![[T]he formalist school, of whom the most eminent representative is Hilbert, have concentrated on the propositions of mathematics, such as '2 + 2 = 4'. They have pronounced these to be meaningless formulae to be manipulated according to arbitrary rules, and they hold that mathematical knowledge consists in knowing what formulae can be derived from what others consistently with the rules.... for example...'2' is a meaningless mark occurring in these meaningless formulae. But... '2' occurs not only in '2 + 2 = 4', but also in 'It is 2 miles to the station', which is not a meaningless formulae, but a significant proposition, in which '2' cannot conceivably be a meaningless mark. (Frank P. Ramsey)](https://cdn.quotesdtb.com/img/quotes_images_webp/49/frank-p-ramsey-arbitrary-959249.webp)
[T]he formalist school, of whom the most eminent representative is Hilbert, have concentrated on the propositions of mathematics, such as '2 + 2 = 4'. They have pronounced these to be meaningless formulae to be manipulated according to arbitrary rules, and they hold that mathematical knowledge consists in knowing what formulae can be derived from what others consistently with the rules.... for example...'2' is a meaningless mark occurring in these meaningless formulae. But... '2' occurs not only in '2 + 2 = 4', but also in 'It is 2 miles to the station', which is not a meaningless formulae, but a significant proposition, in which '2' cannot conceivably be a meaningless mark.
Frank P. RamseyRelated topics
arbitrary example formalist hold knowing knowledge mark mathematics occurring representative school significant others Hilbert miles RulesRelated quotes
Comprehension is neither an arbitrary act nor a passive experience, but a responsible act claiming universal validity. Such knowing is indeed objective in the sense of establishing contact with a hidden reality; a contact that is defined as the condition for anticipating an indeterminate range of yet unknown (and perhaps yet inconceivable) true implications. It seems reasonable to describe this fusion of the personal and the objective as Personal Knowledge. Personal knowledge is an intellectual commitment, and as such inherently hazardous. Only affirmations that could be false can be said to convey objective knowledge of this kind.
Michael Polanyi
When I purchase a food item at the supermarket, I can be confident that the label will state how much riboflavin is in it. The United States government requires this, and for a good reason, which is: I have no idea. I don't even know what riboflavin is. I do know I eat a lot of it. For example, I often start the day with a hearty Kellogg's strawberry Pop-Tart, which has, according to the label, a riboflavin rating of 10 percent. I assume this means that 10 percent of the Pop-Tart is riboflavin. Maybe it's the red stuff in the middle. Anyway, I'm hoping riboflavin is a good thing; if it turns out that it's a bad thing, like "riboflavin" is the Latin word for "cockroach pus," then I am definitely in trouble.
Dave Barry
The success of mathematical physics led the social scientist to be jealous of its power without quite understanding the intellectual attitudes that had contributed to this power. The use of mathematical formulae had accompanied the development of the natural sciences and become the mode in the social sciences. Just as primitive peoples adopt the Western modes of denationalized clothing and of parliamentatism out of a vague feeling that these magic rites and vestments will at once put them abreast of modern culture and technique, so the economists have developed the habit of dressing up their rather imprecise ideas in the language of the infinitesimal calculus.
Norbert Wiener
Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is mathematically conceivable. I am convinced that purely mathematical construction enables us to find those concepts and those lawlike connections between them that provide the key to the understanding of natural phenomena. Useful mathematical concepts may well be suggested by experience, but in no way can they be derived from it. Experience naturally remains the sole criterion of the usefulness of a mathematical construction for physics. But the actual creative principle lies in mathematics. Thus, in a certain sense, I take it to be true that pure thought can grasp the real, as the ancients had dreamed.
Albert Einstein
From whence are these "rights of individuals" derived, and why should we care? Unless we presume the existence of some greater power that determines what is good, isn't it arbitrary to posit that human survival is more important than private property rights, an equally artificially construed concept? Isn't it arbitrary to assume that some sort of equality is preferable to a system where, say, the poor are assumed to have bad karma? If these 'rights of individuals' are derived only from shared humanity, then do 'individuals' (a thoroughly meaningless term, by the way), begin to lose them when they act inhumanely? And isn't it totally arbitrary to grant rights to humans rather than other creatures anyway?
Cornel West