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2 votes

Is mathematical truth empirical?

We can say that there are many questions whose answers coincide with the answers of mathematics, that are empirical. By an "empirical question," I mean a question that can be answered by ...
causative's user avatar
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1 vote

Is mathematical truth empirical?

Mathematics is not empirical: A mathematical proof is independent from any experience. It only relies on the correct application of the usual or a refined logic. To check new and original ideas on a ...
Jo Wehler's user avatar
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3 votes

Why Do Magnetic Field Lines Point Clockwise Around a Current?

Consider the magnetic field, the vector B, originating from a wire of infinite length with constant current density, the vector j pointing in positive z-direction. Then the vector B lies in the (x,y)-...
Jo Wehler's user avatar
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3 votes

Why Do Magnetic Field Lines Point Clockwise Around a Current?

Static magnetic fields have their characteristic shape because of (described mathematically by) Ampere's Law. Ampere's law is empirical; it was inferred from data, not derived from more fundamental ...
g s's user avatar
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0 votes

Why Do Magnetic Field Lines Point Clockwise Around a Current?

Change the direction the current is flowing, i.e. switch which terminals of the power source the ends of your wire are attached to.
JonathanZ's user avatar
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0 votes

Space and time in Kant and space and time in physics

It is a common confusion that the assertion that space and time are merely ideal is the core of Kant's theory of space-time. In any case, this part of his theory is far from contradicting contemporary ...
abracadabra's user avatar
2 votes

Distinction between classical essential (primary) and non-essential (secondary) properties of matter vs. modern primary-secondary qualities?

In Galileo's description of tickling, he adopts a subjectivist, agnostic philosophy because he denies that the nature of "feather," something beyond the senses, can be known; for him, sense ...
Geremia's user avatar
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1 vote

Are infinitesimals in the Newton and Leibniz calculus potential or actual?

The application of the actual/potential distinction to 17th century infinitesimals and/or infinite magnitudes is misguided. This can be demonstrated in a purely mathematical way as follows. Peano ...
Mikhail Katz's user avatar
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1 vote

Can falsehood be measured? If so, would it be continuous or discrete?

If I understand your question correctly, this is something that has a pretty well-established practice around it. I think a big stumbling block around this is that people tend to want to have a single ...
JimmyJames's user avatar
2 votes

Can falsehood be measured? If so, would it be continuous or discrete?

Don't worry about truth. For empirical science, we can compare the distance between our predictions and our measured values; smaller is better. This lets us iteratively improve. Our distances must be ...
Corbin's user avatar
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2 votes

Can falsehood be measured? If so, would it be continuous or discrete?

Given some measurement, if it is in reality 5 ft. And one theory say's it should be 1 ft, and another theory says is should be 4.9 ft, we can compute the error of one theory and says it's +- 4, while ...
Michael Carey's user avatar
3 votes

Can falsehood be measured? If so, would it be continuous or discrete?

Predictive statements - of which scientific theories are a subset - have a model, a domain, a precision, and a level of certitude. Take the statement: If Alice visits the corner store after midnight, ...
g s's user avatar
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2 votes

Can falsehood be measured? If so, would it be continuous or discrete?

Truth means correspondence to reality. A scientific theory either corresponds to reality or it doesn't. A scientific theory may solve a problem that another theory doesn't solve while having different ...
alanf's user avatar
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5 votes

Can falsehood be measured? If so, would it be continuous or discrete?

Fuzzy logic has infinitely many degrees of truth, for any real value from the interval [0, 1]. Truthlikeness (sometimes thought of as "proximity to the truth") is an even more subtle matter, ...
Kristian Berry's user avatar
4 votes

Can falsehood be measured? If so, would it be continuous or discrete?

All models are wrong, but some are useful (GEP Box) All scientific theories are models of reality, and they are all going to be wrong or incomplete in some detail. Asking for "truth" is an ...
Dikran Marsupial's user avatar
1 vote

Why are pure powers of the empty set insufficient as a definition for ordinals?

As Conifold and Michael Carey mentioned in the comments, the Zermelo ordinals do not extend to infinite sets. I want to emphasize this because it's very important to the way ordinal numbers are used. ...
Invariance's user avatar
6 votes

Why are pure powers of the empty set insufficient as a definition for ordinals?

The following sequence is called the “pure” or “irreducible” power sets of the empty set: {}, {{}}, {{{}}}, {{{{}}}}, … Conceptually, this sequence ‘represents’ order, to me. Why is it insufficient, ...
ac15's user avatar
  • 1,422
0 votes

Nothingness: What philosophical concept relates to how the empty set is a subset of every set?

