Good idea and a very natural attempt; but arithmetic properties aren't sufficient. Weirder still, there are numbers that lose associativity as well, such as the octonions. — fishfry
In short though, mathematical structuralism is more subtle than just listing arithmetic properties like associativity.The kinds of properties that they use in category theory are ... well, they're kind of weird and nonintuitive when you first see them. The structural relations they have in mind are various types of universal mapping properties. It's hard to do justice to what this means in a simplified format but I might take a run at it once I get into responding in detail to your earlier post on structuralism. — fishfry
I'm not sure what you mean by "next physical state", but the "program" in my example would clearly be the software in yours. — JustSomeGuy
It's not a "folk psychology misconception", it's just how we talk about these things. It has to do with language, that's all. I think you're the one getting dogged by being nit-picky about language. — JustSomeGuy
Using the computer analogy, if you're running a program on some hardware, that program has to be pre-written to follow certain parameters and do certain things, and everything it does is a result of the program's code. Even if you bring artificial intelligence into it, a program that can learn, it still does everything it does based on the initial code you wrote. Every "decision" it makes is a direct result of following this code. It is all determined by the code (as well as other environmental/outside factors). — JustSomeGuy
Point being, if your brain's processing and decision making are a product of this program, they do what they do automatically, meaning none of your decisions are true decisions because you could not possibly make a different decision than the one you make. — JustSomeGuy
You are talking rubbish and I am probably one of the few people here who can see straight through you. — TimeLine
This is the third time I am going to ask you:
What is this "humongously" large you are speaking of? What are you comparing it to, exactly? — TimeLine
The idea in inflationary terms is that the total energy at the beginning was 0 where the negative contribution to the energy of the cosmic gravitational field - as in gravitational repulsion where the energy density produces these gravitational fields - cancels the energy of matter or the positive energy. Inflation thus becomes eternal because as mentioned earlier the matter is being created by the inflation but controlled by the non-uniformity. — TimeLine
If inflation is pushing omega to 1 with omega being the mass density divided by critical mass density, it means a universe with 0 matter density and critical mass density in the cosmological constant; the expansion of the universe is accelerating and the vacuum energy of this empty space has a mass density (which would mean that it is not actually empty). So Omega is relevant. — TimeLine
Clicking on the graph shows that (nearly) all universes start at the Einstein-de Sitter point with Omega(m) = 1 and Omega(Lambda)=0. This is because if there is a Big Bang (R goes to zero) the density, hence H, hence the critical density, all tend to infinity at R = 0. So Omega(Lambda) tends to zero, while the matter density tends to the critical density.
As far as these experiments tell us anything about free will, they really should be seen as part of a continuum of study on the neurological markers of decision making processes, rather then in isolation. — Pseudonym
I think you just want all the glory or something, hence why you are trying to answer questions directed to me. — TimeLine
Your shape and size of the universe is the observable universe of 46gly from earth and just to help ameliorate your understanding, the singularity - whilst it does not reference a single planck point - is a physically impossible point that we use to explain how the universe came to be. So the assumption is that the early conditions were infinitely dense at the size of 10^-28cm (with energies at 10^16 GeV) and that would mean that anything larger or smaller would blow the universe apart or suck it away — TimeLine
What? First of all, inflation is pushing omega to 1 and the asymptotic curvature would therefore be flattened by the expansion, thus the curvature would equal 0 or at least be very close to 0 and this would cause infinite expansion. The symmetry between these points is explained by fluctuations in the anisotropy of the cosmic microwave background and so the universe is isotropic and homogenous; the best way to explain thermal equilibrium (actually the only as far as I know) is inflation. — TimeLine
It seems that, by current findings, big bang inflation + expansion does not account for the spatial extent of the universe. — jorndoe
When we say "infinite" do we mean infinite volume or infinite mass? Both? Or something else? — T Clark
My remark is entirely agnostic of foundational approach, a point apokrisis does not sufficiently appreciate.
