In written English, "contradiction without" is a grammatically correct phrase.
It indicates a situation where there is a contradiction or disagreement between two elements or ideas, but without a specific external influence or factor causing it. Example: "The speaker's words were filled with contradictions, but it seemed to stem from his own thoughts and not from any outside influence. It was a contradiction without an apparent cause."
And here the poet comes to the fore, insisting on the right to embrace contradiction without shame.
Brouwer's original proof determined the existence of a fixed point by contradiction, without actually exhibiting it (this was quite ironical, due to Brouwer's constructive philosophy).
Inconsistent mathematics is the study of the mathematical theories that result when classical mathematical axioms are asserted within the framework of a (non-classical) logic which can tolerate the presence of a contradiction without turning every sentence into a theorem.
Part 2. We claim that { ∥ u n, m ∗ ∥ ρ } m = 2 ∞ (n fixed) is uniformly bounded according to m. Arguing by contradiction, without loss of generality, suppose that lim m → ∞ ∥ u n, m ∗ ∥ ρ = ∞.
The Internet is basically a walking contradiction without the walking and a lot of the contradiction.
Instead I installed a block of time, unedited, and in it packaged the contradiction without editing.
The Japanese art critic Ichiro Hariu has described Okamoto's polarism as "a philosophy that called for venturing into the depths of contradictions without trying to bring them together with easy solutions or compromises".
And he acutely sees that "the Aquarian project" had its own cultural contradictions: "Without the immensely intricate division of labor developed and constantly elaborated by capitalism, there would have been no mass affluence; without mass affluence, there could have been no counterculture".
Attention to the existence of these contradictions, without illusions, is necessary to meet the policy challenges of the future effectively.
By adopting a paraconsistent logic, a dialetheist can countenance some contradictions without being thereby committed to countenancing everything and, in particular, all contradictions.
There may also be room for a further intermediate position, that is to say, a 'semantic dialetheism' which accepts true contradictions without inconsistent objects or states of affairs as their truth-makers.
