Hey if it is ok I am going to respond to your comment in pieces. I will start with this one. I say
A paradox is the assertion that there can be multiple equally valid truths to a situation.
To which you respond
That sounds a lot like the Fallacy of Grey, even if you meant to say something different. Using the word paradox implies that the “multiple equally valid truths” are contradictory in nature, if so you’d end up with the Fallacy of Grey through the Principle of Explosion.
The reason you see the principle of explosion in my statement is that you are assuming the paradox is dialetheistic, meaning that the multiple equally valid truths I am talking about exist within a single binary. I am not saying Π and –Π are both true. Rather, I am suggesting that to break matrix [Π, Ρ, Σ, Τ, Υ] into binaries (Π, -Π), (Ρ, -Ρ), (Σ, - Σ), (T,-T), and (Υ,-Y) leads to an incompatibility of measurement, and thus multiple equally valid truths.
You say that Antinomy is an outdated Kantian concept. You are correct. It is The reason precisely because of the fact that “we now know the universe isn’t constructed of individual particles” that created antinomy as a type of paradox. Antinomy is a linguistic rather than mathematical paradox. The function of language is to break reality down into schemas of categorization, this process irrevocably takes [Π, Ρ, Σ, Τ, Υ] and transforms it into (Π, -Π), (Ρ, -Ρ), (Σ, - Σ), (T,-T), and (Υ,-Y). As you have said, reality is not constructed of individual particles, but human interaction with reality cannot avoid superimposing individual particles upon it. Because of this, there are instances in the use of language where discourse creates a distinction between elements that does not exist in reality. If we do not acknowledge the potential for such linguistic fallacies, contradiction and competition between these elements cannot be avoided. This is the paradox of antinomy. A talented individual could rephrase this into the dialetheistism “language is both true and not true, but such a statement falls into the very fallacy of language that antinomy as paradox is attempt to warn against, ultimately defeating the purpose of even making the statement.
Not everything can be broken into a tidy maxim or brief summary. Being primarily Bayesians, I am sure you can appreciate that the implementation/ digestion of some ideas have no shortcuts. They do not exist as an individual idea, but rather a monstrous matrix in themselves. Contradicting my own assertion, I will attempt to create my own short maxim to aid in the process of digestion: Language is an inadequate tool for creating reality, but it is the primary tool for creating humans.
Hey if it is ok I am going to respond to your comment in pieces. I will start with this one. I say
To which you respond
The reason you see the principle of explosion in my statement is that you are assuming the paradox is dialetheistic, meaning that the multiple equally valid truths I am talking about exist within a single binary. I am not saying Π and –Π are both true. Rather, I am suggesting that to break matrix [Π, Ρ, Σ, Τ, Υ] into binaries (Π, -Π), (Ρ, -Ρ), (Σ, - Σ), (T,-T), and (Υ,-Y) leads to an incompatibility of measurement, and thus multiple equally valid truths.
You say that Antinomy is an outdated Kantian concept. You are correct. It is The reason precisely because of the fact that “we now know the universe isn’t constructed of individual particles” that created antinomy as a type of paradox. Antinomy is a linguistic rather than mathematical paradox. The function of language is to break reality down into schemas of categorization, this process irrevocably takes [Π, Ρ, Σ, Τ, Υ] and transforms it into (Π, -Π), (Ρ, -Ρ), (Σ, - Σ), (T,-T), and (Υ,-Y). As you have said, reality is not constructed of individual particles, but human interaction with reality cannot avoid superimposing individual particles upon it. Because of this, there are instances in the use of language where discourse creates a distinction between elements that does not exist in reality. If we do not acknowledge the potential for such linguistic fallacies, contradiction and competition between these elements cannot be avoided. This is the paradox of antinomy. A talented individual could rephrase this into the dialetheistism “language is both true and not true, but such a statement falls into the very fallacy of language that antinomy as paradox is attempt to warn against, ultimately defeating the purpose of even making the statement.
Not everything can be broken into a tidy maxim or brief summary. Being primarily Bayesians, I am sure you can appreciate that the implementation/ digestion of some ideas have no shortcuts. They do not exist as an individual idea, but rather a monstrous matrix in themselves. Contradicting my own assertion, I will attempt to create my own short maxim to aid in the process of digestion: Language is an inadequate tool for creating reality, but it is the primary tool for creating humans.