that can only predicate given specific first-order predicates, and it cannot predicate variables for predicates. And so we cannot, as in our example, say all predicates X are unsaturated. For, “are unsaturated” can only be saturated by a first order specific predicate. I will quote now.]

More importantly, Frege’s suggestion does not address the fundamental problem, which was, as we saw, that he has at his disposal no predicate that applies to concepts. Dummett, in his discussion of the problem ((1973), pp. 211–22) suggests that ‘is a concept’ should be eschewed as a pseudo-expression. We need, instead, an appropriate second- order predicate, i.e., a phrase, like a quantifier phrase, that fits together with an ordinary predicate to make a sentence. His suggestion is ‘Everything either is . . . or is not . . . ’. If we use upper-case variables for concepts, this is ∀y(Xy∨¬Xy). The suggestion will not do the job, however – if the job is to express Frege’s theory. Consider, for example, the claim that every concept is unsaturated. This becomes: ∀X(∀y(Xy∨¬Xy) → X is unsaturated), or more simply ∀X(X is unsaturated). This raises the question of the intelligibility of second-order quantification in the present context. But setting that aside, we still have the problem of the predicate ‘is unsaturated’, which is an ordinary first-order predicate; and so this sentence is nonsense.

(Priest 201, citing Dummett M. (1973), Frege: Philosophy of Language, Duckworth.)

 

Priest then says that we might think that we could ‘rejig’ the predicate [‘is unsaturated’ for example] so to make it a “a suitable second-order predicate” (Priest 201). Priest, however, doubts that this will work. He then says that anyway there will still be other worse problems. He has us consider the “claim that concept-words refer to concepts, i.e., ∀x(x is a concept-word → ∃Y x refers to Y)” (Priest 201). [Here perhaps the formula is simply saying that if something is a concept-word, perhaps like, ‘the concept horse’, then it refers to some concept. He says we have the same problem with the predicate ‘refers to’. Perhaps the problem here is that ‘refers to’ should refer to a first-order predicate but instead in this formulation refers to a second-order one. But I am not sure. He then says that we cannot rejig it, but I do not follow why. The idea might be that ‘refers to’ is something that must apply at least to names and objects they refer to, so in that sense it must at least be a first-order predicate. He then seems to be saying that it cannot also be a second-order predicate. Maybe the reason is that it cannot be both at the same time, and it must at least be first-order, therefore it cannot be second-order. But I am not sure. Priest addresses an objection that seems to be that we must distinguish two sorts of reference relations, namely ones for names and ones for concept-words. Priest then quotes Frege where he seems to be saying that there should be one reference relation for both concept-words and names. Thus this objection does not apply in Frege’s case. Priest also says that if we make this distinction of references, it contradicts Frege’s point that “the reference of a complex linguistic expression is a function of the references of its parts”. I am not exactly sure why, but perhaps the idea is that for the reference of a complex expression to be compositionally based on the reference of its parts, that means the parts, namely, the names, must have the same sort of reference as that of the whole expression, in which perhaps the concept-name would be found. Let me quote, as I am uncertain in my understanding.]

Maybe some way could be found to rejig the predicate as a suitable second-order predicate (though I doubt it). But worse is in store. Consider the claim that concept-words refer to concepts, i.e., ∀x(x is a concept-word → ∃Y x refers to Y). The same problem arises with respect to the predicate ‘refers to’ ; and this time there is certainly no way of | rejigging it, simply because it must be legitimate to say that names refer to objects, and so ‘refers to’ must be a predicate that is first order in both its arguments. If it be retorted that the reference relations for names and concept-words must be distinct, then we cannot say with Frege ((c1892), p. 118):

To every concept-word, or proper name, there corresponds as a rule a sense and a meaning [reference], as I use these words.

or that the reference of a complex linguistic expression is a function of the references of its parts.

(Priest 201-202)

 

Priest then notes other cases where Frege’s claims about meaning are really non-sense, for reasons similar to those above. [In this case, Priest seems to be saying that we cannot make any generalization that holds for both concepts and objects. I am not sure why, but the reasoning might again be that by doing so we are applying the same predicate to both objects and concepts when as we have seen that cannot be done. I am guessing. Priest then notes that since we cannot make a generalization for both concepts and objects, we cannot, as Frege tries to do, even say that they are different. Let me quote.]

In fact, we cannot make any generalisations over objects and concepts, as Frege often does, or even say that objects and concepts are different; for example, ((c1892) p. 120):

From what we have said it follows that objects and concepts are fundamentally different and cannot stand in for one another.

Any attempt to express this which paraphrases ‘is a concept’ as a second-order predicate, results in nonsense.

(202)

 

Priest then wraps up this section by saying that we will fail if we try to solve the problem in Frege’s system either by simply making a minor modification to the system hoping it does not change the main philosophical thinking behind it or by removing some purportedly false and unnecessary part of the system.

We see that the Frege/Dummett repair will not solve Frege's fundamental problem. It might be thought that some minor modification of Frege’s views would dispose of it, whilst leaving their essence intact; or that the problem is generated by some quirky and false Fregean doctrine, which should be disposed of anyway. Neither thought is correct; but let us leave the issue there for the time being and move on to Wittgenstein.

(202)

 

 

 

From:

 

Graham Priest. Beyond the Limits of Thought. Cambridge: Cambridge University, 1995.

 

Priests parenthetical page citations for Frege come from:

 

Gottlob Frege. Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Transl. P.T. Geach. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).

 

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