Reading up on the very long chapter on Nothingness in the SEP, one does not find any particular stream of philosophers which expounded on the concept of the empty set as a trivial subset of every set ...
AnoE's user avatar
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0 votes

Was mathematics invented or discovered?

Indications are that mathematics is at its core a language. Arguably the most precise language in the human experience. As such it was invented with the caveat that it was more developed than ...
JOHNS WOOD GADGETS's user avatar
0 votes

Nothingness: What philosophical concept relates to how the empty set is a subset of every set?

Nothingness — a void, the non-existing — is the prerequisite for anything coming into existence. Something that has been created (the world by God, a poem by a poet, a pot by a potter) fills a place ...
Peter - Reinstate Monica's user avatar
-4 votes

Nothingness: What philosophical concept relates to how the empty set is a subset of every set?

Nothingness: What philosophical concept relates to how the empty set is a subset of every set? First, you are confusing the notion of nothingness with the idea that there is nothing, which is always ...
Speakpigeon's user avatar
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2 votes

What does the term "mathematical logic" mean?

Mathematical Logic and Computation, Jeremy Avigad(2022): In the phrase mathematical logic, the word “mathematical” is ambiguous. It can be taken to specify the methods used, so that the phrase refers ...
Poscat's user avatar
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4 votes

What are some critiques of my philosophy about approaching claims of truth using the scientific method?

Even though there has been evidence suggesting possible logical inconsistency (Godel Incompleteness), after 100 years of extensive use, no inconsistencies have appeared. This is simply wrong. The ...
user21820's user avatar
  • 496
-2 votes

What are some critiques of my philosophy about approaching claims of truth using the scientific method?

I must admit I did not understand what "your philosophy" is. But you are not alone. Many if not all of the philosophical terms you are using do not have a single accepted definition, and ...
AnoE's user avatar
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10 votes

Nothingness: What philosophical concept relates to how the empty set is a subset of every set?

In mathematics the empty set is defined as the set which has no element. A set A is a subset of a set B, if each element of A is also an element of B. If A is the empty set and B arbitrary, then there ...
Jo Wehler's user avatar
  • 31.7k
4 votes

What are some critiques of my philosophy about approaching claims of truth using the scientific method?

You might say, that we know 1 + 1 = 2 is certainly true. However, this is essentially a definition, following from the definition of the successor and addition operations. Given certain definitions (...
wizzwizz4's user avatar
  • 2,160
-1 votes

What are some critiques of my philosophy about approaching claims of truth using the scientific method?

Each time, I come to the conclusion that absolute truth about anything cannot be known. I have seen the Munchhausen Trilemma, and have not seen a satisfactory refutation of it. isn't the trilemma a ...
ac15's user avatar
  • 1,422
4 votes

Are all validities isomorphic or equivalent to valid proofs?

Are all validities isomorphic or equivalent to valid proofs? as it stands, the question does not make much sense, but what you may have in mind are soundness and completeness results for a formal ...
ac15's user avatar
  • 1,422
2 votes

Are all validities isomorphic or equivalent to valid proofs?

'Isomorphic' isn't the right term, but in first order classical logic, and many others, there is a simple relationship between a valid sentence and a valid argument form. For any given argument, you ...
Bumble's user avatar
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4 votes
Accepted

Are all validities isomorphic or equivalent to valid proofs?

You’re on the right track, but it’s worth noting that the notion of proof is dependent on which proof system you use, while the notion of valid argument form is more general. A valid argument just ...
PW_246's user avatar
  • 1,262
0 votes

Does Math use the scientific method?

Math does follow the scientific process. For example, the oldest mathematical discipline is arithmetic. This was originally a physical theory about individuals. It was at this stage that it was ...
Mozibur Ullah's user avatar
3 votes

Is the surprising applicability of mathematics to the physical world a brute fact, or something crying out for a theistic explanation?

Craig, Oppy: Premise... "mathematics is surprisingly applicable to physical reality, indicating God exists" Which mathematics is it, that are supposed to be "surprisingly applicable to ...
Alistair Riddoch's user avatar
0 votes

How can mathematical results impact the physical world?

Think of the dominoes as an extension of your phenotype (like a spider's web or the car you are driving). The pressing question is not what caused the last domino to fall but what caused the fall of ...
Niels Holst's user avatar
9 votes
Accepted

Can the laws of physics and the constants of nature exist in a fundamental sense without mathematical realism?

