Numbers can't be measured Edit
http://archive.org/stream/cu31924012236109/cu31924012236109_djvu.txt last page II. The mathematical relations between numbers and magnitudes require separate consideration. In geometry they involve the comparison of dimensions, and dimensions are, in the sense explained above, things. But where mathematics deal with the relations between symbols, whether algebraic or numerical, they do not compare things. They essentially substitute a symbol for the thing itself, and use the symbols to facilitate not measurement but ratiocination con- cerning measurements. Number is not an object, a condition, a property, an attribute, or even an abstraction. Numbers ex- press the result of measurement; they cannot themselves be measured. The relation between them is stated when they are stated. The very conception of number involves the assumption that two things can be identical, or may for a special purpose be regarded as identical. This is neither the result of abstrac- tion nor reasoning ; it is merely a short way of saying that any four things which we choose to regard as identical, may be counted in two ways, described as regards number in two different phrases .
Notes 1 p.263 Edit
- .... Surely the time is past when a theory unsupported by evidence is received as probable, because in our ignorance we know not why it should be false, though we cannot show it to be true.....
Tautologies can neither be refuted nor verified,it Popper unfalsifiable like Samuel Butler and Charles Hodge Fleeming identified the tautological narrative of Darwin's propositions but couldn't nail it down with the term tautology which was coined around 1560 I believe. (See Wolfram search engine)
Popper gave this "....we know not why it should be false, though we cannot show it to be true......." a name: falsifiability.
We know not why A or not-A should be false, though we can't show it be true is a good description of not being able to verify nor refute a proposition due to its logical form. Conclusions which derive from such unfalsifiable forms are Non-sequiturs, which doesn't mean the conclusion itself is either falsifiable,true or erroneous or not but that it doesn't derive logically. The conclusion itself might be true, but didn't derive logically from the premise.
This is why I argued that the conclusion that God exists did not derive logically from the ID falsifiability/empirical premise, nor the conclusion that God doesn't exist from the Dawkins' premise that God's existence is improbable and his falsifiability/empirical major premise.
Notes 2 Edit
Darwin's thought experiment to rephrase his claims of logic
Review of The Origin of Species (1867) Edit
- But if all beings are thus descended from a common ancestry, a complete historical record would show an unbroken chain of creatures, reaching from each one now known back to the first type, with each link differing from its neighbour by no more than the several offspring of a single pair of animals now differ. We have no such record; but geology can produce vestiges which may be looked upon as a few out of the innumerable links of the whole conceivable chain, and what, say the followers of Darwin, is more certain than that the record of geology must necessarily be imperfect? The records we have show a certain family likeness between the beings living at each epoch, and this is at least consistent with our views.