This only works if you already have the concept of "one", and "two" as the whole number that comes after "one". It is otherwise impossible for you to make this observation.
That there is such a thing as a concept is kind of the point. They are distinct from percepts, and percepts are insufficient by themselves to justify any knowledge claim.
It's not so much a game as a response to a claim.
I'd go a step further and say that once you've got a set of foundations that work for you, might as well give the metaphysics hat to Good Will. The only thing that tends to sway people after that is basically down to vibes.
Thanks, Peano.
This isn't some esoteric point, and I'm surprised that someone who calls Goedel, Escher, Bach all you need to know about propositional logic would even attempt this argument. Hofstadter is definitely not an "all knowledge is a posteriori" guy.
No, he's not. But it is true that the book contains within it a comprehensive breakdown of propositional logic, which if you will observe, is all that I have claimed.
He is talking about mathematics and other kinds of axiomatic truths. Logical proofs that are true according to some arbitrary rule set, not because of empirical observation. To me it's all the same thing, but he makes a distinction.
There are many examples of that, but here's one of the more famous.
Well, 150 years ago my family were Indian fighters. If a local tribe went hostile the logical and ethical move was to kill them all. 150 years later this is no longer a logical nor ethical move.
It's a distinction most commonly argued by people who want to wedge a specific belief into the perceived gap between empirical science and the body of all knowledge.
His rant in Portuguese (now banished to the hall of shame) explicitly mentioned rhetoric against "pseudo-skeptics" for improperly rejecting claims on an ideological basis rather than for good rational reasons. Again, whether he intends to argue a paranormal claim or not, he is quoting paranormal-coded rhetoric almost verbatim. And since that latest rant was in his native language, the claim that he can't know what kind of English is being produced becoemes irrelevant. All that's left for him to stand on is the accepted conclusion that the post was generated by AI in Portuguese, and he may yet not understand that his AI is expressly pulling from paranormal-coded arguments in whatever language.
I wouldn't be surprised if his AI is giving him paranormal-coded answers because he's giving it paranormal-coded questions.
...which is why it's sensible that our rules require disclosing the AI prompts. My experience with LLMs is that it's pretty easy to get them to stumble into coded language even when the prompt does not telegraph it. Inasmuch as the OP denies he is advocating for paranormal claims, I'm inclined to take that at face value as long as there remains the possibility that his AI is producing coded language inadvertently. But that's only because it's Friday and I feel generous today.
Whenever someone starts ranting about "pseudo-skeptics", like "social justice warriors" or "woke" it's an excellent sign they have nothing useful to say.
No, you can't. You need the concepts first. There are literally people in the world who are anumeric, for whom this is not an adequate demonstration.
That there are exceptions does not disprove the general principle.
Actually yes, it is good.
Actual is defined as:-
Where real is defined as:-
Only empirical properties of the physical world are 'facts' (aka 'information'). 'I have two ears' is a fact. 1 + 1 = 2 is true in the decimal numbering system, but it doesn't mean I have 2 ears.
Good question. Scientism says you can only know something is a fact if you have empirical data from the physical world, to which you apply the scientific method to determine the truth about it. The paranormal fails this test. Quite a bit of 'science' also fails. But that doesn't apply to mathematical, logical, philosophical or ethical truths.
