What does it mean to mean?

Form and Logic

I have written many posts about formal logic as it can be seen here, so I won’t delve in the mechanics of it. Formal logic, as used here, is all about applying classical logic to abstract forms. Anything can be a form.

Semantics: Saussurian linguistics

Ferdinand de Saussure is mostly known for his concept of the dual ontology of words where a word is made of an arbitrary link between a physical “token” called signifier and an abstract “token” called signified. The physical token (a sequence of sounds, graphemes or tactile patterns) is the physical embodiment of an abstract concept.

Semantics: Networking

When the question ‘what does x mean’ is asked, the answer will inevitably be a network of linguist tokens (standing for concepts) that are related to x. For example, when asked ‘what is an apple’, the answer will yield a particular arrangement of the tokens ‘fruit’, ‘is’ and ‘tree’ among other tokens. And this is essential to what is understood as meaning, it relates known concepts to the concept asked. In the case of the apple, it is related to ‘fruit’ by stating that it is an instance of ‘fruit’ and it can also be related to ‘tree’ through ‘fruit’. It is worth noticing that manipulating concepts without a linked linguistic token tends to be harder than doing it with concepts that have tokens.

It is my view that meaning is a particular type of network. So when we ask for the meaning of x, we are asking for a network of concepts that are related to x.

Semantics: Your Neighbours Make You

It is my view that if a signifier is a physical token and a signified is a network of related concepts. With this in mind, I decided to build a semantic network to test my views. Concepts are connected to other concepts by linguistic “nodes” that we call function words. Function words designate the type of relationship between two concepts. For example: ‘x is in y’ and ‘y is in x’ designate different types of relationships between x and y and the semantic network displaying both types of relationships would be different. Now consider ‘x flies to y’ and ‘x travels to y’ both can be said to be different in the sense that ‘flies’ and ‘travels’ have different semantic networks but they can said to be similar in the sense that both include the semantic network of ‘motion’ and thus, when queried, the semantic network will understand* that ‘motion’ can be inferred from ‘flies’ and ‘travels’.

Semantics: Understanding

Since semantics involves links between abstract concepts, formal logic can be applied to semantic networks. If applied, it gives the semantic network, the ability to reason about its concepts. Thus, motion can be understood from both flying and travelling*. The assumption being made here is that the meaning of objective concepts can be distilled to logical relationships. This assumption leads to the question:

is the semantics of objective concepts a type of logical relationship?

To that I have nothing but speculation. I think that the answer is yes. Given a finite definition of an objective concept, a semantic network of that concept could be built that represents the semantics of that concept in a logical way. This means that the concept of motion would be inferred from the concepts of flying, walking and travelling. Note that due to the limitations of formal logic, any semantics involving the notion of time would be non-expressible in the type of semantic network described here. However, using sequential logic could be an answer to implementing the notion of time in a semantic network.

Semnet: Testing the Waters

I recently built Semnet as a tool to test my ideas about semantics. Semnet operates using ‘x is y’ statements thus, any semantics needs to be transcribed to a ‘x is y’ statement. From the Readme: So to say ‘a tree has the property of being green’, we can say ‘a tree is Pgreen’ and define Pgreen as ‘Pgreen is the green property’ and further define the green property as ‘The green property is a property’ and ‘The green property is green’ whereby the green property is defined as that thing which is green and is a property.

Concluding

It is my view that the semantics of objective concepts, as viewed under Saussurian linguistics, can be formalised and subject to the rigour (and power) of formal logic. Doing this opens the door to semantic reasoning and all the possibilities that this type of reasoning offers. A semantic network has been built by me to test this.

There exists a field known as formal semantics that seems to aim in the same direction, however, the examples I have seen, are purely abstract with no actual application whatsoever.

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