Summary of the 5th class

The Prototype Theory of Concepts (1)

Last Friday we discussed a few introductory matters concerning the Prototype Theory of Concepts.  This collection of theories called the Prototype Theory (PT) emerged in the ‘70s and was developed to address some of the difficulties in Classical Theory. The most significant problem for the definitional structure of concepts that PT tries to account for is the problem of psychological reality. The main tenets of PT are extrapolated from data gathered from psychological experiments. These data proved to be unaffected when studying concepts as definitions.
Here are the main ideas of PT that we mentioned in class:
- Concepts have a structure that encodes a statistical analysis of the properties their members tend to have. Hence, we can identify central or typical members of a category on the one hand, and less typical or peripheral members on the other hand. Concepts with prototypical structure –> their extensions as being graded: birdier, fruitier.
- The features of a concept are not necessary, as there may be items in the extension of a concept that fail to instantiate a certain property(ies). See the zebra without stripes or the 3-legged albino tiger examples.
- Classical Theory –> concept application must satisfy all of the concept’s features, PT –> must satisfy a sufficient number of features, some of which weigh more than others.
- Family resemblance: formal criteria are neither logical nor psychological necessity; open-ended set of properties; falling under the boundaries of a similarity space.
We didn’t say much about the advantages or the criticisms of PT (we’ll do this during the next meeting), but instead we tried to do an exercise.  We chose SCIENCE from a list of four other concepts, and we suggested a list of characteristic features for this concept’s prototype. Furthermore, we discussed some members of the category and tried to grade them for typicality. This task proved to be quite challenging, as you remember, and we had a hard time trying to grade the members we found. Now, let me suggest a rethinking of the exercise as follows:

	SCIENCE	PHYSICS	MATHEMATICS	MUSIC	LAW
Works with demonstrated data	Yes	yes	Yes	No	No
Is built on theories	Yes	Yes	Yes	Yes	No
Has a rigid structure  (is formalized)	Yes	Yes	Yes	No	Yes
Guides our perception of the world	Yes	Yes	?	?	No
Is innovative	yes	Yes	No	Yes	No
Makes predictions about facts and behaviours	Yes	Yes	No	No	No

re: Rosch’s “Principles of Categorization”

This is a classic text. Here are some things that might help you deal with it:

- first, the paper itself [you have it also in the reader]

- Prof. Rosch’s website

- in case you’re curious about the Borges quote, this will help

- btw, that list made quite an impression; please read page xvi of this book

visual note on Wittgenstein & more

A few pics taken yesterday in Vienna. To understand more, please take a look at this paper.

The house built by Wittgenstein for his sister, Margarete:

Cafe Central [gathering place in the early days of the Vienna Circle]

*** 

Alex had us read a poem by Rilke recently. Here is the German original again from the Rilke portal. And an English translation I found on Wikipedia:

I am so afraid of people’s words.
They describe so distinctly everything:
And this they call dog and that they call house,
here the start and there the end.
I worry about their mockery with words,
they know everything, what will be, what was;
no mountain is still miraculous;
and their house and yard lead right up to God.

I want to warn and object: Let the things be!
I enjoy listening to the sound they are making.
But you always touch: and they hush and stand still.
That’s how you kill.

Translated by Annemarie S. Kidder

Q. 2. Do you see any connection between Wittgenstein’s critique of “the Augustinian picture” and the Prototype Theory?

EDIT [March 24th]:

The content of this post has been removed because it did not answer the question and was likely to create confusion. We hope a better version will be online soon.

ape this!

We’re moving to discussing more on prototypes and the main motivation for this view: categorization. This is a good time, and a proper context, to ask ourselves about the relation between the human and the animal mind. Do animals have concepts? Well, animals can tell predators from prey, can’t they? Some animals keep track of complex social relations – if you’re a newbie it will probably hurt you not to know Fred is the alpha male in this community. So what should we say?

Take a look at:

> Susan Rumbaugh on the bonobos

> the late Alex

> chimps kicking &*% in memory tests

Problems of the Classical Theory and their answer in the Prototype Theory

Q1: Consider the following problems for the Classical Theory: psychological plausibility, ignorance and error and typicality. How does the Prototype Theory answer them?

For a long period of time, the Classical Theory has occupied a central place in theorizing about concepts. The reactions to such a theory were inevitable and took the form of critical remarks which eventually developed into other theories regarding the structure of concepts. These new theories tried to resolve the incoherencies and misunderstandings of the Classical Theory: Plato’s problem, the problem of psychological reality, the problem of analyticity, the problem of ignorance and error, the problem of ignorance and error, the problem of conceptual fuzziness and that of typicality effects. One such theory is the Prototype Theory.

