Priceguy, I want to thank you for doing the scutwork here. I have tried to get Liberal to walk me through it in the past but have been unable to engage him as you have. This has been a fascinating thread to follow and I think what he has been saying is much clearer now.
As it happens, proving one’s own existence is logically impossible because of a logical fallacy called petitio principii (begging the question). In other words, in order to do anything at all, including prove that you exist, you must first exist, making your existence an unstated premise (audiatur et altera pars). Because your conclusion (that you exist) is the same as your premise (that you exist), your argument is circular and, although valid, is unsound and therefore worthless. Descarte’s own famous proof (“I think; therefore, I am”) falls victim to this.
Nor can one prove one’s own existence empirically. The problem, scientifically speaking, is a problem with the experiment. Your senses are themselves a part of the physical universe, and therefore any differentiation between you and the monitor you’re looking at is physically arbitrary (because it was assigned analytically). This becomes very apparent at the subquantum level, where one one string is indistinguishable from another except for its vibration. Emprically, you are nothing but a bag of mostly water. Your consciousness is a physical gestalt, and the fact that you are unable to experience any consciousness other than your own is convincing evidence that you are viewing the world entirely subjectively. And if existence is subjective, then it cannot be scientific. Falsification requires criteria that are objective.
One’s own existence, in the end, is a matter of faith.
Thank you for that advice, and for delivering it with such grace. My experience with you in this thread has edified me.
Can you make a distinction between discussing something like “evolution of species”, which deals with concrete objects, and “1+1=2” which deals with abstract concepts? You can’t handle one. You can’t pick two up, or find out what equals tastes like. They are not things - they are ideas, metaphysical constructs. “1+1=2” works because we’ve defined what 1 and 2 are, not because of something natural. And the math to understand this, and to start proving such things, is well beyond my abilities, and clearly beyond yours too. Math as a system is partially a human construct. So “1+1=2” doesn’t have meaning in the real world because there are no ones and twos to play with. There’s just things that we (somewhat arbitrarily in fact) declare to have the property of oneness or twoness.
That pretty much describes it. We group things because we like grouping them. That’s what cardinality is: grouping things into sets of a certain size. We also like to put things in some order that we perceive. And that’s what ordinality is: ordering things into sets of a certain precedence. Cardinality and ordinality are the two primary attributes of numbers.
We say there are two stones because we group a subset of stones together out of the whole set of stones, and assign the group a size: 2. But the nonconscious universe makes no such distinctions. It doesn’t group any number of stones. Neither do other animals. Birds group twigs, but not to count them. Beavers group logs, but again for a less abstract purpose.
Sorry to hijack, and please forgive my lack of education in the matter, although I do enjoy the little philosophy I do read. I have a question regarding the deductive proof of the special theory of relativity. How can someone say that the proof is deductive when the second axiom is inductive? (And, I think, in fact, by a very small percentage since the Big Ban not true.) It seems confusing to me that a deductive axiom rests upon a potentially flawed induction. The constant speed of light principle is based on the same induction that a non Peano-based proof would be, is it not?
All axioms are inductive. They are, by definition, offered without proof. It is from the axioms (or premises) that the inferences of deduction begin.
Liberal would you mind if I opened a thread to ask you more about axioms?
No, I wouldn’t mind. But there’s not a whole lot to it. An axiom is a premise that is offered without proof as the starting point for a deductive argument. If you think about it, there always has to be a first statement, and it obviously won’t follow from any other one.
I won’t bother to create a new thread since this thread seems to have died down already.
I understand what an axiom is, and I agree you have to have a first statement, but what I don’t understand is how a deduction can be considered a logical proof if it is possible that the initially inducted axiam can be flawed. Especially, since as I understand your arguments in this thread, a deduction is absolute (or closer to absolute, if that makes sense) and an induction which is contingent on not being falsified.
I will have to dig through my Penguin Dictionary of Philosophy this weekend, that and a few martinis will make this rainy weather tolerable. 
Well, not every deductive argument is a logical proof. To qualify as proof, it must meet three criteria: (1) it must be valid — that is, all its inferences must follow from each other in accordance with the rules of logic; (2) its axioms (or permises) must be true; and (3) it must contain no logical fallacies. A deductive argument that meets ALL those criteria is called “sound”. Every sound proof is incontrovertible.
So… it’s easy to determine whether the inferences follow the rules of logic (like modus ponens, modus tollens, etc.) or the argument contains logical fallacies (like petitio principii, circulus in demonstrando, etc.) But who determines whether the axioms are true? Well, you do. That is to say, every interpreter of the argument is entitled to accept or reject any or all axioms. Denial of an axiom is the ONLY intellectually honest way to deny the conclusion of a valid, well-formed argument.
Here are some examples:
Invalid
All cats die. Socrates is dead. Therefore, Socrates was a cat.
Fallacy of inference: affirmation of the consequent
Valid but unsound
All cats die. Socrates is dead. Therefore, every cat will die.
Fallacy of form: petitio principii
Valid but unsound
No cats die. Socrates is dead. Therefore, Socrates was not a cat.
Untrue premise
Sound
All cats die. Socrates is a cat. Therefore, Socrates will die.
The conclusion is inescapable.
“Denial of an axiom is the ONLY intellectually honest way to deny the conclusion of a valid, well-formed argument.” makes sense to me, and answers the unspoken question, thanks!
Would your argument constructs be considered syllogisms? I am probably just asking a very obvious question
I will let this thread go now, but since you have been so kind, I will probably hit you up with questions in the future… If for no other reason than to validate the adage that no good deed goes unpunished.
Yes, they were all syllogisms: major premise, minor premise, conclusion. See ya later.