A Quote by Frank P. Ramsey
Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.
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The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.
In other words, the propositions of philosophy are not factual, but linguistic in character - that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly we may say that philosophy is a department of logic. For we will see that the characteristic mark of a purely logical enquiry, is that it is concerned with the formal consequences of our definitions and not with questions of empirical fact.
There are areas of philosophy that are important, but I think of them as being subsumed by other fields. In the case of descriptive philosophy, you have literature or logic, which, in my view, is really mathematics.
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.
The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.
Before my encounter with Thomist philosophy through Maritain, I had almost reached the same conclusions through the logical development of my work, intuition and thought, but what a great sense of joy I felt upon discovering, in Maritain, the confirmation of certain thought patterns, certain ways of clarifying these to myself and to others.
Certain issues in philosophy of science (having to do with observation and the definition of a theory's empirical import) had beenmisconstrued as issues in philosophy of logic and of language. With respect to modality, I hold the exact opposite: important philosophical problems concerning language have been misconstrued as relating to the content of science and the nature of the world. This is not at all new, but is the traditional nominalist line.
The positivists have a simple solution: the world must be divided into that which we can say clearly and the rest, which we had better pass over in silence. But can anyone conceive of a more pointless philosophy, seeing that what we can say clearly amounts to next to nothing? If we omitted all that is unclear, we would probably be left completely uninteresting and trivial tautologies.
Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry.
Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.
The simple sense of wonder at the shapes of things, and at their exuberant independence of our intellectual standards and our trivial definitions, is the basis of spirituality.
Management philosophy: Pay attention to the vital fiew and ignore the trivial many. I could go insane if I obsessed over every little details of all my companies.
I could go insane if I obsessed over every little detail of all of my companies. My management philosophy is to pay attention to the vital few and ignore the trivial many.
Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend.
One thing I really like about philosophy is that it's possible actually to do work in a wide range of different areas. I am particularly happy that I've even been able to do work in logic that has allowed me to use and develop my mathematical abilities, as well as to work on quite distant topics in philosophy of language and mind.
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