Before presenting the three of the problems posed by the Classical Theory and how the Prototype Theory answers them I will sketch the basic characteristics of the two theories.

The Classical Theory considers that concepts have a definitional structure and that in order for them to be applied they must meet a set of necessary and sufficient condition.

There are two essential characteristics of the Prototype Theory that differentiate it from the Classical Theory:

Concepts can be applied by “satisfying a sufficient number of features, where some may be weighted more significantly than others”(Laurence and Margolis, p. 27)

Lack of definitional structure.

1. Psychological plausibility.

Laurence and Margolis consider that “lexical concepts show no effects of definitional structure in psychological experiments.” They give an example of a psychological experiment made by Walter Kintsch. Two subjects were given the task to listen to a set of sentences. They had to indicate as fast as possible the occurrence of a phoneme. Also, in order to be sure that they don’t just listen to the sentences they were asked to repeat the sentence or create a new sentence that had similar meaning. The sentences had the same phoneme positioned in the same place. What differed was the word before the given phoneme: one was more complex than the other in the sense that it had as a constituent the less complex word. Here is the example given by the authors (the word “convinced” is supposed to be the complex term):

The doctor was convinced only by his visitor’s pallor.

The story was believed only by the most gullible listeners.

What Kintsch examined was the reaction times of the subjects for identifying the given phoneme. His findings were that the speed at which the phoneme is identified is unaffected by the complexity of the term (in other words, by its definitional structure).

2. Ignorance and error.

According to the Classical Theory, one can possess a concept only “by representing necessary or sufficient conditions for its application” (Laurence and Margolis, p. 22). However, experience tells us otherwise: in the past, for example, people could have had a different understanding of a concept than we have today; their conception is considered an erroneous and ignorant one but still they had that particular concept. Laurence and Margolis conclude that “It is possible to have a concept in spite of massive ignorance and/or error, so concept possession can’t be a matter of knowing a definition.”

3.Typicality effects.

The Classical Theory implies that “all instances of a given concept are on equal footing” (Laurence and Margolis, p. 24); this means that items in a category cannot be classified as more typical or less typical in comparison to each other. However, in the 1970s psychologists have proven through a series of experiments that the speed at which items are categorized and the errors which occur when categorizing items are directly affected by typicality. This proves that the Classical Theory is inconsistent when it comes to typicality whose “effects can’t be accommodated by classical models.” (Laurence and Margolis, p. 27).

The first two problems of the Classical Theory are resolved by the simple fact that the Prototype Theory implies a lack of definitional structure of concepts.

The third problem seems to be resolved by including the idea of typicality in its model of categorization (The Accumulator Model). The prototype theorists’ arguments are the following:

- the mechanism of categorization is based on finding similarities; similarity is considered to be a graded notion, therefore some items that are part of a given category are considered more typical than the others.

- some items have in more properties in common with the given category and some have less. Therefore some can be considered more typical than others.

All in all, one can consider the Prototype Theory a reinterpretation of the Classical Theory which resolves the problems previously analyzed. However, it too has its downfalls and therefore cannot be considered superior the Classical Theory.

Summary of the 4th class

1.  Last week’s course started with a recap of Wittgenstein’s two separate positions regarding the relation between world and language. The first way of seeing this relation is that depicted in Tractatus Logico-Philosophicus, Wittgenstein’s first and sole consistent work published during his lifetime. In this short book Wittgenstein shows how language and thought can be analyzed using the tools of modern logic. He describes a theory in which words stand for objects in the world and, hence, language mirrors the world. This view is significantly influenced by the ideas of Frege (to a larger extent) and Russell.

2.   Later, in his maturity writings, Wittgenstein does what no other philosopher had ever done before: he totally brakes with his previous way of thinking. In Philosophical Investigations (PI) Wittgenstein reconsiders the relation between world and language, and the way this is reflected in thought. In fact, he admits he had been wrong and rejects the Tractatus. He initially wanted the two works – Tractatus and Investigations –to be published together so the reader could see the radical differences between the ideas presented. In the PI Wittgenstein shows that there is nothing wrong with natural language (in Tractatus he stated, following Frege, that all the problems of philosophy dwell in the fact that natural language is imperfect Sorry, this was the wrong way to put it; there’s nothing wrong with natural language, Wittgenstein does not follow Frege here; in this case Wittgenstein didn’t change his mind moving from the Tractarian period to his later ideas;  see e.g. 3.032; to the extent a language is a language, it is in perfect logical order; of course, we tend to force language beyond its expressive powers), the problems come from the fact that people use language wrongly. Wittgenstein proposes a new way of looking at philosophy: as a therapeutic activity whose purpose is to help the thought to escape the deep incumbent automatisms. These automatisms are the consequence of using language wrongly.

