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«Abstract We develop on the idea that everything is related, inside, and therefore determined by a context. This stance, which at first might seem ...»

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Contextuality: A Philosophical Paradigm,

with Applications to Philosophy of Cognitive Science

Carlos Gershenson

School of Cognitive and Computer Sciences

University of Sussex

C.Gershenson@sussex.ac.uk

Abstract

We develop on the idea that everything is related, inside, and therefore

determined by a context. This stance, which at first might seem obvious, has several

important consequences. This paper first presents ideas on Contextuality, for then

applying them to problems in philosophy of cognitive science. Because of space limitations, for the second part we will assume that the reader is familiar with the literature of philosophy of cognitive science, but if this is not the case, it would not be a limitation for understanding the main ideas of this paper. We do not argue that Contextuality is a panaceic answer for explaining everything, but we do argue that everything is inside a context. And because this is always, we sometimes ignore it, but we believe that many problems are dissolved with a contextual approach, noticing things we ignore because of their obviousity. We first give a notion of context. We present the idea that errors are just incongruencies inside a context. We also present previous ideas of absolute being, relative being, and less- incompleteness. We state that all logics, and also truth judgements, are context- dependant, and we develop a “Context-dependant Logic”. We apply ideas of Contextuality to problems in semantics, the problem of “where is the mind”, and the study of consciousness.

1. Introduction How do we decide if something is “right” or “wrong”? This seems at first hand a strange question, since we make such decisions every day, without putting much attention into it nor noticing anything unusual. But since these decisions are such an important part of our lives, we should study them thoroughly. Let’s begin with an example: Do parallel lines intersect?

Well, a couple of centuries ago, any mathematician would have said: “no, of course not! What a silly question...”, following Euclides teachings in geometry. But in the last century we have learned that we can give an affirmative answer, if we are using, for example, geometries defined by Lobachevski or Riemann. What makes the difference for giving an answer is the geometry we are using. Since they have different axioms, in some cases parallel lines intersect, in some others they do not. We will argue that in order to make a decision, it must be related to a context. This might sound obvious, but perhaps it is so obvious that we ignore it, and the possibility of failing to notice our mistakes is increased. We are always speaking in | in1 a context. Perhaps this is why we fail to notice it so easily.

We can see that there are many questions that will have different answers depending on their contexts. Another example: Is the “morning star” the same as the “evening star”?

Well, it depends on our context, and the answer can be yes, no, or yes and no depending on our context. If we are in an astrophysical context, both evening star and morning star are Venus (not even a star, though). But in a contemplative context, they are different, precisely because one can be seen in the morning and another in the evening (in different subcontexts). If our context contains the both mentioned above, we can just say ‘yes and no’.

But what do we mean by “context”?

2. Contexts

We are not able to give a definition of context, because usually definitions castrate the flexibility of concepts by making their boundaries sharp. This sharpness is necessary in some cases, especially in formal languages (Heylighen, 1999), but we will have to take the risk of being misunderstood preferring not to take any flexibility from the concept of “context”.

Therefore, we will just attempt to give a notion of what do we mean by “context”.

A context consists of the set of circumstances and conditions which surround and determine an idea, theory, proposition, or concept. These circumstances and conditions can be spatial, temporal, situational, personal, social, cultural, ecological, etc. Notice that we are giving a relative notion, but it should serve our purposes, because in an open system2, contexts cannot be completely described (Gershenson, 2002). We can see that in nature contexts are dynamic, since the relations of the system inside the context with the rest of its world are changing constantly, therefore changing the context. But the relevant3 changes might be considered to occur sporadically.

For example, the concept ‘cat’ will be determined by the context in which it is used. It can be a context of veterinary medicine, naughty pets, violent cartoons, cute animals, Broadway musicals, etc. The way we refer to ‘cat’ will change considerably depending on the specific context that we are using. Moreover, it seems that we cannot find a definition of ‘cat’ which would be fully explanatory in all possible contexts, nor a property shared by the concepts of ‘cat’ in all possible contexts more than the property of being a cat itself; even when most ‘cats’ (used in different contexts) have four legs, two eyes (not the ones with accidents or mutations...

which would be cats anyway), fur (not some breeds), whiskers (if naughty children haven’t cut them), are mammals (not a wooden cat), etc. But anyone fluent in English language understands when someone says “hey, look! A cat!”, and that anyone is able to understand what does that someone means. This is because they share a context, or the necessary parts of a

–  –  –





3 The relevant features of a context are decided by a n observer, i.e. they are relative to the o bserver’s context.

context for the understanding to take place. Therefore, any use of a concept needs a context to be used in. Concepts are determined (in part) by the context they are used in. This context can be very narrow (e.g. in a private conversation, for example), or very broad (e.g. in a formal description), or of some degree in between (e.g. in a written text) (Heylighen, 1999). But formal concepts are as context-dependant as any other, the only thing is that they depend on a broader context. Another example can be seen with the concept of birds (feathers, fly, etc.). We cannot find any property common to all birds in all possible contexts.

Contexts are also necessary because they make information implicit. We cannot make explicit all the properties of any object, since they are infinite. We need to refer only to the ones relevant to our situation|context|use of them.