There is no general definition in math that tells us what a number is. — fishfry
how can a universe that has expanded from a point explosion be anything other than a sphere, — T Clark
And while we're on the subject, how can portions of the universe which were next to each other 14 billion years ago be more than 14 billion light-years apart now? — T Clark
... which, in turn, suggests that something is missing. — jorndoe
Perhaps something an established unification of relativity and quantum mechanics could shed light on? — jorndoe
To the extent that he associates race with riches, there's a racist element to his thought, but primarily he's thoughtless and speaks from his gut fear of / contempt for the dispossessed. — Baden
Donald Trump, who has on many occasions called the tradition of shaking hands “barbaric,” confessed in his 1997 book The Art of the Comeback: “One of the curses of American society is the simple act of shaking hands, and the more successful and famous one becomes the worse this terrible custom seems to get. I happen to be a clean hands freak. I feel much better after I thoroughly wash my hands, which I do as much as possible.”
But Trump’s germophobia goes beyond an unwillingness to shake hands—an aversion he has had to forgo during his run for the presidency. Trump is also reported to have a preference for drinking with straws and eating pizza with a fork, a distaste for pressing elevator buttons and a revulsion to fans and the public getting too close to him, such as for autographs.
In an op-ed for the U.K. newspaper The Independent, Gurnek Bains, author of Cultural DNA: The Psychology of Globalization and founder of a corporate psychology consultancy, suggests that Trump’s fear of communicable diseases is the root of his anti-immigrant political stances.
His obsession with cleanliness is why he prefers mass-produced or processed food. His preferences are not complicated: KFC. McDonald’s. The occasional taco bowl.
“I like See’s Candies.” “I like hamburgers.” “I’m an ice cream fan from way back.”
“I don’t like rich sauces or fine wines,” Trump wrote in his book Surviving at the Top. “I like to eat steak rather than pheasant under glass.” So long as the steak is well-done—so well-done, according to his longtime butler, “it would rock on the plate.”
His simplistic palate is a function of his desire for cleanliness. “One bad hamburger, you can destroy McDonald’s,” he explained to CNN’s Anderson Cooper earlier this year. “I’m a very clean person. I like cleanliness, and I think you’re better off going there than maybe someplace that you have no idea where the food’s coming from. It’s a certain standard.”
https://www.politico.com/magazine/story/2016/10/the-7-oddest-things-donald-trump-thinks-214354
The entire observable universe is finite. — tom
A bit like the old questions, only more pressing. — tom
Saying that a number is anything that's number-like is a circular definition. No better than the poster above who said that a quantity is anything that's quantitative. You are defining a thing in terms of itself. It's not a definition. — fishfry
Matrices can be added, subtracted, multiplied, and sometimes divided. In fact the set of nxn matrices for fixed n forms a ring, an important algebraic structure. But matrices are not regarded as numbers. — fishfry
I was surprised at the, let's say, passion of some of the responses to this tame and factual assertion. — fishfry
It's surprisingly tricky to give a good definition of number. I hope my examples bear that out. — fishfry
The paper that proves that any finite physical system may be emulated... — tom
The statement of the Church-Turing principle (1.2) is stronger than what is strictly necessitated by (1.1). Indeed it is so strong that it is not satisfied by Turing’s machine in classical physics. Owing to the continuity of classical dynamics, the possible states of a classical system necessarily form a continuum. Yet there are only countably many ways of preparing a finite input for T . Consequently T cannot perfectly simulate any classical dynamical system.
“Why are we having all these people from shithole countries come here?” Trump said, after being presented with a proposal to restore protections for immigrants from those countries as part of a bipartisan immigration deal.
I don't deny colonialism — Thorongil
If a country wants to refuse you entry, they can, and it's tough luck for you. — Thorongil
New Orleans was a shithole before Katrina though, and that's why Houston didn't want New Orleanese coming there. — Hanover
Early reporting during Hurricane Katrina heavily used racist tropes and stereotypical narratives that often vilified the victims of the hurricane, whose impact disproportionately affected the low-income, but vibrant Black communities of New Orleans.
