Formalists do not commit themselves to probabilities, just as they do not commit themselves to numbers
And yet, if I set one apple next to one apple, there are two apples. Arithmetic predicts facts about the world with such reliability that it is perfectly reasonable to say that sentences about numbers have real-world truth values, regardless of whether numbers “exist”. We come up with arithmetic because it enables us to make sense of the world, because the world actually does behave that way.
Is that so? I never said the buckets averaged more than half full.
Yes. You definitely have two buckets.
If there is some parlance in which you can refer to “a bucket of water” and mean “less half a bucket of water” without just being misleading to the point of falsehood then one of those buckets will be an empty bucket and the other bucket has an unspecified amount of water in it. Unless, I suppose, you also failed to mention that after you emptied one bucket into the other bucket you replaced the water with a lemur. Then you would have two buckets, one with water in it and another with a lemur.
Regardless if there is some argument by analogy to be made which requires something which when added to another thing produces just one thing it is best to focus on the water, not the buckets. ‘Buckets’ is going to rfer to either the actual object or be an ad-hoc unit for water measurement—exactly the thing that the analogy wants to avoid!
If I am a pessimist and have a glass that is only half-full (or knowing this sorry world, less than that), and I throw it in your face, are you ‘being misleading to the point of falsehood’ when you yell that I threw a glass of water at you and then punch me?
Or would you say instead ‘You threw a glass of uncertain description which may or may not have a lemur in it at me!’?
If I am a pessimist and have a glass that is only half-full (or knowing this sorry world, less than that), and I throw it in your face, are you ‘being misleading to the point of falsehood’ when you yell that I threw a glass of water at you and then punch me?
But it takes a machine besides the universe to count apples. Namely, humans. Arithmetic is turing complete, as is probability theory, so we should not be confused when we notice that it can practically talk about everything under the sun, including things out there in being.
And yet, if I set one apple next to one apple, there are two apples. Arithmetic predicts facts about the world with such reliability that it is perfectly reasonable to say that sentences about numbers have real-world truth values, regardless of whether numbers “exist”. We come up with arithmetic because it enables us to make sense of the world, because the world actually does behave that way.
And if I pour one bucket of water into another, do I now have two buckets?
(Yes, there’s something being conserved in this example, but is it ‘number of buckets’/‘number of apples’?)
Yes? One empty bucket, one full bucket and a bunch of water that overflowed and went on the floor.
Is that so? I never said the buckets averaged more than half full.
Yes. You definitely have two buckets.
If there is some parlance in which you can refer to “a bucket of water” and mean “less half a bucket of water” without just being misleading to the point of falsehood then one of those buckets will be an empty bucket and the other bucket has an unspecified amount of water in it. Unless, I suppose, you also failed to mention that after you emptied one bucket into the other bucket you replaced the water with a lemur. Then you would have two buckets, one with water in it and another with a lemur.
Regardless if there is some argument by analogy to be made which requires something which when added to another thing produces just one thing it is best to focus on the water, not the buckets. ‘Buckets’ is going to rfer to either the actual object or be an ad-hoc unit for water measurement—exactly the thing that the analogy wants to avoid!
If I am a pessimist and have a glass that is only half-full (or knowing this sorry world, less than that), and I throw it in your face, are you ‘being misleading to the point of falsehood’ when you yell that I threw a glass of water at you and then punch me?
Or would you say instead ‘You threw a glass of uncertain description which may or may not have a lemur in it at me!’?
I now have one glass.
But it takes a machine besides the universe to count apples. Namely, humans. Arithmetic is turing complete, as is probability theory, so we should not be confused when we notice that it can practically talk about everything under the sun, including things out there in being.