>In all propositions concerning numbers, a condition is implied,

His point is better stated without the use of arithmetic at all. But he's right. J.S. Mill was a great writer, so sad he was agnostic.

In all seriousness the point that one does not equal one doesn't make any sense in a strictly fundamental geometrical or arithmetical sense. But in the theoretical way he uses it, maybe that's why it's so effective.

What is it, exactly, you think Mill is saying here, OP?

In your own words.

>>9042315
Not OP but I think he's saying math is useless as a foundation for epistemology, because even though it's coherent you can't draw any real-world conclusions from it.

compare with the Bible, which is flawless and gives us a practical reference point by which we can come to know truths.

>>9042315
One is not always one because 40 horse power engines are not always the same strength, and horses are not the same strength. Thus, no arithmetic is true.

>>9042390
But that doesn't mean one doesn't equal one. What you're referring to is a gap in the level of equivalence, a broad materialistically definite spiritually vague definition of the world which is what causes much of the mis-extrapolation of statistical surveys or alienation from feeling identified as an individual.

It has nothing to do with a unit being a unit, which is the foundation for arithmetic and geometry.

>>9042399
>arithmetic and geometry
Total bullshit. Arithmetic is just a bunch of empirical claims that we know from counting oranges and haven't been proven false yet. Read A System of Logic, Ratiocinative and Inductive

>>9042441
>Arithmetic is just a bunch of empirical claims that we know from counting oranges and haven't been proven false yet. Read A System of Logic, Ratiocinative and Inductive

I mean, if the OP is anything to on, Mill doesn't seem to be suggesting that arithmetic is empirical. Rather, the practice of arithmetic is founded on an assumption of |value| identity, and that this assumption remains undemonstrated. This implies that, contrary to what you claim of him, Mill sees the 'truth value' of arithmetical 'propositions' extends from this axiom.

He says it right here:
>>In all propositions concerning numbers, a condition is implied, without which none of them would be true; and that condition is an assumption which may be false. The condition is, that 1=1; that all the numbers are numbers of the same or of equal units. Let this be doubtful, and not one of the propositions of arithmetic will hold true.

His point in this passage seems to be that human beings are not simply data points. So, to extend the methods of statistical analysis via arithmetic--that is, as a DEDUCTIVE enterprise--is to treat humans as mere data points, as units of absolute value. Any inductive judgments one is then inclined to carry out from one's prior deductions are, as such, fallacious.

>>9042158

here's a non bullshit formulation of this

https://en.wikipedia.org/wiki/Wittgenstein_on_Rules_and_Private_Language#The_rule-following_paradox

>>9042517

Maybe not fallacious, but requires further demonstration beyond reference to the arithmetical deduction.

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More classicalist antirational garbage, gosh the 19th century would have de-progressed if it were not for capitalism.

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>replying to this thread

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>The Aristotelian logic of the simple syllogism starts from the proposition that ‘A’ is equal to ‘A’. This postulate is accepted as an axiom for a multitude of practical human actions and elementary generalisations. But in reality ‘A’ is not equal to ‘A’. This is easy to prove if we observe these two letters under a lens—they are quite different from each other. But, one can object, the question is not of the size or the form of the letters, since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar—a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is this true—all bodies change uninterruptedly in size, weight, colour, etc. They are never equal to themselves. A sophist will respond that a pound of sugar is equal to itself “at any given moment”.

>Aside from the extremely dubious practical value of this “axiom”, it does not withstand theoretical criticism either. How should we really conceive the word “moment”? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that “moment” to inevitable changes. Or is the “moment” a purely mathematical abstraction, that is, a zero of time? But everything exists in time; and existence itself is an uninterrupted process of transformation; time is consequently a fundamental element of existence. Thus the axiom ‘A’ is equal to ‘A’ signifies that a thing is equal to itself if it does not change, that is, if it does not exist.