As is the case with many questions on this and related topics, the real difficulty in making any progress is that the word 'exist' and phrases such as 'exist in a fundamental sense' are inherently ...
Marco Ocram's user avatar
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5 votes

Can the laws of physics and the constants of nature exist in a fundamental sense without mathematical realism?

Can the laws of physics and fundamental constants of nature exist without fundamental mathematical constants, operators, and equations also existing? Kinda depends on what in particular you mean by &...
haxor789's user avatar
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0 votes

Is there a partly physical nature to infinitesimal limits that connects the utility of calculus with the quantized nature of small-scale physics?

Whether or not infinitesimals are to be found in "physical nature" was actually the subject of a dispute at the end of the 17th century, between Leibniz on the one hand and his disciples l'...
Mikhail Katz's user avatar
  • 1,351
1 vote

Are there recent coherence theory of truth for mathematical truths?

Two strands of coherentism in mathematics (one more alethic, the other more epistemic): firstly, "plenitudinous Platonism": This view is characterized by a plenitude principle to the effect ...
Kristian Berry's user avatar
1 vote

Is there a partly physical nature to infinitesimal limits that connects the utility of calculus with the quantized nature of small-scale physics?

Is there some part of abstract infinitesimal limits that is physical enough to justify calculus being inherent to physical nature? It doesn't seem to be the case that 'classical' calculus/analysis is ...
ac15's user avatar
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-3 votes

Is the surprising applicability of mathematics to the physical world a brute fact, or something crying out for a theistic explanation?

This site's post and edit functionality is HORRIBLE! This was properly edited and formatted. Now look at it! It will not let me space out the bottom part of my answer. I am really not interested in ...
series0's user avatar
4 votes

Is the surprising applicability of mathematics to the physical world a brute fact, or something crying out for a theistic explanation?

No one's really given what I think is the best answer yet. First of all, let's grant Premise 2 here. I think it is absolutely correct that mathematics is surprisingly applicable to the physical world. ...
user73418's user avatar
0 votes
Accepted

Is there a partly physical nature to infinitesimal limits that connects the utility of calculus with the quantized nature of small-scale physics?

Quantum mechanics discovered the importance of discrete physical quantities to formulate the laws of the microworld. This discovery did not diminuish the importance of calculus with its integrable, ...
Jo Wehler's user avatar
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1 vote

Is the surprising applicability of mathematics to the physical world a brute fact, or something crying out for a theistic explanation?

Null. Your question, Is the (surprising) applicability of mathematics to the physical world a brute fact or something crying out for a (theistic) explanation? only addresses two options. It does not ...
Line Item's user avatar
-1 votes

Was mathematics invented or discovered?

Not All Math is Equally Created Some invented. Some discovered. Some sought. Some built. Some inspired. Some devised. Some engineered. Some gets doodled into being. Math gets published. ...
Alistair Riddoch's user avatar
2 votes

Is the surprising applicability of mathematics to the physical world a brute fact, or something crying out for a theistic explanation?

From the transcript in the question (emphases mine): Oppy: ... We suppose also--and this is the only kind of new assumption that we're going to make to go along with the kind of metaphysical picture ...
Jed Schaaf's user avatar
3 votes

Is the surprising applicability of mathematics to the physical world a brute fact, or something crying out for a theistic explanation?

Mathematics is the study of assumptions, and the consequences of those assumptions. If, then. If x is a real number and x^2 + 6 = 5x, then x=2 or x=3. The natural numbers have applications to the ...
wizzwizz4's user avatar
  • 2,160
5 votes

Is the surprising applicability of mathematics to the physical world a brute fact, or something crying out for a theistic explanation?

No, the applicability of mathematics to the physical world is not surprising - to me at least, and evidently to many others - with or without explanation, theistic or otherwise. Nor is it necessarily ...
Corey's user avatar
  • 328
0 votes

Is the conceptual possibility of amorphous infinite sets "evidence against" countabilism?

A strong countabilist would likely choose to use at most PA or, say, some theory of hereditarily finite sets, so no 'infinite' objects of any kind to worry about For a classical weak countabilist, ...
ac15's user avatar
  • 1,422
3 votes

Simple question really: If pi is an irrational number, what does that say about circles and our measurements?

You are assuming that your pieces of thread have well-defined lengths, which is incorrect. To begin with, the length of the threads will vary with humidity and temperature. More fundamentally, however,...
Marco Ocram's user avatar
  • 21.7k
1 vote

Simple question really: If pi is an irrational number, what does that say about circles and our measurements?

All measurements and all ratios of measurements are rational because all measurements have a limited precision. Numbers can be irrational because they are abstract objects that can be specified to ...
g s's user avatar
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