honestrosewater said:
The example given ("3+2=5" entails "2+3=5") has no epistemic value unless evaluated in terms of other logical statements, in this case axioms, and notably the commutative property of addition. In other words, it Have I misunderstood something? Perhaps the point is that we can theoretically know everything in the formal world, but not in the physical world. And I'm not yet sure that's true.
You are close. My point is that we can know that our logic is correct, but we cannot know if the conclusion of correct premises
corresponds to an actual circumstance in reality. I emphasized "corresponds" to let you know my preference for determining the truth of statements is the
correspondence theory of truth. That is, a statement is true when it corresponds with the way reality actually is.
Consider the example of 3+2=5 entails 2+3=5. In the world of math/logic, it is a perfect inference. Will physical reality correspond every time to that statement? Notice the only difference is the order of 2 and 3. Let's say in reality there is a combination of two materials, 2 pints of one, and three pints of the other, that is altered by which is added to the other; the 2+3 order produces 5 pints, but 3+2 order causes one material to absorb more of other and consequently reduces the overall volume from 5 to 4.9.
For me, logic is nothing without an actual reality to relate it to. Another variety of thinker believes reason alone can produce truths. I have never been able to accept that.
honestrosewater said:
In your snake bite example, the doctor makes inductive inferences, notably that the presence of bite wounds implies the presence of venom. I doubt she could tell they were sea snake bite wounds either- the size of the fangs would be the only evidence I can think of which could be precise enough (quantifiable, measurable to a given degree of precision), and the variation of fang size within sea snakes and all fanged snakes should make a unique match impossible. Even if the person was bitten while in waters sea snakes are known to inhabit, and so on...
However, if the victim observed everything possible for him to observe about the snakes that bit him, the situation gets interesting.
P: every observable fact about the snakes that bit him
Q: every observable fact about all snakes
Assuming the victim knows p, and the doctor knows q. Can they figure out what kind of snake bit him?
Let's take away all the ambiguity except what the issue is we are trying to decide. Let's say the doctor was diving with her husband, and it was he who got bit. The doctor is also a herpetologist, has perfect vision, can count to 30, and recognized the snakes. Since she herself witnessed the event, the doctor is certain 30 sea snakes bit the man. Let's add one more fact. No sea snake has ever been observed biting a human without injecting venom.
To restate your statement in terms of my question of closure:
P: every observable fact about the snakes that bit him
Q: every PAST observable fact about all snakes ("past" is added because all we know for certain is how things have been)
Assuming the doctor knows P and Q, does she know her husband's life is in danger? Or is it the case that rather than "know," the doctor is "reasonably certain" her husband's life is in danger?