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-1

If by this you mean for example a universe with two spatial dimensions and one of time, the answer is yes- at least in the world of physics. Physicists often try to formulate their theories in spaces simpler than (three space, one time) when it isn't known yet how to do it in (3+1) space. Then they look for clues in (for example) two-space, one time ...


8

There is a lot of writing both in favor and against AC from a philosophical standpoint - e.g. in favor see Penelope Maddy's Believing the axioms. However, there are also more mundane issues. I think that, whether or not it's ideal, a key point here is usability. An answer like this may seem dubiously appropriate at philosophy.stackexchange, but I think it'...


0

Afaik the theories of physics have no need to decide ERH. It is a metaphysical hypothesis of no concern in physics. I'm unable to think of a scientific theory that depends on ERH being true or false. This may be why no examples are given in the paper. ERH is not testable in physics so a theory dependent on it would not normally be considered scientific. ...


0

Wikipedia describes paraconsistent logic as follows: A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or "inconsistency-tolerant") systems of logic. Max Tegmark has four ...


-1

I don't think so. The subject of [formal proofs of mathematical logic] is 'formal proofs' or 'proofs'. The subject of [sound deductive inference] is 'sound deductive inference' or 'inference'. The subject of 'formal systems that have [deductively sound formal proofs of mathematical logic]' appears to be 'formal systems'. An inference is, among other ...


0

How about metaproof? I did a web search for the term, and found the following excerpt in a paper entitled, "'Metaproofs' (and their Cryptographic Applications)"1: We develop a non-interactive proof-system which we call “Metaproof” (µ-NIZK proof system); it provides a proof of “the existence of a proof to a statement”. This metamathematical notion ...


0

Two descriptors that may fit the requirement are non-constructive proof and pure existence proof. From wikipedia: In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an ...


0

Its true because of what we think of a single unit as. For example one apple or one stick. When you put them next to each other they preserve their identity or individuality. This is not true for all things. If you place a drop of water closer and closer to another, they eventually cohere into one drop of water. The point I'm making is that there are many ...


1

The eternal return not only requires infinite time but also a finite number of configurations that can take place during that infinite time. Wikipedia points this out by referencing Walter Kaufmann's quote of Heinrich Heine's earlier idea: Walter Kaufmann suggests that Nietzsche may have encountered this idea in the works of Heinrich Heine, who once ...


1

In Peano arithmetic 2 is defined as the successor of 1 (in symbols : s(1)) and 1 in turn is s(0). Thus : 2=s(s(0)). In the same way : 4=s(3)=s(s(s(s(0)))). To prove the equation : 2+2=4 amounts to prove : s(s(0))+s(s(0)) = s(s(s(s(0)))). Repeated application of the axiom : n+s(m)=s(n+m) will produce the desired result. The "number ...


0

It may be better to start with 0 as the pre-eminent number rather than 1 and leave 1 undefined except to the extent the successor function needed it for incrementing. This would allow one to conclude that these numbers exist as a set within logic. The successor function would define these numbers existing as members of the set. As members of a set they are "...


2

It depends on what you mean by semantics, and by "work strictly with what equations or statements express." (In fact, I think this is vague enough that the question is borderline unanswerable; however, what follows may help clarify the issues.) The first point I want to make is that in my opinion natural language isn't an appropriate proxy. Natural language ...


1

In truth-functional logic the semantic way to show validity is to use a truth table. The syntactic way would involve a derivation using rules of inference to go from any premises, line by line, to the conclusion. For example, suppose we want to show that the argument P, P → Q ∴ Q is valid. A Fitch-style natural deduction derivation would look like the ...


0

As said above, there are no extant works or fragments of Pythagoras. Ancient Pythagoreanism comprised sixth-, fifth- and fourth-century thinkers and many of them attributed their ideas to the founder of the school. Having said that, the source of Simone de Beauvoir seems to be Aristotle's overview of Pythagoreanism; see Met, Book I, 986a : the so-called ...


1

Neither Pythagoras nor a Pythagorean may have written the passage in question. One place to look for something like the passage would be Kenneth Sylvan Guthrie's The Complete Pythagoras which provides four surviving biographies of Pythagoras from antiquity and "a complete collection of the surviving fragments from the Pythagoreans". (page 1) Since Simone de ...


0

David Corner describes two kinds of miracles. Violation miracles are violations of natural law. However, getting 100 heads in a row does not violate any law of nature. It is merely unexpected. Hence it would not be a miracle. Coincidence miracles are not violations of natural law but they have to be "religiously significant". In this example God predicted ...


1

The famous 1964 paper of John Stewart Bell, in which "Bell's inequality" is established, begins by assuming two things. (The paper can be found here: https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf) One of them is "locality", which means (non-mathematically) that distant objects cannot affect one another instantaneously. Mathematically, Bell ...


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ZFC is susceptible to Gödel's incompleteness as was the Principia Mathematica. See Gödel’s Incompleteness Theorems for an introduction to the theorem : Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor ...


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Probability is the connection between the mathematical apparatus of quantum mechanics and experimental observation, data in the real world (it's what gives quantum mechanics the status of a scientific theory). A more appropriate question (for the philosophy section ) is related to the multitude of interpretations of quantum mechanics, but there is not ...


0

Probabilities in quantum mechanics always respect the calculus of probabilities by definition. The square amplitudes of a set of orthogonal states, which are the quantities used to compute probabilities in quantum mechanics, don't always respect the calculus of probability, see: https://arxiv.org/abs/math/9911150


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