# Tag Info

28

We run into essentially the same problem almost any time we try to combine the real numbers as described by mathematics with probability theory. When applying probability theory to something like a coin flip, a die, or a deck of cards, we use what's known as a Probability Mass Function to assign a probability value to each possible result. What's the ...

13

Zeno's Paradox is not a paradox. It is an attack on loose thinking. By emphasising the infinite nature of one thing, and not mentioning the infinite nature of another, it confuses people into thinking something is impossible. The emphasis, in Zeno's Paradox, is upon the infinite number of times a distance can be subdivided, giving the impression that it ...

10

The problem is that probability 0 does not mean 'impossible'. If you have someone flip coins forever, what is the probability that he will never encounter a head? Well, it's zero. But it's possible! In fact, every specific infinite sequence of heads and tails is infinitely improbable; that is, its probability is zero. Still, none is impossible: one of them ...

9

A universe having a finite volume can be unbounded in length and have unbounded cross-sectional area. The example I have in mind is mathematical, not physical. It's called Gabriel's Horn. It's a standard example in first-year calculus. It's also called Toricelli's Trumpet, after Evangelista Torricelli, a student of Galileo. His discovery of this strange ...

8

There are some people who believe our universe is contained within a "multiverse" which contains all possibilities (which personally I find a depressing prospect, since it would arguably reduce to meaninglessness any given event happening anywhere). The "multiverse" is highly speculative, however, and there are plenty of other people who disbelieve in it ...

6

Look at what Peter van Inwagen says in his book "metaphysics" (an excellent read) on this issue. He accuses physicists who claim to have solved the philosophical problem of origin or creation of conflating the notion of "philosophical nothingness" with "physical nothingness". The problem with many answers from physics, as @infatuated pointed out, is they ...

6

Plato's thought has been hugely influential on world religions, with Platonic ideas having been integrated into Christianity (and arguably Islam), via the intermediary of Plotinus, a influential philosopher in the Platonic tradition. You can legitimately argue that Plato's orientation to philosophy is essentially religious, with the philosopher's ...

6

A question like, How can I prove something exists? must be placed in a context. Who is asking, and what will they accept as proof? In an ordinary everyday sort of way, it might be answered by saying that something is the object of our senses: I can prove this apple exists because I can see it, touch it, smell it, taste it. In less simple examples, one ...

6

Mathematics is a study. That requires an agent. From Wikipedia on Mathematics: Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. But the next sentence says: [Mathematics] has no generally accepted definition. ...and goes on to link to Definitions of ...

5

Think of ∀xP(x) as an implicit conditional: ∀x(xϵU → P(x)), where U is the universe. In an empty universe the antecedent is always false, hence the conditional is vacuously true. In contrast, ∃xP(x) is an implicit conjunction ∃x(xϵU ∧ P(x)), so it is vacuously false. This is in line with the standard way of transcribing "all humans are liars" with a ...

5

The issue is complex and any "significant" answer is hardly reducible to the Yes/No pattern. In modern mathematics, 2+2=4 is a theorem of arithmetic provable from Peano axioms. In a nutshell, assuming the definition of 1 as "the successor of 0" and of 2 as "the successor of 1" and ... and of 4 as "the successor of 3" (and thus "the successor of the ...

5

Theory of Everything does not explain everything The Theory of Everything is a hypothesized way of describing all four of the fundamentals forces within one theory. Today only three of those fit together, with Gravity being the odd one out. But even if we find out such a theory, that does not — in any way — describe everything else we need to do science ...

4

There's a whole bunch of related questions in there - too many for a concise answer. What you are asking is related to three main questions: 1. The question of strong AI, i.e. can there be a computer that does everything humans do? 2. The hard problem of consciousness: even if there is such a computer, would it be conscious like us? 3. The simulation ...

4

"Possible" really depends on what you have accepted as true Solipsism: Assuming you're the only perceiving being and everyone else is a figment of your imagination, your subconscious keeping you company then yes. Perhaps you're a lonely "God" who has created some world within their mind and proceeded to live inside it and wipe their mind of the memory of ...

