axocanth
Registered Senior Member
It occurred to me that Dave's heroic but confused attempts to revolutionize mathematics -- i.e., to show that 2 + 2 needn't equal 4 -- are not entirely unrelated to recent discussions here. Let's take a look again at what precipitated Dave's unsuccessful coup d'état of mathematical foundations, the post that he reacted to . . .
Philosophers and logicians draw a distinction between statements that are contingently true and those that are necessarily true.
To say that something is contingently true is to say that it is true, but it could have been otherwise. The truths or facts discovered by science fall almost entirely into this category. For example, it is true that the orbit of Mars lies between the orbit of Earth and Jupiter, though we can easily imagine things being otherwise. It just happens to be this way in our universe, but it didn't have to be this way.
Likewise, it is contingently true that Thomas Jefferson is/was the third president of the United States. It could conceivably have been someone else, though, if events had taken a different turn.
Contingent truths are contrasted with necessary truths. These are usually what we regard to be definitions (vixens are female foxes), analytic truths (All bachelors are unmarried), as well as the truths of mathematics and logic. What Write4U is telling us above is that "2 + 2 = 4" is not only true, but necessarily true, it could not have been otherwise, it is true in all counterfactual situations, or as you'll commonly hear it stated, it is true in all possible worlds.
To repeat, science is usually taken to be discovering contingent truths of our universe. You're not going to discover whether the continents move, for example, by sitting in your armchair and thinking about it. It's an empirical matter. You have to get out there and look. You have to get your hands dirty, so to speak, and do some science.
Mathematicians and logicians, on the other hand, keep their hands clean and their callipygous fundaments firmly in their armchairs. Any truths that they discover are necessary truths, therefore no empirical inquiry is required. You don't have to do field work in New Guinea to gather evidence to support the proposition "2 + 2 = 4" or that there is no largest prime number. Mathematical truths, unlike scientific truths, can be discerned by thought alone.
Richard Dawkins has been heard to express the view that if evolution is found to occur on other planets, he believes it will proceed according to Darwinian natural selection. Richard Dawkins, I submit, is also confused.
There are no possible worlds where 2 + 2 ≠ 4, where dogs are not dogs, where triangles have more or less than three sides, and there are no possible worlds where vixens are not female foxes -- though they may not be called "vixens" or "foxes" by the local inhabitants (Dave's mistake!), assuming there are any language-using inhabitants and any foxes at all. These are all necessary truths.
One other thing you're not going to find anywhere in our universe, or any other universe for that matter, is -- as a matter of general principle -- those better able to do something being outdone by those less well able to do the same thing. You're not going to find -- as a general rule -- the less fit surviving and reproducing more successfully than the more fit.
If -- as a general rule -- they were surviving and reproducing more successfully than their rivals they would not be less fit!
But isn't that to endorse what Richard Dawkins said? -- evolution, if it happens at all, will proceed according to the (utterly vacuous!) principle of natural selection?
Not quite. Dawkins presents this as an empirical matter, a possible contingent truth: i.e., We won't know for sure till we get out there and look.
You don't need to get out there and look! There is no safer bet -- in this or any other world -- than "2 + 2 = 4" and "The more fit outdo the less fit". They are both necessary truths.
And for those who haven't quite grasped the consequences yet . . . this is bad news!
Philosophers and logicians draw a distinction between statements that are contingently true and those that are necessarily true.
To say that something is contingently true is to say that it is true, but it could have been otherwise. The truths or facts discovered by science fall almost entirely into this category. For example, it is true that the orbit of Mars lies between the orbit of Earth and Jupiter, though we can easily imagine things being otherwise. It just happens to be this way in our universe, but it didn't have to be this way.
Likewise, it is contingently true that Thomas Jefferson is/was the third president of the United States. It could conceivably have been someone else, though, if events had taken a different turn.
Contingent truths are contrasted with necessary truths. These are usually what we regard to be definitions (vixens are female foxes), analytic truths (All bachelors are unmarried), as well as the truths of mathematics and logic. What Write4U is telling us above is that "2 + 2 = 4" is not only true, but necessarily true, it could not have been otherwise, it is true in all counterfactual situations, or as you'll commonly hear it stated, it is true in all possible worlds.
To repeat, science is usually taken to be discovering contingent truths of our universe. You're not going to discover whether the continents move, for example, by sitting in your armchair and thinking about it. It's an empirical matter. You have to get out there and look. You have to get your hands dirty, so to speak, and do some science.
Mathematicians and logicians, on the other hand, keep their hands clean and their callipygous fundaments firmly in their armchairs. Any truths that they discover are necessary truths, therefore no empirical inquiry is required. You don't have to do field work in New Guinea to gather evidence to support the proposition "2 + 2 = 4" or that there is no largest prime number. Mathematical truths, unlike scientific truths, can be discerned by thought alone.
Richard Dawkins has been heard to express the view that if evolution is found to occur on other planets, he believes it will proceed according to Darwinian natural selection. Richard Dawkins, I submit, is also confused.
There are no possible worlds where 2 + 2 ≠ 4, where dogs are not dogs, where triangles have more or less than three sides, and there are no possible worlds where vixens are not female foxes -- though they may not be called "vixens" or "foxes" by the local inhabitants (Dave's mistake!), assuming there are any language-using inhabitants and any foxes at all. These are all necessary truths.
One other thing you're not going to find anywhere in our universe, or any other universe for that matter, is -- as a matter of general principle -- those better able to do something being outdone by those less well able to do the same thing. You're not going to find -- as a general rule -- the less fit surviving and reproducing more successfully than the more fit.
If -- as a general rule -- they were surviving and reproducing more successfully than their rivals they would not be less fit!
But isn't that to endorse what Richard Dawkins said? -- evolution, if it happens at all, will proceed according to the (utterly vacuous!) principle of natural selection?
Not quite. Dawkins presents this as an empirical matter, a possible contingent truth: i.e., We won't know for sure till we get out there and look.
You don't need to get out there and look! There is no safer bet -- in this or any other world -- than "2 + 2 = 4" and "The more fit outdo the less fit". They are both necessary truths.
And for those who haven't quite grasped the consequences yet . . . this is bad news!
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