3.   Before saying something about the paragraphs we managed to discuss in class, let me go back to the first paragraph where Wittgenstein presents one of the most powerful misconceptions concerning language: the representational view of language, or the “Augustinian picture”. According to this view, language is a set of labels (names) that apply to the world and describe “entities” in the world (things, phenomena, actions, attributes). Wittgenstein rejects this “picture” and shows how this view may hold for special “narrowly circumscribed regions” of language (see paragraphs 2 and 3). Such particular situations may include proper names and definite descriptions, for example (remember Frege’s analysis of the relation between “Aristotle”, “Plato’s pupil” and “the teacher of Alexander the Great”). Wittgenstein proposes a range of intellectual exercises regarding simple cases of learning and natural language use in order to identify the weaknesses of the “Augustinian picture” of language. It is here where he introduces the concept of language-game. Although he never fully explained this concept, it is fundamental for the core idea of the PI.  Language-games – simple (social) activities interwoven with typical use of certain words – help us better grasp the specificity of natural language. Language is embedded in social structure and linguistic actions and other actions mix together.

4.   The first paragraph we discussed is the one in which Wittgenstein’s imaginary opponent accuses him of “taking the easy way out” (65): providing the reader with too many examples of language-games without specifying what unifies all these examples, what is common to all of them, i.e. a definition of the language-game. It is the mere concept of (language-) game (and a little later, the concept of “family resemblance”) that Wittgenstein uses to point out the vulnerabilities of the Classical Theory.

5.   In 66, Wittgenstein shows how what we call “game” cannot be defined (there are people who think otherwise, e.g.  Bernard Suits, who considers that games can be defined) , meaning that we cannot provide a set of necessary and sufficient conditions that will fix the features for all things that fall under the concept of “game”. Wittgenstein doubts that we can provide conditions that would capture the commonalities between all games. In fact, he urges us to “look and see” different types of games (board-games, ball-games, card-games, etc.) and search for what is common to all. We’ll discover that common to all are similarities and relationships, but no features (remember here the example that George discussed in class with the features of several pieces of furniture).

6.      Further on, Wittgenstein introduces the concept of family resemblance for characterizing the similarities between different sorts of games (67). This concept is rooted in the analogy with the members of a family. How can we explain concepts, if not by providing definitions for them? Well, we can explain how hey relate to other concepts, how they resemble a family. But the opponent from the imaginary dialogue might object to this by saying that what is common to concepts such as game is the “disjunction of all their common properties”. At this point Wittgenstein replies that this is nothing more than “playing with words”. For it need not be so that the concept of game (or number) is explained as “the sum of the corresponding set of sub-concepts”,  or as the disjunction of, say, board-games n card-games n ball-games n etc. We may explain the concept – decide if an item falls under the concept or not –by identifying the relationships, the similarities between the items and their use in a language.

7.   In the sections 68-70, Wittgenstein addresses the problem of concept boundary. According to the Classical Theory, by giving the definition of a concept we also fix the limits of that concept. The author of the PI thinks, on the contrary, that the extension of a concept need not be “closed by a frontier”. But if we look at the way people use language we realize that they employ a word (“number”, for example) for a rigidly limited concept. Therefore, concepts have strict borders. This is not exactly true, says Wittgenstein, for we cannot give the boundary of a concept (set by its definition), but we can draw one. And we draw the boundary of a concept when we use that concept for a specific purpose. We can redefine a concept for technical purposes – we redefine “number” for using it in mathematics or physics, “game” for applying it to a certain activity in which two or four people throw a ball to each other by using rackets and obeying to certain rules.

8.   But if concepts lack strict borders how can we know if something falls under a concept or not? Wittgenstein admits that there are rules that specify what items the extension of a concept may include. However, we don’t need to specify all these rules when we use a concept. Remember the examples he gives in 69 and 70: the definition of a pace and the definition of a plant. We can draw a boundary of a concept and still use it inexactly; the exactness of a concept is relative to a specific purpose and to a set of “language-games”.

