Patricia had been gone for a while looking for a public restroom while leaving Nell on a bench. Inefficiently Patricia had walked randomly finding nothing of the sort for at least fifteen minutes.
Upon returning she found Nell sitting on a different bench looking sternly on her tablet screen.
P: “I’m sorry for the delay. You look busy.”
N: “I’ve dug myself into a hole. See, I had this idea that we should move focus from marxist anti-philosophy to the ideological polar opposite, namely analytical philosophy. Great idea, except I had forgot how difficult I find these discussions.”
Patricia had already grown accustomed to viewing Nell as the all-knowing big sister who could help her with homework. Seeing Nell out of her comfort zone displeased her.
P: “So let us discuss it together.”
Nell would have preferred to retain their current relationship, but suddenly realized how impolite and immature her behavior was.
Nell sighed and smiled gently.
N: “Very well. Okay, my angle was going to be along the lines of a critique of the conservative critique of socially constructed reality. Such counter criticism would consist in pointing to the fact that analytic philosophy has largely demolished itself. But I can’t just go around and say it without understanding the arguments.”
Another deep sigh.
N: “I’m not the bright woman you believe I am.”
P: “Who cares as long as we enjoy helping each other!”
Pleased to realize Patricia had a friendly and unselfish side to her, she got to work.
Is logic logical, Spock?
First starting point was the ever helpful Stanford Encyclopedia of Philosophy (they had even signed up as donators) with an article on the analytic versus the synthetic
N: “So why are all bachelors unmarried? That claim has a terribly long history. It starts out as obvious but ends up even less than self-evident.
- Kant: Because ‘unmarried’ is contained in ‘bachelor’.
- Frege: Because through substitution with a synonym, we get ‘all unmarried men are unmarried’, and once a sentence fits into a few proven logical forms, it will itself be true. Why? Because the truth value is woven into the logical forms themselves.
- Quine: We don’t know. It concurs with ‘all unmarried men are unmarried’, but the latter appears true because we know the world.”
Patricia was reading the same article and silence fell over the two of them. Now she had the same disturbed look as Nell.
P: “It’s difficult, because the article traces the development of interdependent concepts.”
N: “Yes. As history progresses, the emphasis changes. Let’s see if we can unravel it. In fact, let me make a new note:”
Kant: The meaning of A contains the meaning of B
It really all started with Kant’s deliberations:
Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A;
or B lies entirely outside the concept A, though to be sure it stands in connection with it.
In the first case, I call the judgment analytic, in the second synthetic.
Such a humble beginning for a long quest in the history of philosophy.
Kant tried to show that the activity of synthesis was the source of the important cases of a priori knowledge
P: “Man, I’d really like to go back to this theme at a later point! The one about a priori and synthesis.”
N: “Let’s promise each other to get there later. Right, so Kant is interested in synthetic statements, which requires looking at the world. Filtering out all the analytic sentences which brings him no closer to the a priori seems like a good move.”
P: “But philosophically, the idea is born: There is some part of our quest for knowledge, which can be discovered with your eyes closed, just by analyzing. Next comes Frege”
Frege: A rigid form reveals the analytic truth
He believes the key is formalization: Convert a proposition to a very specific form, and if truly analytical, it can be proven true.
He defined a perfectly precise “formal” language, i.e., a language characterized by the “form” – standardly, the shape—of its expressions, and he carefully set out an account of the syntax and semantics of what are called the
“logical constants,”such as “and,” “or,” “not,” “all” and “some,” [ ∧, ∨, ¬, ∀, ∃]
- Analytic truth does not depend on mental states. A person who has wrong information doesn’t counter the truth-value of an analytical truth.
- A person who does not necessarily get a logical connection doesn’t make it less true. The connection exists outside psychology.
- F. developed a basis for mathematics based on logic.
N: “Formalism enters the stage.”
P: “Ah, now it begin to see. Formalism is like a language inside our language. These basic primitives touches on meaning itself in a way that may lead to truth in any world under any circumstances.”
N: “Yes. And when you put it like that, it reeks of »world intelligence «. "
P: “Universal logical laws. Laws that the entire universe obeys.”
N: “Because we as human beings cannot imagine them bent.
Anyway, the idea was that if you suspect a sentence to be analytic, you transform it using substitution with definitions (so substituting a word with its full definition or vice versa) or with synonyms. If that ends with a sentence conforming to the logical language, presto: You have gone from an informal to a formal analytical sentence. However:”
Of course, these notions of definition, meaning and synonymy would themselves need to be clarified, but
they were thought at the time to be sufficiently obvious notionswhose clarification didn’t seem particularly urgent until W.V.O. Quine raised serious questions about them much later.
P: “And with Frege’s success in grounding mathematics on logic, the project of logical positivism was born.”
N: “But this is also one of those shifts in focus that we talked about earlier.”
Logical positivism: Meaning, not form.
The bigger scope of logical positivism, i.e.:
Many thought this project would also perform the more metaphysical work of explaining the truth and necessity of mathematics,
… demanded a higher standard than Frege had bestowed on his logical foundation.
What I shall call a ‘full-blooded theory of analytic truth’ takes the analytic truths to be those that hold
solely by virtue of meaningor that are knowable solely by virtue of meaning.
Frege’s formalistic language had trouble holding up to this much higher standard.
Going from
All bachelors are unmarried
To
All unmarrieds are unmarried
Is easy using substitution. But ‘unmarrieds’ is really just a set. We can loosely accept that the unmarrieds are not married, but if this foundation is going to be able to carry all science, it had better be stronger than that.
On what deeper metaphysical level are ‘unmarrieds’ actually, well, unmarried?
The sentence is indeed true partly in virtue of the fact that ‘unmarried’ must refer to anything that ‘bachelor’ refers to but it is also true partly in virtue of the truth of ‘All unmarrieds are unmarried.’
N: “Metaphysics… This is where metaphysics roars its head again. We want something solid.”
Separating metaphysics from epistemology
If Holmes killed Sikes, then Sikes is dead
It sounds simple, but where are the two sentences connected?
Frege wants the logical form to save us. Holmes kills Sikes ⇒ Sikes is dead.
In other words, the connection is in the language itself.
Utterances of sentences are one thing; the propositions (or thoughts) many different sentences may express, quite another, and the two shouldn’t be confused.
The positivists wanted meaning to be the reason for a connection, not language.
What then happened was that others started to discern between the metaphysical and epistemological aspect of a sentence.
Once the metaphysical and epistemic issues are separated, it becomes less obvious that mere matters of meaning could really explain all necessities.
Nell leaned back. Patricia noticed her frown and further noticed she had developed one herself. Nell showed a sulky, sad look to Patricia.
N: “Are we getting this right? Perhaps we should start over.”
P: “Perhaps we should go for a walk and then come back to this same bench. It’s too soon to leave the park. But God I could use a nap right now.”
•P•A•R•A•D•O•X•