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How to handle definitions in professional philosophic/scientific contexts?

So I had multiple instances, where a word in a paper or similar had to be defined. In the past, I employed or was thinking of employing various techniques to go about defining a certain word e.g.: I ...
telion's user avatar
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2 votes
0 answers
33 views

Axiomatic and formal establishment of Plato's dialectics

After years of studying Plato I have seen some attempts to formalize somehow Plato's dialectics. To be more precise, I have found writers who present Plato's dialectics (especially as it is presented ...
SK_'s user avatar
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3 votes
7 answers
214 views

Are two persons equally rational in choosing different dogmatic stopping points in their chains of justification as per the Münchhausen trilemma?

In epistemology, the Münchhausen trilemma is a thought experiment intended to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without ...
Mark's user avatar
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1 vote
0 answers
90 views

Completeness in finished system

Gödel's incompleteness theorems addresse formal axiomatic théories. Incompleteness of arithmetic of natural numbers is an example. My question is if a theory regarding a finite class of numbers cannot ...
kouty's user avatar
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11 votes
11 answers
3k views

Can axioms be false?

I have often wondered, can axioms be false? For example, I could take as an axiom that "Dogs don't exist", but that is false. To give a more mathematical example, I could take as an axiom ...
user107952's user avatar
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1 vote
1 answer
31 views

If it is verisimilar that A, is it verisimilar that it is verisimilar that A?

Truthlikeness, AKA verisimilitude or a function of "proximity to the truth," is such as when we might say, "The number of planets (in the Earth's solar system) is 10," vs., "...
Kristian Berry's user avatar
0 votes
0 answers
134 views

What are the First Principles of Euclidean Geometry (Besides the Axioms)?

On first principles, Wikipedia says: A first principle is an axiom that cannot be deduced from any other within that system. The classic example is that of Euclid's Elements; its hundreds of ...
DDS's user avatar
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6 votes
3 answers
610 views

What does "unqualified notion of truth" mean in this passage?

From pages 252-253 of The Laws of Truth by Nicholas Smith: If we consider bare, uninterpreted closed wffs, we can say that they are true in some models and false in others, but we cannot say that ...
user51462's user avatar
  • 483
2 votes
1 answer
98 views

Axioms for Non Duality

I am interested in teachings about non-duality and I was wondering whether there are any texts that build up assertions of non-duality from a set of axioms. I am aware of Spinoza's ethics and already ...
eeqesri's user avatar
  • 149
2 votes
4 answers
198 views

Is it legitimate in science to use two contradictory axiomatic systems?

For example, in Zermelo–Fraenkel set theory (ZF), the addition of the axiom of determinacy(AD) is inconsistent with the addition of the axiom of choice(AC). Is it legitimate to adopt ZFC (ZF+AC) as ...
BonBon's user avatar
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0 votes
2 answers
112 views

Axiomatically prove □(A ∨ ¬B), ¬□A, ⊢ ◇¬B in modal system K

This time I have a more "complex" problem at first glance. I need to create a direct proof using the axioms of system K and rules of inference, but I have been unable to do so. □(A ∨ ¬B), ¬□...
l0ner9's user avatar
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2 votes
1 answer
153 views

Basic truths as self-justified or parajustified

Some foundationalists maintain that basic truths are self-justifying, which means they are allowing, in some exceptional cases at least, a form of circular reasoning; petitio principii or begging the ...
user1113719's user avatar
-1 votes
1 answer
72 views

Could we use the foundation axiom to generate counterexamples to almost any substantial axiom?

Here's the argument scheme I have in mind ("F" refers to a substantial/positive property/description; negative qualifiers like "inaccessible" do not sustain this scheme correctly): ...
Kristian Berry's user avatar
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0 answers
46 views

Filling in the gaps in an erotetic argument for pluralism about the Continuum Hypothesis

Syntax assumption/stipulation. I have decided to work with an erotetic function that is parenthetical. So I will not start with some proposition A and then have A? as its associated question, but I ...
Kristian Berry's user avatar
1 vote
4 answers
172 views

Can there be a solution to these three problems?

I have read many times that some problems or logical propositions do not have solutions or are outright impossible. These are three examples of such problems: [The Russell's paradox] which is deemed ...
vengaq's user avatar
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0 answers
62 views

Do set theories have inconsistency strengths, on top of consistency strengths?

Caveat: this question is fairly technical in nature, and I have reason to believe it would be more fitting for the MathOverflow, especially in terms of potentially informative responses (there are ...
Kristian Berry's user avatar
11 votes
11 answers
6k views

Is the fact that ZFC implies that 1+1=2 an absolute truth?

