We have reason to care about the topic-neutral expressions, and to treat them differently from others, because we are interested in logic as a universal canon for reasoning, one that is applicable not just to reasoning about this or that domain, but to all reasoning.
One universal standard, the reasoning goes, would protect all consumers with the best safety features while simplifying the design of vehicles sold worldwide.
Are there universal forms of reasoning and understanding that enable us to distinguish between rational beliefs and those that are demonstrably false, or is everything relative?
Arithmetic and set theory make distinctions among objects, and so are not topic-neutral in the first sense, but they might still be topic-neutral in the second sense, by virtue of their universal applicability to reasoning about any subject.
Leibniz envisioned a universal language of reasoning (his characteristica universalis) which would reduce argumentation to calculation, so that "there would be no more need of disputation between two philosophers than between two accountants.
Their argument is that if universals were not real, reasoning based on universals would not apply to reality.
The logical gap between particulars and universals that inductive reasoning proposes is a gap that no amount of human reasoning could hope to span.
He also devised a universal method of deductive reasoning, based on mathematics, that is applicable to all the sciences.
In principle, its developers say, the method can be used on any problem in business or academia because shortcomings in human reasoning are universal.
(See DOS 449) Without the consideration of things together with the rationes rerum for example, that 'divisible' is more universal than 'line' no reasoning could be done about them (DOS 450).
Newton's main reason for doing this appears to have been the need to validate a measurement pivotal to the evidential reasoning for universal gravity in Book 3. From a philosophic standpoint, however, what is striking is not merely his recognizing this need, but more so the trouble he went to to fulfill it.