During the crisis, commentators from CNN to Fox News lampooned Black and poor New Orleanians for being unable to leave the city quick enough, while others devoted special news segments highlighting the “criminal element,” which condemned the “looting” by Black residents, many of whom had just lost their homes, their possessions, and who were facing dehydration and starvation.
These early reports helped shape the narrative that some were undeserving of national assistance and help, while heavily drawing on historical fears and tropes of a scary, lazy, poor Black underclass that is deserving of oppression and neglect.
https://www.telesurtv.net/english/analysis/Deserving-and-Undeserving-Victims-Reporting-Hurricane-Katrina--20150827-0041.html
You seem to be one of those people who imagines precolonial life in countries like Haiti to be paradises without problems. — Buxtebuddha
Before the arrival of Europeans, Arawak (also known as Taino) and Carib Indians inhabited the island of Hispaniola. Although researchers debate the total pre-Columbian population (estimates range from 60,000 to 600,000), the detrimental impact of colonization is well documented. Disease and brutal labor practices nearly annihilated the Indian population within 50 years of Columbus’s arrival.
www.nationsonline.org/oneworld/History/Haiti-history.htm
We come to know moral truths in a very similar way to how we come to know mathematical or logical truths — darthbarracuda
Ethical intuitionism suffered a dramatic fall from favor by the middle of the century, due in part to the influence of logical positivism, in part to the rising popularity of naturalism in philosophy, and in part to philosophical objections based on the phenomenon of widespread moral disagreement. C. L. Stevenson's emotivism would prove especially attractive to Moorean intuitionists seeking to avoid ethical naturalism.[11] In the later parts of the 20th century, intuitionism would have few adherents to speak of; in Bernard Williams' words: "This model of intuition in ethics has been demolished by a succession of critics, and the ruins of it that remain above ground are not impressive enough to invite much history of what happened to it."
https://en.m.wikipedia.org/wiki/Ethical_intuitionism
A country is a great or terrible place regardless of why. — Hanover
The links you provide prove the opposite of your argument. — Buxtebuddha
So, Mr. Politically Correct, how many Congoians would you want coming to the UK versus how many Dutch would you want? — Hanover
A sovereign nation can pick and choose who immigrates to it for a variety of reasons. The operative reason for denying Haitians, say, might be that they wouldn't contribute economically. — Thorongil
The Congo Crisis (French: Crise congolaise) was a period of political upheaval and conflict in the Republic of the Congo (today the Democratic Republic of the Congo)[c] between 1960 and 1965. It began almost immediately after the Congo became independent from Belgium and ended, unofficially, with the entire country under the rule of Joseph-Désiré Mobutu. Constituting a series of civil wars, the Congo Crisis was also a proxy conflict in the Cold War, in which the Soviet Union and United States supported opposing factions.
https://en.wikipedia.org/wiki/Congo_Crisis
Haitian poverty is a deep-seeded problem that started many years ago. During the 1700's Haiti was under French rule and was the wealthiest country in the New World and represented a quarter of France's economy. In 1801 a Haitian slave revolt defeated the French army and the newly independent colony became the first country in the New World to abolish slavery. France agreed to recognize Haitian independence if Haiti paid a large indemnity. This kept Haiti in a constant state of debt and put France in a position of power over Haiti's trade and finances.
The 20th century brought three decades of American occupation, multiple corrupt regimes, natural disasters, environmental devastation and HIV to Haiti. The United States gained complete control over Haitian finances, and the right to intervene in Haiti whenever the U.S. Government deemed necessary. The U.S. Government also forced the election of a new pro-American President, Philippe Sudré Dartiguenave, by the Haitian legislature in August of 1915. The selection of a President that did not represent the choice of the Haitian populace increased unrest in Haiti. In 1929, a series of strikes and uprisings led the United States to begin withdrawal from Haiti. By the time U.S occupation ceased in 1934, Haiti was left with a decimated economy and facing a future full of poverty and desperation.
