An alternative approach to meaning comes from formal semantics ( Cann 1993, Portner and Partee 2002). This involves
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Establishing a grammar (a set of production rules) which will generate a subset of English sentences
A set of translation rules such that sentences generated by the grammar can be mechanically translated into expressions in a formal language
A way of interpreting the meaning of expressions in the formal language.
The interpretation of expressions in the formal language is based on truth-conditional semantics, which takes the meaning of a sentence to be those states-of-affairs under which the sentence is true. For example, the meaning of 'The cat sat on the mat' is those states of affairs in which the proposition The cat sat on the mat is true. Adopting a formal language approach to the analysis of natural languages was first proposed by Montague (1974), and such creations are often called Montague grammars.
The advantage with this approach is the clarity and precision with which the analysis of sentences can be carried out by formal means. However that comes with several restrictions. It separates meaning from, for example, the speaker's mental state, and gives a single meaning for every sentence. It is also only applicable to utterances which are assertions, and not interrogatives or imperatives. For example it would not give:
(1) "Do you think it's hot in here?"
any precise meaning, since it is not a proposition, while in fact (1) would typically be understood to mean a request to reduce the temperature in the room. However it has been argued that formal semantics provides a core, propositional sense of meaning, which people elaborate upon in actual conversation.
How does this relate to the touchstone question - "What does 'static' mean?" In one sense none, since the interviewee understands the question in pragmatic terms, as described above. But 'static' is a term used in Java, which is a formal language with an explicit formal grammar. In effect the context of programming with a Java compiler corresponds to a model (Cann 1993 page 39), which represents some state-of-affairs in the context of
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which formal meaning is established. In other words a Java program which contains the word 'static' will behave in a certain way, and this effectively defines a 'real' meaning of static. This then goes beyond 'normative' views of the meaning of 'static', since in practice there may exist a range of such views (for example, see Reddy 2002 for alternative concepts of class and object). Intuitively this corresponds to how the student will interpret the question, as meaning something like "what difference does it make if you use the word 'static' in a Java program", and consequently "when is it appropriate to use 'static'?". Consequently we have a two-level situation:
1. The meaning of 'static' with truth-functional meaning, as determined by the Java compiler, and corresponding to Putnam's meaning not in the head. This relates to the definition-based view of concepts.
2. The students' mental representation of that meaning - which may or may not be a good representation, in that a student may incorrectly predict what a Java program will do when compiled or executed. This relates to the concept image view (Tall and Vinner 1981).
2.5 The philosophy/psychology border - Fodor and the Language
of Thought
Fodor‟s work is located somewhere on the border of psychology and philosophy - he calls
The Language of Thought (Fodor 1976) an essay in 'speculative psychology'. He argues
that:
1. Folk psychology is correct (discussed below) 2. Cognition is a computational process
3. The representational theory of mind is true
4. Those representations exist within a 'language of thought', which is not a natural language
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Folk psychology, or what Fodor calls 'common-sense psychology', holds that thinking beings have desires, and seek to achieve those desires according to a set of beliefs. (Fodor 1987, Fodor 1976 page 27). Cognition is claimed to be concerned with deciding which action among the various possibilities will give the best chance of achieving the desired outcome, and as such is a computational process.
A representational theory of mind treats cognition as operating not directly upon aspects of the real world, which many would think impossible, but on some kind of representation of those aspects. If we equate 'representation' with 'idea', this goes back to Hume deriving ideas from sensory impressions: (Hume 1999 page 98) :
"We may prosecute this enquiry to what length we please; where we shall always find, that every idea which we examine is copied from a similar impression" He treats cognition as computation (Fodor 1994 page 7)
"I assume that psychological laws are typically implemented by computational
processes"
and that (page 8)
"Computational processes are ones defined over syntactically structured objects; viewed
in extension, computations are mappings from symbols to symbols; viewed in intension,
there are mappings from symbols under syntactic description to symbols under syntactic
description."
(Intension and extension are discussed in 2.6.2). Fodor argues that as soon as we have 'syntactically structured objects', we must have a 'language of thought', since we cannot have syntax without a language. That this is not simply a natural language is shown by the fact that animals and pre-verbal infants can think.
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How does this relate to the touchstone question? The folk psychology viewpoint seems tolerable - students have desires to understand, and beliefs in the form of what they have learnt, and sometimes doubts as to the 'accuracy' of what they have learnt. Cognition as computation seems questionable, although his view of concept learning (Fodor 1976 page 34) is interesting:
"I think that what concept learning situations have in common is fundamentally this:
The experiences which occasion the learning in such situations (under the theoretically
relevant descriptions) stand in a confirmation relation to what is learned (under its
theoretically relevant description). A short way of saying this is that concept learning
is essentially a process of hypothesis formation and confirmation."
This is said in the context of lab-based experiments of artificial categories (Bruner, Goodnow and Austin 1956), but it can also be seen as fundamentally constructivist. Hypothesis formation and confirmation correspond to Skemp's (1983 page 107) 'building and testing'. Constructivism is examined in more depth later on.
Further, a representational theory of mind seems essential when dealing with non-physical items such as Java keywords, and corresponds to the idea of a mental model. The touchstone question might be re-phrased as "Describe to me your internal representation of 'static' in Java".