Combining Texts

All the ideas for 'fragments/reports', 'What Numbers Are' and 'Letter to Peter Wilhelm Lund'

unexpand these ideas     |    start again     |     specify just one area for these texts

5 ideas

3. Truth / A. Truth Problems / 8. Subjective Truth
16005 I recognise knowledge, but it is the truth by which I can live and die that really matters [Kierkegaard]
     Full Idea: The thing is to find a truth which is true for me - the idea for which I can live and die. I still recognise an imperative of knowledge, but it must be taken up into my life, which I now recognise as the most important thing.
     From: Søren Kierkegaard (Letter to Peter Wilhelm Lund [1835], J-1A)
     A reaction: A quintessentially existential idea. Note that he still considers objective knowledge to be quite important, but how we act and relate to those ideas is what really matters for us human beings. [SY]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813 Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
     Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers.
     From: Nicholas P. White (What Numbers Are [1974], V)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
     Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege.
     From: Nicholas P. White (What Numbers Are [1974], IV)
     A reaction: [He adds Quine 1960:268 as a reference]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.