http://poverty-haiti.weebly.com/causes-of-poverty-in-haiti.html
Yet there is not one single definition of number. It's an amorphous concept. Mathematicians "know one when they see one." I don't know if this has caught the attention of philosophers. But there is no definition of number. — fishfry
The theme of mathematical structuralism is that what matters to a mathematical theory is not the internal nature of its objects, such as its numbers, functions, sets, or points, but how those objects relate to each other. In a sense, the thesis is that mathematical objects (if there are such objects) simply have no intrinsic nature. The structuralist theme grew most notably from developments within mathematics toward the end of the nineteenth century and on through to the present, particularly, but not exclusively, in the program of providing a categorical foundation to mathematics.
Mathematical structuralism is similar, in some ways, to functionalist views in, for example, philosophy of mind. A functional definition is, in effect, a structural one, since it, too, focuses on relations that the defined items have to each other.
A structure is the abstract form of a system, which ignores or abstracts away from any features of the objects that do not bear on the relations. So, the natural number structure is the form common to all of the natural number systems. And this structure is the subject matter of arithmetic.
http://www.iep.utm.edu/m-struct/
In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality.
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system.
The historical motivation for the development of structuralism derives from a fundamental problem of ontology. Since Medieval times, philosophers have argued as to whether the ontology of mathematics contains abstract objects. In the philosophy of mathematics, an abstract object is traditionally defined as an entity that: (1) exists independent of the mind; (2) exists independent of the empirical world; and (3) has eternal, unchangeable properties. Traditional mathematical Platonism maintains that some set of mathematical elements–natural numbers, real numbers, functions, relations, systems–are such abstract objects. Contrarily, mathematical nominalism denies the existence of any such abstract objects in the ontology of mathematics.
In the late 19th and early 20th century, a number of anti-Platonist programs gained in popularity. These included intuitionism, formalism, and predicativism. By the mid-20th century, however, these anti-Platonist theories had a number of their own issues. This subsequently resulted in a resurgence of interest in Platonism. It was in this historic context that the motivations for structuralism developed.
Acting mindfully, thoughtfully and consciously means never having to apologise. — charleton
There's nothing "spooky" or "queer" about objective morality under an intuitionist view. I think we come to know moral truths in a similar way we come to know mathematical truths, or understand logical reasoning — darthbarracuda
I'm of course championing intuitionism - I think there is a clear difference in kind between facts and values, and that any sort of morality that can be recognized as morality must employ some form of rational intuition. — darthbarracuda
"What works for society" is ambiguous, because it hides the fact that society only works if people do actually believe in some form of transcendent value - even the social contract theory implicitly holds that life, or something similar, is good. — darthbarracuda
Our premotor cortex moves our bodies before we are even have made the decision to move. I very much think we have an illusion of free will. — FlukeKid
The subjects were asked to relax while fixating on the center of the screen where a stream of letters was presented. At some point, when they felt the urge to do so, they were to freely decide between one of two buttons, operated by the left and right index fingers, and press it immediately. In parallel, they should remember the letter presented when their motor decision was consciously made
The temporal ordering of information suggests a tentative causal model of information flow, where the earliest unconscious precursors of the motor decision originated in frontopolar cortex, from where they influenced the buildup of decision-related information in the precuneus and later in SMA, where it remained unconscious for up to a few seconds.
This substantially extends previous work that has shown that BA10 is involved in storage of conscious action plans9–11 and shifts in strategy following negative feedback12. Thus, a network of high-level control areas can begin to shape an upcoming decision long before it enters awareness.
The decisions the skier makes are based on what his body understands, its training, its memory, the same habitual movements. I think the phenomena you are referring to is similar. It does not impinge on the notion of an existential will, in my opinion. — Cavacava
There's nothing incoherent from what I can tell with the notion that there is an actual transcendent morality but it's muddled and "gray" in the colloquial way of looking at it. — darthbarracuda
But I will say that apologizing only to get to a better standing with another person is insincere, even manipulative. — darthbarracuda
