II 178
Intuitionism: shows us that
Truth is not
assertibility.
X 118
Intuitionism/Quine: one could characterize it as follows: it rejects adjunction if one does not know how to decide which of the subsets is true.
Sentence of the excluded middle: we had wanted to protect it via the negation.
>
Excluded Middle/Quine.
Logic/Quine: in reality you cannot make any distinction: once you have changed the relationships between the logical operators ((s) logical constants), you can consider any or all of them as changed. (>
Holism).
You can tell from that:
Adjunction/Negation/Logical Operators/Quine: are inherent, not transcendent. Because with a deviating logic we cannot maintain its meanings.
Intuitionism: is therefore not a different opinion about the laws for the operators. He rather fights them as useless for science.
QuineVsIntuitionistic Logic: it lacks manageability and familiarity. Their sentence links have no probability function but an intuitive meaning, which we explain with the help of "refute" and "follow from...". However, these explanations become unclear if one wants to maintain the difference between pronouncing a sentence and speaking about the sentence (mention/use)!
Quine: then you can also go straight to Heyting's axioms and not interpose a translation, but
X 119
apply the direct method of the language teacher.
Intuitionism: gained even more impetus through Goedel's proof of incompleteness.
QuineVsIntuitionistic Logic: changes the meanings of quantification and constants.
Solution: one can proceed constructivistically, but still use the orthodox logic: this is Weyl's constructive set theory.
X 121
Ontology/QuineVsIntuitionism/VsIntuitionist Logic: we may not even find what the Intuitionist declares existing.
Solution: we have to translate his language into ours first. And not necessarily into our logic, but in our overall language!
Then we can say what he sees as existing (in our sense of "exist").
