Regi,
You post good, well-thought out responses!
Certainty is the normal attitude of the psychologically stable. It is pathological to doubt everything, which one must, if nothing is certain. Once you have identified something and understand its nature, without some particular evidence to the contrary, one can be certain that what has been identified is what it is, and has the nature it has. When you are not being a, "philosopher," this is always your attitude. Many would say that it's the sense of certainty that's pathological, not uncertainty! Religious fundamentalists, cultists, the insane, Leonard Peikoff etc all have a strong sense of certainty.... ;)
This idea that we cannot be certain about anything always astounds me. Are your really not certain, vaccination works, wireless communication is possible, heavier than air flight is possible, painless surgery is performed daily, antibiotics kill bacteria (but not viruses), machines can perform millions of mathematical functions that no single human being could ever perform, and that man can (and did) walk on the moon?
I really do not see that reasoning requires certainty. All reasoning requires is that we can obtain probabilities which are high enough for all practical purposes. In the examples you gave, reason does enable us to assign a very high probability for all of them, and this is sufficient for me to say that I know these things to be true. But I do not see that any of them are absolutely 100% certain. 99.999999999999999% maybe, but not 100% ;) I take it that we 'know' something when we have used reason to establish it 'beyond reasonable doubt’ (This is the legal definition by the way!). But this doesn't require certainty.
Now then, Fountain Head:
You are not 50% sure of the outcome—you are certain that the outcome will be one or the other. It is your odds of being correct with your guess as to what the outcome will be, which are 50/50.
Look at it this way: were you not certain of the potential outcomes, and the concepts involved with tossing a coin, then from where are you assigning odds from, and to what? Your certainty in the act of coin tossing--and all that goes along with it--is implied when statistical analysis is applied.
I don't think so. The range of possible outcomes to the coin toss (Heads or Tails) is itself a theory based on empirical examination of the world. Who is to say that for a very few coins the bank made a mistake and produced a coin with Heads on both sides? Or perhaps the coin will land on its edge? Or may be the coin will suddenly disappear in mid-flight? Of course these are 'arbitrary' possibilities which we can reasonably reject, but not with certainty. We can be say 99.999% sure that the result will be either heads or tails, but not 100% sure. The statistical analysis itself is not certain, because statistics is, like every other piece of knowledge, empirical in nature and thus not 100% certain. Read on...
For you to, not only state certitude concerning what is impossible, but also assign how percetage-ly sure you are as well, you would need to demonstrate, with certitude, the conditions by which would render it impossible.
Firstly, I did not state anything with 'certitude', nor do I need to demonstrate anything with certitude. I gave a figure of 98% likelihood that certainty is impossible. Where did the figure come from? It was based on the use of something called 'Bayes Theorem', which calculates probabilities based on input from each piece of knowledge relevant to the hypothesis. The figure is itself not absolutely certain. Nor is the Bayes Theorem. But this is not paradoxical if we regard reasoning as a self-referential network, where each belief in our mind supports the others. For instance take two pieces of knowledge A and B. Belief A can support B, and B can support A.
In order to support my claim that certainty is impossible, all I need to do here is present good and sufficient reasons to place my claim 'Beyond reasonable doubt' (but not 100% certain). So what reasons do I have for thinking that certainty is very unlikely? It's worth me repeating in this thread the reasoning I gave in the other thread. Here's what I argued:
'We are always operating off incomplete information (relative to the entire universe). Rand said that we could fix the problem by specifying a 'context'. But how do we know that there isn't something outside this context which is screwing with our reasoning faculties? (Remember, brains are physical objects, existing in the physical universe like everything else). We don't. So a confidence level of 100% can't be justified.'
...
'To specify a context we need a working rational mind. But this mind cannot be separated from that context! For any given physical context, we could take a 'God's eye' view of it and imagine an observer looking at that context. The mind of an observer is itself a physical object, and so we need to consider whether or not this mind is working properly. But this would create a new context (physical context + mind of observer). But then we could imagine a second observer looking at this new context - a watcher watching the watcher ;) And this in turn would create yet another new context (physical context +mind of observer 1 + mind of observer 2) and so ad infinitum. And that is precisely why specifying a context doesn't escape from uncertainty.'
All you need to do is apply Rand's own reasoning. Firstly, consider that there is no analytic/synthetic distinction. Rand herself came to this conclusion, and said that empirical knowledge was all there is. Next, consider that brains are physical objects - there is no mind/brain dichotomy. Again, this is Rand's own conclusion. So your mental process themselves are physical in nature, and open to empirical uncertainty. And now you should easily be able to see that certainty is very likely to be impossible (although of course I do not state this with certainty, just a high probability).
If anyone can rebut me, fire away.
As to married bachelors: You may be uncertain as to whether a person is a bachelor or not, but not that there can be married bachelors, as marriage and bachelor are concepts that humans invented concerning the contractual state of a male in relation to some other female/male.
Without putting too much thought into this, human inventions, such as marriage and bachelor, are not empirical, as the moon is perceived, but are constructed/invented to indicate a state of relationship with another person. You seem to be confusing the two.
Brendan rebutted you there. Your argument has adopted the philosophy of Kant, not Rand! It was Kant who tried to classify knowledge into two different kinds. One kind he called 'analytic' (truth by definition or constructed/invented truth) and the other kind 'synthetic' (whose truth had to be established empirically). But the analytic/synthetic dichotomy is false! All knowledge is empirical in nature. Rand was right about this, surely. So there is no such thing as invented/constructed true concepts. Hence your argument is invalid.
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