9.   In 71, Wittgenstein discusses the problem of “blurred concepts”. It is an issue that had been addresses before, by Frege, under the name of “vague concepts”. Frege thought that these particular concepts should be abandoned, removed from language, as we “cannot do anything with them”. On the contrary, Wittgenstein admits that we use lots of blurred concepts and manage to communicate and understand each others. When using a concept, we don’t always need to be exact (except for the technical purposes, where we may want to give definitions). If we need to explain to someone what a game is, we can give him or her examples which should be taken in a particular way. This doesn’t mean that we explain them the concept, but that we help them see the similarities and the relationships between those examples. Another way of dealing with blurred concept is to point to the entity in the world expressed by a concept (ostensive use). Remember here the example with the glass of water (if someone is thirsty and ask for a glass of water, he or she doesn’t have to be exact and ask for 350 milliliters of water so that others understand what she means).

10. To sum up, in the paragraphs we discussed Wittgenstein proposes an alternative to the Classical Theory and to the idea of the existence of a “common core” to all things specified by a word. He considers that the semantic coherence of the majority of expressions (and concepts) lies in their family resemblance and not in their common characteristics stipulated by their definitions. Therefore, definitions don’t seem to work for concepts as much as the proponents of the Classical Theory thought. We should look and see something else that may be o a greater help; something such as family resemblance.

update: next class

There is a small change in the syllabus. We will not move directly to Rosch’s paper, so, for next time, please read section #3 [pages 27-43] of the introductory chapter from Margolis&Laurence. It’s in the reader and you can also find it online here. 

Neural Networks

I have mentioned in the 2nd seminar something about neural networks. It would be interesting to have a look at it here    or read much more about it here. I recommend reading at least a bit of the first source, as it might get you another perspective on how the mind works and what concepts can be at another level.

summary of the 3rd class by Diana

Diana was a bit late, but she wrote a very good - and concise – summary. My comments, as before, in square brackets. 

In the 3^rd class we disscused:

- the distinction between types and tokens
- Frege’s sense-reference distinction
- a brief biography of Wittgenstein

1. The type-token distinction is useful in our discussion about concepts. Very roughly, this marks a distinction between sorts (types) of things, and instances (tokens) of sorts of things. For example, when we say ‘apples are red’ and ‘lemons are yellow’, we have two types (apples, lemons – fruits and red, yellow – colours) and 2 tokens for each type.

[Good. Let's also say why the type/token distinction is useful - because it explains how we can share concepts. That is, we share concept types, e.g. FRUIT, though concept tokens are 'attached' to individual minds - when we both think about fruits there is something in your head, and there is something in mine; two different things, since they have different locations - but they belong to the same type, they're the same kind of beast.]

2. Frege: “Sense and Reference” (1892)
We talked during our second class about the classical theory of definition, according to Aristotle. Who is Aristotle? He was Plato’s student. He was the teacher of Alexander the Great. He was the author of the classical theory of definition. We have here 3 senses of the expresion “Aristotle” and one referent – Aristotle. We can think of senses as ‘modes of presentation’ of the same referent. There are also nonrefering expressions – expressions that don’t have a reference, for example “the greatest integer”. Since there is not a greatest integer, the expression doesn’t refer to anything. But it seems perfectly meaningful, since we seem to understand claims like “The greatest integer is larger than one million”. Employing the sense-reference distinction, we can say that the expression has a sense but lacks a reference.Another important distinction is the one between senses and ideas. Two persons can have the same sense about an object to which they refer (for example, they both define the Moon as ‘Earth’s natural satellite”). Let’s imagine that we are watching the Moon through a telescope: we have the object (referent) – the Moon. The image on the telescope is an objective image of the referent (the sense). But the way we see this image is different, the retinal image of the objective image is different for each of us. This retinal image is our idea of the moon, which is subjective, psychological. The sense (objective image) is public.

[Both the Aristotle example and the Moon analogy can be found in the first few pages of Frege's paper]

We also discussed about subjectivity. Each person has a different point of view, he gives a certain interpretation to facts, language, experiences. Can we talk about objectivity (a distant, and unbiased point of view)? A proof we can talk about objectivity is that we understand each other. Relativistic doctrines try to show that some central aspect of experience, thought, evaluation, or even reality is somehow relative to something else (our subjective interpretation).

 [Here we can also point to something that Frege says. Translation poses all kinds of problems about 'importing' meaning from one language to another, and about subjectivity - traduttore traditore. Frege says that a good translation should capture the sense of what is said. Since natural languages are imperfect according to him, a translation is still OK if it misses what he calls the 'emotional coloring' of a text. So the suggestion is that semantics/meaning and psychology should stay separate. So e.g. Alex tried his best with Rilke in the previous post - but do they say the same?]