This question is somehow of a follow up to to this other one, and it's something that has bugged me for a while. I understand the notion that there's no "absolute truth" in math, in the ...
Juan's user avatar
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1 vote
1 answer
161 views

If axioms are subjective, how could anything be objective?

Axioms are subjective (?), and, since propositions are based on axioms, isn't everything subjective? (of course, the answer should be from the perspective of someone who believes in objectivity) Or am ...
human's user avatar
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1 answer
128 views

Does Tarski Indefinability theorem impose a computational lower bound on the axiomatization of the reality?

Based on the Tarski's Indefinability Theorem (TA in standard model is not arithmetic (no FOL formula can represent TA, a formula represent a predicate relation definition: under Tarski's first order ...
LambdaDelta34's user avatar
0 votes
1 answer
92 views

Is the axiomatic method an inherently well-founded method?

It occurred to me a little while ago, that there is a trichotomy in set theory that maps to the positive solutions to the problem of the regress of inferential reasons. Namely, well-founded sets map ...
Kristian Berry's user avatar
1 vote
0 answers
75 views

The Anthropic principle as a physical embodiment of the Axiom of Choice

This question pertains to physical reality, but it would be deemed inappropriate in Physics.SE because of its speculative, metaphysical nature. It also touches on the subject of singling out elements ...
lurscher's user avatar
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1 vote
2 answers
218 views

Is there a proof that we can't prove a physical theory?

I am thinking of physical theories (e.g. Newtonian Mechanics) as axiomatic systems. We have a list of axioms and from there we can derive theorems, make predictions etc. If the prediction don't agree ...
Anton's user avatar
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-1 votes
1 answer
85 views

What does it mean for one geometrical axiom to be considered _equivalent_ to another geometrical axiom?

What does it mean for one geometrical axiom to be considered equivalent to another geometrical axiom? For example consider Playfair`s axiom: In a plane, given a line and a point not on it, at most one ...
Euclid Looked On Beauty Bare's user avatar
0 votes
1 answer
523 views

Are these valid examples of axiomatic statements?

I'm trying to understand if a couple of statements would be considered axiomatic: Example 1: "murder is the unjustified killing of a person; if there was a murder, then a person was killed ...
Kiril's user avatar
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1 vote
0 answers
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Axiom of Choice: correspondence or derivability?

I'd like to ask about a specific impression that I have about issues concerning the Axiom of Choice. It seems to me that either one claims that the axiom is an obvious fact about the modelled concept (...
user avatar
-1 votes
3 answers
168 views

Can the axioms of set theory be themselves well-ordered?

In "Independence and Large Cardinals", Peter Koellner writes: ... it turns out that when one restricts [attention] to those theories that "arise in nature" the interpretability ...
Kristian Berry's user avatar
6 votes
7 answers
3k views

Are pursuing the well-being and reducing the suffering of sentient beings objectively good things?

I think most people intuitively agree that increasing their own well-being and minimizing their own suffering are the right things to do. Everyone wants to be happy, enjoy a good health, etc. The ...
user avatar
1 vote
2 answers
121 views

How to construct logic from nothing as a step by step procedure? [closed]

I am thinking of constructing logic from scratch. I tried the law of thought as a fresh start but not totally convinced this is a correct way for the following reason: if law of identity is the first, ...
laziestperson1's user avatar
0 votes
3 answers
206 views

Do contemporary logicians generally claim that classical logic can be simply reduced to these 5 logic principles?

Do contemporary logicians generally claim, as Wikipedia does, that classical logic can be simply reduced to the 5 logical principles below? Or is it more complex than that and are there principles not ...
Sayaman's user avatar
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1 vote
0 answers
210 views

What is the current status of Foundation-of-Mathematics programmes?

I have been reading 'A Very Short Introduction to Mathematics' by Timothy Gowers and at one point he mentions that most of the mathematical proofs can be finally resolved to a set of logical ...
Tangent's user avatar
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9 votes
4 answers
430 views

Is faith required to believe any axiomatic assumption the scientific method is built upon?

It's my understanding that the scientific method builds upon certain axiomatic assumptions, such as uniformitarianism and the principle of induction. Is faith required to believe these axiomatic ...
user avatar
2 votes
4 answers
324 views

Is it possible to create an axiomatic system where 1+1 doesn't equal 2? What would be the consequences of such a system? [closed]

1+1=2 is a result (perhaps arguably more of a definition than a theorem?) of Peano Arithmetic, as well as other systems such as ZFC. I understand that 1+1 doesn't necessarily have to equal 2 if we ...
mark-antoin9977's user avatar
0 votes
1 answer
170 views

Why do we rely upon scientific approach when its foundational axioms are assumed and agreed without proof?