We can identify contexts inside contexts. Most contexts can be subcontexts or supercontexts, it just depends on the relative context we are using. Contexts are recursive. For example, the context ‘9:40 pm, September 15th, 2002, the mind of Víctor Gershenson, thinking about his cat Ginebra’ determining the concept of ‘cat’, can be a subcontext of ‘the mind of Víctor Gershenson, thinking about his cat Ginebra’, which can be subcontext of ‘the mind of Víctor Gershenson’, which can be subcontext of ‘the people in México City’, which can be subcontext of ‘the people in México’, which can be subcontext of ‘the people in the world’, which can be subcontext of ‘all people who have lived on this planet’, which can be subcontext of something

Abstract

enough not to have much practical relevance. We can see that ‘cat’ will be more defined in subcontexts than in supercontexts. Supercontexts contain more “instantiations” of ‘cat’ (more things can be considered to be a ‘cat’), than subcontexts, where concepts are more specific. In other words, more “objects” will be identified with a concept (or category) in supercontexts. For example, the context ‘the mind of Víctor Gershenson, thinking about his cat Ginebra’ probably will only consider as ‘cats’ those females with black fur and white paws, while the context ‘the mind of Víctor Gershenson’ will consider as ‘cats’ males, striped, gray, white, etc.

We can refer to our physiological | psychological |philosophical context with the word Seelenzustande4. This would be to make a distinction between a personal context, and other types of contexts (the context of a frog, the context of Viking invasions, the context of subliminal propaganda, the context of planet Mars, the context of Euclidean geometry, etc.).

Each person has her or his own Seelenzustande, even when most parts of all Seelenzustandes seem to be very similar. A common social context can be seen as the intersection of different Seelenzustandes inside a society.

Before developing Contextuality any further, we need to briefly introduce some of our previous philosophical ideas.

3. Absolute Being and Relative Being We have defined two types of being: absolute (a-being) and relative (re-being) (Gershenson, 2001; 2002). The a-being is the being which is independent from the observer, and is for and in the whole universe. Therefore, it is infinite and uncomprehensible, although 4 German for “soul state”.

we can approximate it as much as we want to. The re-being is the being which is for ourselves, and it is different for each individual, and therefore dependent from the observer. It is relative because it depends on the context where each individual is, i.e. Seelenzustande. This Seelenzustande is different for all individuals, and even the Seelenzustande of an individual is changing constantly, with his or her representations of what re-is. The re-being depends on experience, reason, and beliefs, which in turn depend on each other. The being would be the conjunction of a-being and re-being.

Everything re-is a generalization of what a-is. This is because things a-have an infinitude number of properties, but can re-have only a finitude of them, no matter how huge. Therefore, we need to ignore most of these properties (e.g. the spins of the electrons of a table), making a generalization of what things a-are. However, it seems that most of the properties contemplated by different re-beings are the most relevant for their contexts, and there is not much inconvenience in ignoring many of the properties. But we need to be aware that we will never have a complete description of what things a-are, because it would have to be infinite.

We continue developing ideas related to Contextuality.

4. Errors and Mistakes

With the aid of our ontological distinction between a-being and re-being, we can restate the initial phrases of the Tractatus Logicus-Philosophicus (Wittgenstein, 1918): what re-is the case?

People determine|define what re-is the case (i.e. it is context-dependant). Our world is everything that re-is the case for us. We cannot speak about what a-is the case without falling into imprudence. Once we mention it, it is relative, relative of our contexts. But we can agree that something re-is the case for all of us.

Experience helps us in agreeing what re-is the case by expanding and making compatible our contexts. While experiencing we can test incongruencies of our context. When they are detected, we call them an error or mistake. There a-are no errors or mistakes, because we believe that things follow the laws of nature at all times. Only when our experience does not match our expectations, we say “there was an error”. But there only re-was an error, in the sense that a system did not do what we expected or wanted to do. All errors are dependent of an observer.

For example, when I am programming, I type the code following the laws that control the mechanisms of my brain and body, whichever they a-are. When I make an error, it is not that the mechanisms “went wrong”, but that the mechanisms did not do what I expected or wanted. We say that errors occur in a system when the context of the system is unable to contain as much as we do (if there re-is such error, but our context does nor contain it, we cannot detect it). Errors are relative to the context from where they are judged (something reis an error from one context, but re-is not from another...). An error is given when an inconsistency is detected inside a context (otherwise we do not detect any error).

The fact that our context cannot contain what a-is the case leads us to say that there will always be potential errors to be found, when the enlarging parts of our contexts become incongruent with the previous ones. Natural contexts are constantly changing, developing, and evolving. And formal or defined contexts cannot ignore natural contexts if they want to have any relation with “reality”.

For example, when I am programming, I have a different Seelenzustande before and after I detect an error, because the experience of detecting an error (i.e. incongruence with my Seelenzustande) expands my Seelenzustande, and part of my previous Seelenzustande stops being consistent with my actual Seelenzustande because the results were not the ones I expected. Only then, I can say that I had a mistake. If my experience would give the expected results, it would also expand my Seelenzustande, but there would have been no incongruence, and therefore no error. We can learn not only from mistakes. Any experience expands our Seelenzustandes. But anything we forget, reduces our Seelenzustandes. All experience carries learning, even just to be less unsure of our Seelenzustande. For example, the experiences of blue skies on days without clouds reinforce my idea that “skies are blue”, every time I see the sky blue. This does not prove that I will never see a green sky, but if I “always” have seen blue skies (not counting twilight), I will believe that skies a-are blue, when blueness is a property we ascribe to the skies (Gershenson, 2001) (the skies just a-are...).

This view leads us to say that all ideas are valid in the context they were created (Gershenson, 2001; 2002). This is because when ideas are generated, there cannot be errors inside the context they are generated, since they are generated according to their actual context. It is when the context is enlarged (in a few seconds or in two thousand years...) that inconsistencies of the previous context can be detected, but from a new context.

We can see that we cannot get rid of all possible mistakes because our contexts are incomplete. But we can make them as less-incomplete as we want to (Gershenson, 2001; 2002).

5. Less-incompleteness



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