11
votes
Accepted
Are pursuing the well-being and reducing the suffering of sentient beings objectively good things?
In the proposition IX, part III of Ethics, Spinoza operates the following reversal of concepts: it is not because we judge that something is good that we desire that thing, but it is because we desire ...
- 5,124
11
votes
Accepted
Is the fact that ZFC implies that 1+1=2 an absolute truth?
Is the fact that ZFC implies that 1+1=2 an absolute truth ?
No. it is possible to create or imagine systems of logic in which the axioms of ZFC are true but 1+1=2 is false (or, at least, not provable)...
- 274
10
votes
Accepted
What is the difference between depth and surface information?
1) Semantic Information
Let us start with what information is. Suppose we have a set of sentences we know to be true, this allows us to answer (some) questions about the world. As we learn more ...
- 42.5k
6
votes
Is the fact that ZFC implies that 1+1=2 an absolute truth?
Someone asked:
Isn't: 1 < 2, true everywhere?
My answer was thus:
In order to assign truth value to the proposition, one has to assign meaning to the symbols of the proposition. Else it is simply ...
- 2,143
6
votes
What does "unqualified notion of truth" mean in this passage?
You understood that correctly
A qualified truth is simply a truth that is conditioned, ie. the truth of it depends on other conditions.
In this case, a theorem is a qualified truth in the sense of it ...
- 13.5k
5
votes
What are the assumptions adopted by the scientific community?
There are varying assumptions, as not everyone agrees on what science is. However, there do seem to be some common patterns.
Indeed, the first common assumption is that "there are patterns in ...
- 17.5k
5
votes
Accepted
What kinds of proofs can be given for axioms, e.g. the modal axiom S5?
There are two general ways of "proving axioms": deductive and semantic. Deductively, one can take a different system with its own axioms, and ask whether the given "axiom" is deducible in it as a ...
- 42.5k
5
votes
Is it possible to create an axiomatic system where 1+1 doesn't equal 2? What would be the consequences of such a system?
Your question is grammatically sound but it sort of defeats itself by suggesting to rewrite definitions but then judge them by the old definition. I'm not accusing you of any illegal substance abuse, ...
- 1,292
3
votes
Accepted
Is faith required to believe any axiomatic assumption the scientific method is built upon?
First, let's define faith. What makes faith different from mere trust ? An effective definition is "belief in something without, or even in spite of, the evidence".
Boarding a plane trusting ...
- 5,124
3
votes
Accepted
Do contemporary logicians generally claim that classical logic can be simply reduced to these 5 logic principles?
I take your question to be, are the listed features sufficient to precisely and completely distinguish classical logic from all non-classical logics? There are certainly lots of other things one would ...
- 22.8k
3
votes
Are pursuing the well-being and reducing the suffering of sentient beings objectively good things?
Maximising wellbeing and avoiding suffering are just subjective heuristics required for evolution of replicating genes. A great deal of research shows things like having a job with autonomy is more ...
- 20.5k
3
votes
Is the fact that ZFC implies that 1+1=2 an absolute truth?
Yes, it is an absolute truth.
You are asking: "Is the fact that ZFC implies that 1+1=2 an absolute truth?"
Or equivalently: "Is the proposition ZFC implies that 1+1=2 an absolute truth?&...
- 1,972
2
votes
What are the assumptions adopted by the scientific community?
Most of science is a matter of testing the nature of external things to establish their properties and test causal relationships. That kind of work presupposes confidence in some stability of the ...
- 1,856
2
votes
Is constitution of a country simply a set of axioms?
Legal principles are axiomatic in the sense that they provide a rational framework... But they aren’t nearly precise enough to provide unambiguous resolution to specific legal arguments, and are maybe ...
- 9,482
2
votes
Accepted
Are axioms in mathematics comparable to hypotheses in experimental sciences?
To state it short, no. The two are not comparable.
Now for the long winded version: the question is simultaneously relevant to two branches of philosophy: philosophy of science and philosophy of ...
2
votes
Is constitution of a country simply a set of axioms?
In normal usage, an axiom is something that is self-evident or tautologically true. For instance, if we think about the algebraic reflexivity axiom (a=b ⬄ b=a) or Euclid's postulate that any line ...
- 18.5k
2
votes
Accepted
Do philosophers generally reject that philosophical reasoning relies on axioms?
If you look at how philosophy is usually taught and practiced, the answer you quoted is certainly correct.
At least in my experience the strict axiomatic method you took for granted is something you ...
- 116
2
votes
Does reality have axioms?
It's interesting to note Wigner's drawing attention to the unreasonable ineffectiveness of mathematics outside of physics
I think you make a mistake, confusing axioms, and 'atomic rules'. To ...
- 20.5k
2
votes
Do contemporary logicians generally claim that classical logic can be simply reduced to these 5 logic principles?
Short Answer
The answer to your question is at the start of the article you cited:
Each logical system in this class shares [these 5] characteristic properties... While not entailed by the preceding ...
- 22.8k
2
votes
Are pursuing the well-being and reducing the suffering of sentient beings objectively good things?
In light of your pre-assumed objective/subjective philosophical view, there're possibly several schools of thought to account for what's "good" for a person or a species. There's ...
- 3,843
2
votes
If axioms are subjective, how could anything be objective?
You can fix any group of axioms you like and start deducing consequences. You built a theory in that way. Your theory is useful if there are models of the theory that are interesting to someone and ...
- 129
2
votes
Is the fact that ZFC implies that 1+1=2 an absolute truth?
No proof in any formal system is a statement of absolute truth. It's a statement that given some axioms and some rules that we agree on, we can derive the validity of some proposition within the ...
- 2,818
2
votes
Is the fact that ZFC implies that 1+1=2 an absolute truth?
The word "absolute" itself is not absolute. "Absolute" is in opposition to "relative". It's generally easier to explain what "relative" means and then say that &...
- 7,474
2
votes
Basic truths as self-justified or parajustified
Talk of "self-evident" truths, sometimes called "axioms" (though "axiom" now carries mainly the sense of "not inferred," regardless of the attendant ...
- 12.3k
2
votes
Axiomatically prove □(A ∨ ¬B), ¬□A, ⊢ ◇¬B in modal system K
Please show that these derived rules hold.
(i): ☐(A -> B) -> (◇A -> ◇B)
(ii): ~☐A -> ◇~A.
Now recall that A or B is classically equivalent to ~A -> B.
- 2,099
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