4

What you describe is a fundamental aspect of probability distributions (in Mathematics), i.e. the probability of each point tends to zero, which is why probabilities are calculated on intervals or areas (in case here is an introduction). The smaller the interval the smaller the probability. At the level of a point, it is considered zero. Nevertheless, you ...

4

The problem is that all positions on the table have the same probability. That means the probability for the ashtray to hit any position on the table is zero. Not quite. The probability for the ashtray to hit any given position on the table is zero. But as you have observed, you can most certainly lay the arrow on the table and get a new position. ...

4

I will present a possible explanation for why the fiercest defenders of natural sciences often ended up with the most idealistic metaphysics in the history of the philosophy of science: Science is incomplete without a metaphysical background, i.e. methodological and ontological reflections on its very possibility. Hellmuth Plessner delivers a nice argument ...

4

There's a distinction dating from Frege (or earlier, perhaps the Stoics or Aristotle) between identity and individuation. There is no way of individuating the universe (taken as a whole of reality) since there is nothing (else) to distinguish it from. If, however, following Frege, we interpret identity as continuity over time, there seems no insuperable ...

4

Using the links provided by the OP, there are differences in concepts and results between pandeism and atheism. For pandeism, the Wikipedia link states: Pandeism ... holds that the creator deity became the universe (pantheism) and ceased to exist as a separate and conscious entity (deism holding that God does not interfere with the universe after its ...

3

Yes, there have been attempts to construct different rules for logic. You list some of them in your question, i.e. modal, fuzzy, etc. A more radical revision is paraconsistent logic, which does not accept the law of noncontradiction. Logics that deviate from classical logic are called (not surprisingly) non-classical logics. A great survey of them, both of a ...

3

I think the answer to your question also depends on the definition of 'Falling' as well as the definition of 'Bottomless Pit'. If endless free-fall is your goal, pretty much any ol' orbit will do. You will be constantly falling, but barring a chance collision with an object whose orbit crosses your own at just the right time you would never collide with ...

3

A black hole is effectively a bottomless pit because as something falls closer to it the relative time slows down and approaches zero. As long as the object being dropped into a black hole does not collide with anything else on its way then it will effectively fall for the entire life of the black hole which is/may be infinite (depending on which theory you ...

3

It sounds like you're referring to the "Law of Cause and Effect," which tells us that every material effect has a prior cause. I counter that your question is an example of special pleading, suggesting that everything requires a cause, except for this super special uncaused cause which started everything. Either every "cause requires a cause" or "not every ...

3

Pi is not infinite; indeed it is smaller than the very finite number 4. What is infinite is the number of digits you need to represent pi in decimal representation. But that's a thing it shares with every irrational number, like the square root of 2, the golden mean, or the Euler number e. Moreover, this cyclic universe you describe was never the mainstream ...

3

I think your reasoning is is begging the question. You define infinity like this: Infinity = a place where everything every human being ever thought of or will think of physically exists, no matter whether it defies the laws of physics or logic. Of course, in this definition, everything you think of exists in "the void of infinity". But is this really the ...

3

You mention the big bang, which would place the question into the realm of physics and not philosophy. There are various answers to the question, "Where did the universe come from?" in physics but I believe in general these assume it did not come from nothing (excepting the quantum definition of "nothing", which is perhaps a deflection of your question). ...

3

I hate to rain on your parade ( I hope it was good stuff ), but our science and philosophy posits a formal law called The Second Law of Thermodynamics. This law says that our universe is moving from a state of order to a state of disorder, or chaos. Although nature (or ourselves) can intervene locally to impose order on the environment, the universe as a ...

3

Your position is phrased as a definition, so the assumption that it is true is tautological. If you assume that the word "object" can be defined by a set of atoms, and you assume there is a finite number of atoms (which is science's best guess, but not certain), then by definition there are a finite number of objects. The question that does remain is "is ...

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