25
votes
Accepted
Does every truth have to be provable based on evidence?
The answer is a point of contention between realism and anti-realism. Truths that "do not have evidence" are termed verification-transcendent truths (coined by Dummett), and realists are committed to ...
- 42.3k
24
votes
How to prove (A v B), (A → C), (B → D) therefore (C v D)
Here is part of the question:
My only idea is v must be introduced, but how would I use subproofs to show one of A/\C or B/\D is never false if A v B?
It might be best to think of using ...
- 19.2k
17
votes
Is watching an amputated limb regrow proof of the supernatural?
Logically, if we could prove that God healed amputees then it would as a corollary prove the existence of God. (it is simply the argument that; "if X is specifically observed to do Y, then X must ...
- 2,512
14
votes
Does software exist to automatically validate an argument?
You are looking for a so-called automated theorem prover.
See e.g. pyPL or Tree Proof Generator for two implementations of the calculus of analytic tableaux for classical propositional and first-order ...
- 2,489
14
votes
Can we doubt all knowledge?
To answer the question in the title:
Yes. That's a key trait of any good scientist.
To answer your last question in the body:
Because we have no better option to depend on or behave according to.
- 275
13
votes
What makes something mathematics?
Both definitions are outdated. As Husserl put it already back in 1901:
"Only if one is ignorant of the modern science of mathematics, particularly of formal mathematics, and measures it by ...
- 42.3k
13
votes
Does theism have the burden of proof?
First of all "the burden of proof" is a matter of "sportsmanship" not logic. Where the idea is that the person making a claim, demanding change or accusing someone of something is ...
- 4,337
11
votes
Is watching an amputated limb regrow proof of the supernatural?
The term 'supernatural' is generally used by modern skeptics in the sense: "That which cannot be explained by natural processes using the natural sciences." However, any event that can be ...
- 18k
11
votes
Accepted
Is watching an amputated limb regrow proof of the supernatural?
Short Answer
As an athiest who advocates for philosophy, I would suggest there would be many rational bases for attacking your attribution of the regrowth to the supernatural which by definition ...
- 20.6k
11
votes
Can we doubt all knowledge?
You can of course do anything you want... But to doubt all knowledge is to indulge in radical skepticism, is it not? If we were all radical skeptics, then we'd be living in a world in which knowledge ...
- 7,473
11
votes
Does theism have the burden of proof?
It seems like the other answers so far, and the question itself, do not clarify what is meant by "God". The definition really matters.
If God is treated as an entity just like any other ...
- 227
10
votes
How is Wittgenstein’s “notorious paragraph” about the Gödel's Theorem not obviously correct?
Timm Lampert, cited by the OP, quotes Wittgenstein (§8 of Remarks on the Foundations of Mathematics, Appendix 3):
‘True in Russell’s system’ means, as was said: proved in Russell’s system; and ‘...
- 19.2k
9
votes
Accepted
Does predicate logic have truth tables?
NO, because validity for predicate logic means true in all interpretations, and thus we have to take into account also interpretations with infinite domains, like the set N of natural numbers.
Every ...
- 35.9k
9
votes
Proof for the absence of free will?
Seems like no one brought up Frankfurt and hierarchical compatabilism.
First-order desires: desires that are directed to objects or states of affairs.
We desire things like being healthy, being well-...
- 2,302
8
votes
Is a proof still valid if only the author understands it?
"A language that I don't understand is no language." (Wittgenstein, MS 109)
Is a proof still valid if only the author understands it?
I do not think so.
See Yuri Manin, A Course in Mathematical ...
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8
votes
Accepted
Are axioms tautologies?
It is worth separating the logic from the epistemology. Let's start with the logic.
A (first order) theory is a set of sentences. Usually we are interested in deductive systems, so we require a ...
- 22.2k
8
votes
Can we logically prove that anything exists?
IMO, there are two related but different issues here.
We prove statements : in math and logic we prove a theorem from axioms. There is no way of proving a statement "from scratch", i.e. without ...
- 35.9k
8
votes
How to prove (A v B), (A → C), (B → D) therefore (C v D)
You can use proof by contradiction:
p1: A v B
p2: A -> C
p3: B -> D
assume ~(C v D)
~C & ~D (from 1, De Morgan's law)
~C (from 2, conjunction elimination)
~D (from 2, conjunction elimination)
~...
- 81
8
votes
Accepted
How to show (in a hand waving manner) that the Godel sentence is true
Gödel’s Incompleteness Theorem is a result about formal systems.
Its proof requires certain assumptions about the properties of specific formal system F: basically, about its "expressive capabilities"...
- 35.9k
7
votes
Given P ∨ ¬ P prove (P → Q) → ((¬ P → Q) → Q) by natural deduction
1) P ∨ ¬ P --- premise
2) (P → Q) --- assumed [a]
3) (¬ P → Q) --- assumed [b]
4) P --- assumed [c] for ∨-elimination
5) Q --- from 4 and 2 by →-elimination
6) ¬ P --- assumed [d] for ∨-...
- 35.9k
7
votes
Accepted
How to find redundant premises?
Regarding the statement from your question:
"it isn't valid"
By definition, an argument is valid if the premises and our accepted working of logical rules create a situation such that if all of ...
- 815
7
votes
Accepted
The difference between argument, inference, deduction and proof?
One issue is that different authors use "argument" and "inference" in ways different from each other, and from the colloquial meaning. For example, your source interprets "argument" as just the list ...
- 42.3k
7
votes
Is any aspect of the supernatural testable? What level of proof is possible for the supernatural?
Yes, of course.
You can *scientifically prove** things deemed supernatural. But once you do, they are no longer supernatural. They are "natural," as demonstrated by the methods of the natural ...
- 13.3k
7
votes
Proof for the absence of free will?
This argument constructs a paradox of the type popularized by Zeno, i.e.:
one cannot do x until one has done x'
one cannot do x' until one has done x''
one cannot do x'' until one has done x'''...
...
- 18k
7
votes
Does theism have the burden of proof?
A few, ex mea sententia, salient points:
A positive claim precedes a negative claim. The statement God exists comes before its negation that God does not exist. The onus probandi falls on the ...
- 2,868
6
votes
What makes something mathematics?
From a modern point of view mathematics is considered the science of formal structures. Simple examples of such structures are topological spaces, groups, vector spaces, differentiable manifolds.
A ...
- 20.8k
6
votes
What is the relation between proof in mathematics and observation in physics?
This point of view is better reflected if we change "observation" to "experiment" in the title, mere observation is more analogous to conjecture, so it may be somewhat misleading. This is how Jaffe ...
- 42.3k
6
votes
Accepted
How do you prove A <-> C given the following premises?
given that the two main things you need to prove are A -> C and C -> A. As a general strategy, it is often the easiest to do so with conditional proofs. Given the three assumptions you've been given, ...
- 24.5k
6
votes
Accepted
The Principle of Explosion v. Reductio ad Absurdum
In classical and intuitionistic logic, the Principle of Explosion is often a basic law of inference.
Wiki's entry deduces it from Disjunctive syllogism:
Assume P as true; then (by Disjunction ...
- 35.9k
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