Possibly Stove intended this only as an extended Take That to philosophers he dislikes; but it seems to me that he is a bit too dismissive of his own project, the ‘nosology’. Without wanting a Fully General Counterargument, I think it might be useful to have a set of, say, five or six different classes of erroneous statements; and I also think Stove is too eager to insist on the singularity of each of his examples. For example, he states that the objection “not verifiable” cannot be applied to his example 8; I don’t see why not. Anything whose “name and nature are not to be revealed” has just been declared unverifiable, no? Similarly 3 through 7 look pretty unverifiable to me.
Then he has some examples further down the list which look reasonably testable, such as 13 : “3 is a lucky number”. One could easily do an experiment on this by submitting lottery tickets with and without 3′s filled in; and as for 14, I think a simple “false-to-fact” would suffice to dismiss it.
So far then there are three classifications: False to fact, contradiction, meaningless through having no connection to observation. We may need a fourth to cover such statements as 26: “The tie which unites the number three to its properties (such as primeness) is inexplicable”. This seems somehow vaguely related to observation, in that there does seem to be something called three which has the property of primeness, and nobody has really explained the tie between triples of objects and these properties. (It is perhaps not strongly coupled to observation, but I hesitate to dismiss it completely on that ground.) I suggest a fourth classification of ‘uninteresting’ or ‘unfruitful’: A proposition which, when adopted as an axiom, yields few or no deductions, is unfruitful. One might also call it the ‘So What’ error: Making statements which even if true are not useful to know.
There does seem to be some overlap here; for example, Stove’s 25: “Five is of the same substance as three, co-eternal with three, very three of three: it is only in their attributes that three and five are different.” This looks to me quite unverifiable, but even if it were true, So What? What conclusions or prediction would you draw from this?
Contrary to Stove, I think these four will cover all his list: False to fact, contradiction, meaningless, and So What. I am not certain, however, whether this insight is useful.
I’d unify your “So What” with “meaningless” into a single category “does not constrain observations”. Math passes the test inasmuch as it constrains observations about outcomes of proof checking.
But now some people will complain (are already complaining) that we reject the majority of humanity’s thought.
Again, it does seem observable that nobody has explained why three is prime and four isn’t. (I’m not sure you can actually use ‘why’ in an intelligible way here; possibly I’m being confused by non-mathematical language applied to math.) It’s not an observation I would expect anyone to care about, and possibly it may be the equivalent of nobody having seen something invisible; but it does seem to make a statement that could in principle have gone the other way.
I agree that I’m not sure how you’re intending to use ‘why’ here, and I’m pretty sure there’s a good answer for any particular meaning.
To answer the question in a possibly unsatisfactory way, 3 is prime because it is a natural number which has exactly two distinct natural number factors, whereas 4 is not prime because it has more than two distinct natural number factors.
What humanity does isn’t “thought”, by and large. Not in any meaningful sense. It’s mostly the expression of prejudices combined with associational triggers and repeating what others say.
Part of becoming an effective thinker is recognizing that unpleasant realities need to be acknowledged even when we’d prefer they weren’t the case. For people living in this time, in this place, one of those truths is that we’re surrounded by blatant stupidity. Even worse, we’re blatantly stupid a lot of the time.
Deriving those conclusions from the evidence, and then acknowledging their validity, is one of the basic necessary steps to becoming better. No problem can be (expected to be) solved if we deny its reality.
Possibly Stove intended this only as an extended Take That to philosophers he dislikes; but it seems to me that he is a bit too dismissive of his own project, the ‘nosology’. Without wanting a Fully General Counterargument, I think it might be useful to have a set of, say, five or six different classes of erroneous statements; and I also think Stove is too eager to insist on the singularity of each of his examples. For example, he states that the objection “not verifiable” cannot be applied to his example 8; I don’t see why not. Anything whose “name and nature are not to be revealed” has just been declared unverifiable, no? Similarly 3 through 7 look pretty unverifiable to me.
Then he has some examples further down the list which look reasonably testable, such as 13 : “3 is a lucky number”. One could easily do an experiment on this by submitting lottery tickets with and without 3′s filled in; and as for 14, I think a simple “false-to-fact” would suffice to dismiss it.
So far then there are three classifications: False to fact, contradiction, meaningless through having no connection to observation. We may need a fourth to cover such statements as 26: “The tie which unites the number three to its properties (such as primeness) is inexplicable”. This seems somehow vaguely related to observation, in that there does seem to be something called three which has the property of primeness, and nobody has really explained the tie between triples of objects and these properties. (It is perhaps not strongly coupled to observation, but I hesitate to dismiss it completely on that ground.) I suggest a fourth classification of ‘uninteresting’ or ‘unfruitful’: A proposition which, when adopted as an axiom, yields few or no deductions, is unfruitful. One might also call it the ‘So What’ error: Making statements which even if true are not useful to know.
There does seem to be some overlap here; for example, Stove’s 25: “Five is of the same substance as three, co-eternal with three, very three of three: it is only in their attributes that three and five are different.” This looks to me quite unverifiable, but even if it were true, So What? What conclusions or prediction would you draw from this?
Contrary to Stove, I think these four will cover all his list: False to fact, contradiction, meaningless, and So What. I am not certain, however, whether this insight is useful.
I’d unify your “So What” with “meaningless” into a single category “does not constrain observations”. Math passes the test inasmuch as it constrains observations about outcomes of proof checking.
But now some people will complain (are already complaining) that we reject the majority of humanity’s thought.
Again, it does seem observable that nobody has explained why three is prime and four isn’t. (I’m not sure you can actually use ‘why’ in an intelligible way here; possibly I’m being confused by non-mathematical language applied to math.) It’s not an observation I would expect anyone to care about, and possibly it may be the equivalent of nobody having seen something invisible; but it does seem to make a statement that could in principle have gone the other way.
I agree that I’m not sure how you’re intending to use ‘why’ here, and I’m pretty sure there’s a good answer for any particular meaning.
To answer the question in a possibly unsatisfactory way, 3 is prime because it is a natural number which has exactly two distinct natural number factors, whereas 4 is not prime because it has more than two distinct natural number factors.
What humanity does isn’t “thought”, by and large. Not in any meaningful sense. It’s mostly the expression of prejudices combined with associational triggers and repeating what others say.
Part of becoming an effective thinker is recognizing that unpleasant realities need to be acknowledged even when we’d prefer they weren’t the case. For people living in this time, in this place, one of those truths is that we’re surrounded by blatant stupidity. Even worse, we’re blatantly stupid a lot of the time.
Deriving those conclusions from the evidence, and then acknowledging their validity, is one of the basic necessary steps to becoming better. No problem can be (expected to be) solved if we deny its reality.