Synthetic expressions are expressions of language that also require sense data from the sense organs. Example: "I see a cat in my living room right now". — PL Olcott
Why did you write down a meaningless gibberish? — Corvus
Synthetic expressions are to add new knowledge or information to the expressions, — Corvus
I am defining Analytic(Olcott) and Synthetic(Olcott) so that they can be unequivocally divided. — PL Olcott
That is fine but your definitions will not be picked up because that is not what analytic means neither is it for synthetic. When the word 'synthetic' is used it never implies sense data in any context. When the word 'analytic' is used it does not always imply language. — Lionino
Every element of the body of analytic knowledge can be verified as true in that it is either an axiom of {BOAK} or is deduced from the axioms of {BOAK}.
The {body of analytic knowledge} (BOAK) is the subset of expressions of analytic truth that are known to be true. — PL Olcott
There is circularity here.
From 1): if an expression is part of a Body of Analytic Truth (BOAK), it is true and analytic.
From 2): if an expression is true and analytic, it becomes part of a Body of Analytic Truth (BOAK)
Given the proposition "X is Y", how do we know whether this is part of the Body of Analytic Truth (BOAK)? — RussellA
That is not what Synthetic(Olcott) means.
โ PL Olcott
Then what is the formal definition of "Synthetic" in expressions? Are expressions correct here? Should they not be propositions or judgements? — Corvus
Analytic(Olcott) is a lot like the conventional meaning of {Analytic} in that every expression is verified as completely true entirely on the basis of its meaning. — PL Olcott
Therefore, if the expression "cats are animals" can only be analytic on the basis of the meanings of the words "cat" and "animal", but there is no absolute meaning of either "cat" nor "animal", then the expression cannot be analytic. — RussellA
The meaning of those terms is the sum total of every detail of all of the general knowledge that applies to those terms (that can be written down using language). — PL Olcott
All of the words have every slight nuance of their meaning assigned to them by Rudolf Carnap / Richard Montague Meaning Postulates. — PL Olcott
Our explication, as mentioned above, will refer to semantical language-systems, not to natural languages. It shares this character with most of the explications of philosophically important concepts given in modern logic, e.g., Tarski's explication of truth. It seems to me that the problems of explicating concepts of this kind for natural languages are of an entirely different nature.
So why use existing terms whose definition is different and well known? — Lionino
I think Rorty actually uses something close to the example in the OP. "Cats are animals." But suppose we discover tomorrow that "all cats are actually very cleverly crafted androids introduced by ETs onto the Earth to spy on us." What then? It no longer seems to be true that cats are animals; they are actually androids. Different genus. — Count Timothy von Icarus
Rudolf Carnap derived the basis for Richard Montague to mathematically formalize natural language. — PL Olcott
Consider the two sentences John finds a unicorn and John seeks a unicorn. These are syntactically alike (subject-verb-object), but are semantically very different. From the first sentence follows that there exists at least one unicorn, whereas the second sentence is ambiguous between the so called de dicto (or non-specific, or notional) reading which does not imply the existence of unicorns, and the de re (or specific, or objectual) reading from which existence of unicorns follows.
It seems to me that Montague Semantics is about how expressions are built out of the words used, not whether the expression is true or not. IE, as the expression "John finds a unicorn" may or may not be true, the expression "cats are animals" may or may not be true.
Montague Semantics provides the basis to encode the current body of knowledge. This would exclude expressions that are not true facts or derived from true facts.
Montague Semantics may be able to analyse how expressions are constructed out of their parts, but not whether the expression is analytic or not. — RussellA
A stipulative definition is a type of definition in which a new or currently existing term is given a new specific meaning for the purposes of argument or discussion in a given context.
https://en.wikipedia.org/wiki/Stipulative_definition
More generally anything that can be encoded in language (including formal mathematical languages) <is> Analytic(Olcott). — PL Olcott
As an example, how is "cats" encoded in language? — RussellA
Kingdom: Animalia...We can determine that a {cat} is an {animal} on the basis of the above knowledge tree. — PL Olcott
The problem is that there are an infinite number of possible analytic expressions including cats. For example, "cats are animals", "cats are elephants", "cats are part of the Kingdom Monera", "cats are part of the Kingdom Protista", "cats are trees", "cats are not anmals", etc. — RussellA
A stipulative definition is a type of definition in which a new or currently existing term is given a new specific meaning for the purposes of argument or discussion in a given context. When the term already exists, this definition may, but does not necessarily, contradict the dictionary (lexical) definition of the term. https://en.wikipedia.org/wiki/Stipulative_definition
I have already stipulated {the body of analytic knowledge} which necessarily excludes {cats are elephants} and includes {cats are animals}. — PL Olcott
I stipulate the definition of cat as "a very large plant-eating mammal with a prehensile trunk, long curved ivory tusks, and large ears, native to Africa and southern Asia", meaning that the expression "cats are elephants" is analytic and true. — RussellA
e referring to PL Olcott's private language — RussellA
Only when we clarify that analytic excludes sense data from the sense organs can we know that the full meaning of a {red rose} is excluded from analytic — PL Olcott
I already said that expressions that are not elements of the body of analytical knowledge are excluded. — PL Olcott
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