Why do we rely upon scientific approach when its foundational axioms are assumed and agreed without proof? Foundation of the scientific explorations are seem to be the mathematical axioms at its root....
Sazzad Hissain Khan's user avatar
3 votes
1 answer
592 views

Do philosophers generally reject that philosophical reasoning relies on axioms?

The way I've always thought that philosophy worked is that philosophers have a certain set of tools (deduction, laws of thought, basic sources of knowledge) which they use to come to reasoned answers ...
Chris's user avatar
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-1 votes
1 answer
141 views

In a deductive reasoning system, what happens if we have unfounded axioms? [closed]

What if our axioms are false? What happens then?
asdfasfasdgf's user avatar
2 votes
3 answers
588 views

What are the most rational basic beliefs?

I understand that this question might be difficult or even unresolved. But within a foundationalist view of knowledge, has anyone proposed a set of basic beliefs that seem to be the most rational for ...
blue-raven's user avatar
1 vote
4 answers
420 views

Do complex quantities and irrational numbers exist in nature?

Completeness Theorems of Model Theory, a branch of Mathematical Logic. Together, these two Theorems show that: under the Field Axioms (the rules of the game for scalars) existence of rationals is ...
zeraoulia rafik's user avatar
0 votes
0 answers
161 views

Is there an infinity of axioms in mathematics?

As I was trying to find a list of mathematical axioms used in modern branches of mathematics, I wondered if there's any meaning to the question of "how many mathematical axioms are there ?", and then ...
Gloserio's user avatar
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0 votes
0 answers
42 views

What are the axioms of personalism?

I've read some authors whose works are held as belonging to personalism. However while their works elaborated based on principles of personalism, they never clearly explained what the axioms were ...
bad_coder's user avatar
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2 votes
2 answers
456 views

How do philosophers formally characterise mathematical objects?

In the Stanford Encyclopedia of Philosophy article, 'Platonism in the Philosophy of Mathematics', the following formalisation is given for the existence of a mathematical object: Existence can be ...
Samuel's user avatar
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7 votes
7 answers
1k views

Does reality have axioms?

Mathematics is considered the queen of sciences as it allows us to build simplified but functional models of the reality that surrounds us. However, I do not understand if this isomorphism could be ...
Yamar69's user avatar
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0 votes
1 answer
234 views

What kinds of proofs can be given for axioms, e.g. the modal axiom S5?

From John Bigelow and Robert Pargetter's book, titled, 'Science and Necessity', they assert the following: . . . . The resulting system, S5, contains all the theorems of S4 and all the theorems of ...
Kurt Gödel's user avatar
0 votes
1 answer
105 views

Is it possible to prove that a particular statement cannot be disproved without creating a contradiction?

In the following link (http://www.importanceofphilosophy.com/Metaphysics_ExistenceExists.html) the authors are basically arguing that there are statements that we cannot deny without contradicting ...
TKN's user avatar
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1 vote
3 answers
870 views

What does it mean for a statement if we cannot disprove it?

In the following link (http://www.importanceofphilosophy.com/Metaphysics_ExistenceExists.html) the authors are basically arguing that there exists some truth that we cannot disprove by any other ...
TKN's user avatar
  • 355
0 votes
1 answer
73 views

How do we call a statement that is unthinkable for any person to not be the case? [duplicate]

The example of such an unthinkable or unimaginable thing for a person could be non-existence, therefore argument against existence seems to be so absurd. Aren't we calling such things axioms or ...
TKN's user avatar
  • 355
1 vote
2 answers
168 views

Do we have a name for the following axiom?: We can never know for sure whether we know everything that exists

Let's assume that our words and sentences are able to describe the truth. It is clear that whatever we know - even if we have knowledge about an entire universe and every position and momentum of its ...
TKN's user avatar
  • 355
5 votes
3 answers
378 views

Axiomatization of philosophy?

In mathematics, many theories are built on assumptions that are taken to be true, and they are most often called axioms, and then, with the help of logical laws and definitions and with various ...
Grešnik's user avatar
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1 vote
3 answers
286 views

Is constitution of a country simply a set of axioms?

Is it valid to think of a constitution or law in general as an axiomatic system? Because what they do is actually stating some rules one-by-one which we just accept. This means we accept also all ...
Turkhan Badalov's user avatar
0 votes
0 answers
23 views

Term for the idea that regardless of our philosophy, only the observable/physical matters

I'm looking for terms that define the following presuppositions: every action should be valued based on its outcomes, not choosing is a choice impact of an action must be valued based on the ...
Probably's user avatar
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0 votes
0 answers
95 views

Can social sciences have a non-subject -related axiomatic foundation? Why not?

Can social sciences have a non-subject -related axiomatic foundation? Why not? Problems: Interpretation is always relative to subjective interpretation. Which is not similar in natural sciences. In ...
mavavilj's user avatar
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