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Utopia began from this pessimistic assumption, and one could argue that it has remained on some level a negative concept.
In its modern form, dating from Victorian times, leisure's a negative concept: it's defined in contrast to work, as non-work - the time we gain, as a result of earning money, that we don't need to spend earning money.
The negative concept "non-P" used in the paraphrases of O- and A-judgements is more problematic.
Locke, for example, is normally thought of as one of the fathers or classical liberalism and therefore as a staunch defender of the negative concept of freedom.
After Berlin, the most widely cited and best developed analyses of the negative concept of liberty include Hayek (1960), Day (1971), Oppenheim (1981), Miller (1983) and Steiner (1994).
We can start with the thesis 'organic living bodies' and if we proceed to negate it we see that the merely negative concept '~ organic living bodies' immediately results in the positive concept 'dead mechanical bodies'.
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Reading recent work on Italian Thought and biopolitics, one might be forgiven for thinking that biopolitics and biopower are deeply negative concepts.
Positive concepts are lodged at the harmonious third, fourth, sixth, eight and ninth "notes", which were considered to be most harmonious with the 12th; while negative concepts are found at the more dissonant fifth, seventh, 10th and 11th.
At the largest scale, many of the dialogues have total numbers of lines that are multiples of 12. Dividing whole texts by 12, Kennedy found "positive concepts" in the dialogues coinciding with harmonious intervals of Pythagoras's scale, and negative concepts at dissonant intervals.
In this way, negative concepts can be formed by reflecting on acts of negative judgement.
Brentano admits, however, that for practical reasons it may be convenient to use negative concepts, e.g., for simplifying inferences.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com