“I should insist [that we not accept the logical impossibility] as a starting point for our discussion of the synthetic a priori” (Denial, 258).
He changes the fundamental question.
‘Are there synthetic a prioris?’ ‘Are there necessarily true informative propositions?’
Johnson then dedicates the rest of his work to more closely examine why the logical empiricists deny synthetic, a priori knowledge.
He starts with their proposition no synthetic propositions are a priori.
Is this proposition a priori or a posteriori?
If a posteriori it is an empirical hypothesis capable of being disproven.
It would be disproven if we could find a synthetic, a priori proposition.
To this, Johnson asks ‘but would it really?’
Empirical Disconfirmation:
“All swans are white” --> Wait, this swan is black!
The original proposition is therefore empirically disconfirmed.
The original hypothesis is disconfirmed because it “predicts the experience of a certain colour sense datum when we view swans but in fact in the disconfirming instance the observer experiences a different sense datum” (Denial, 259).
Main point: this disconfirmation relies on sensory data.
Would it be possible for an observer by means of sense observation to confirm that a synthetic proposition is also a priori?
Johnson says this is intrinsically impossible: just by the notion that the proposition is a priori it cannot be proven or disproven by empirical data.
Can’t we just write a synthetic, a priori truth on a piece of paper and show it to everyone?
Johnson: “Sure.”
“God is two-headed.”
What if someone writes “God is three-headed”?
The original, written statement is disconfirmed. This is, obviously, useless.
“The objection rests on a confusion, between a proposition and its empirical manifestation” (Denial, 259).
We cannot observe a synthetic a priori proposition as we do the black swan.
Therefore, even if it were possible for a synthetic a priori proposition to exist it could not disconfirm empirically the proposition “No synthetic propositions are a priori.”
In order for a proposition to be a posteriori it must be possible to disconfirm it empirically. Therefore, “No synthetic propositions are a priori” is an a priori proposition.