Re: Time and Truth
Posted: April 16th, 2010, 5:57 pm
Hi nerd
Infinity is not so much a number as a property of several numbers who existence can be inferred from the numbers we do know. So if we say the numbers we do know are real objects and the law of excluded middle is valid we can infer the existence of a vast number of infinite numbers, so many in fact that there are more infinite numbers than finite numbers. I'm not a mathematician but I'm reliably assured this is the case. So if you are going to reject the excluded middle for infinite numbers then I would think you have to reject it for finite numbers as well since it is by its application to finite numbers that we infer by reductio absurdam that infinite numbers exist. Of course you can keep the excluded middle but then you are going to have to keep the infinite numbers as well. But ask a mathematician, I could be mistaken. Just to remind you my point was that the laws of logic are not so fixed we can assume in advance that they must apply to everything.
I don't really get the idea of things being both real and true. Lewis says somewhere that truth is always about something and reality is what it is about. So normally something that is true, usually a statement of some kind, would not be true about itself but about something else.Whether we think infinite numbers are real will depend on our philosophy of number but if you say they are not real why would you say some other numbers are real? And what does real mean here?
The Lewis Anscombe debate has been discussed several times in these forums. For a case study on it see For Russell and Copleston try
Infinity is not so much a number as a property of several numbers who existence can be inferred from the numbers we do know. So if we say the numbers we do know are real objects and the law of excluded middle is valid we can infer the existence of a vast number of infinite numbers, so many in fact that there are more infinite numbers than finite numbers. I'm not a mathematician but I'm reliably assured this is the case. So if you are going to reject the excluded middle for infinite numbers then I would think you have to reject it for finite numbers as well since it is by its application to finite numbers that we infer by reductio absurdam that infinite numbers exist. Of course you can keep the excluded middle but then you are going to have to keep the infinite numbers as well. But ask a mathematician, I could be mistaken. Just to remind you my point was that the laws of logic are not so fixed we can assume in advance that they must apply to everything.
I don't really get the idea of things being both real and true. Lewis says somewhere that truth is always about something and reality is what it is about. So normally something that is true, usually a statement of some kind, would not be true about itself but about something else.Whether we think infinite numbers are real will depend on our philosophy of number but if you say they are not real why would you say some other numbers are real? And what does real mean here?
The Lewis Anscombe debate has been discussed several times in these forums. For a case study on it see For Russell and Copleston try