• Is mathematics discovered or invented
    ↪Mephist
    You should be careful about how you ask this question. What mathematics are we talking about? Viewed from the most general perspective, mathematics is a logical game. You set up some rules and then you use those rules to construct abstract structures and prove theorems about them. There is an infinite variability of such games; the enterprise as such does not dictate to you which rules you should select and what you should construct from them, so there is nothing preexisting for you to discover.

    If, however, you are talking about the mathematics that we historically developed (and you are likely thinking about Euclidean geometry and 18th-early 20th century algebra, calculus and statistics, as that is what we mostly study at school and what is most widely used in the sciences), that is a very different question. You mention different axiomatizations of numbers, but you don't question the concept of a number itself, because it seems very natural and indispensable (at least to a contemporary person with some education) to think in terms of numbers. You can construct different axiomatizations of numbers in terms of more primitive concepts, such as sets, but the concept of a number is pretty much assumed beforehand: we know what properties we want that entity to have, we have the requirements. Likewise with lines and other geometrical entities.

    But why did we choose numbers and geometrical objects for our mathematical exploration? Stepping back to an abstract remote once again, they are nothing but mathematical constructs - a drop in an infinite sea of such constructs. There is no a priori reason to favor those concepts over any other. So the reason will not be found in the abstract enterprise of mathematics, but in the world that we inhabit, and perhaps in the contingencies of our cognitive and cultural evolution. It is difficult to speculate about inhabitants of other planets, but if they are what we usually imagine them to be, that is to say, cognitively quite similar to us and, of course, sharing the same universe with us, then it is not unreasonable to suppose, as you did, that they would converge on the same or very similar concepts of numbers and geometrical objects as we did - and then, of course, they could not fail, as long as they have the mental capacity for it, to prove all the same theorems about those mathematical entities: how could they not if they have presupposed essentially the same properties?
  • 'Poofed' into existence from nothing?
    The general idea here is that there is a world, and there is non-existence. Prior to ones birth into the world, one was in a state of non-existence, and was somehow plucked or pulled out of that state into being. — Inyenzi

    It is an error in thought to mistake these worldly concepts for actual things or states (which is what we do when we talk about coming from nothing, or not existing in any sense prior to our birth). — Inyenzi

    It is a mistake all right, but who actually makes that mistake? When I say that I did not exist prior to my birth, I do not necessarily commit myself to such a self-contradictory notion as existing in a state of nonexistence - that is just your uncharitable interpretation.
  • Should the future concern me?
    ↪Inyenzi
    I think the OP is suggesting an argument against presentism (only that which exists now has genuine existence): It would not make sense to care about something that does not exist. Caring about something is having a relation with that thing. But if there exists are relation, how can one of its subjects not exist?
  • Quality Content
    I am totally in favor of adding a hidden elite forum where only Jake can post, and henceforth restricting him to posting in that forum.
  • If the universe is infinite
    ↪JohnLocke
    You chose an extremely unfortunate framing for your topic. For one thing, it falls victim to Cunningham's Law: as you can see, everyone who responds to your post focuses on its most obviously wrong or controversial aspect (no need to restate what that is). Plus, it's ostensibly about infinity, so a certain obsessive moron is going to have a field day (or more, depending on how long this thread floats on the front page).

    But the more philosophically interesting and problematic issue with your OP has nothing to do with its physical premise. Rather, it is the unstated and unexamined assumption that personal identity supervenes on nothing other than the person's instantaneous physical substrate. At first glance, that might seem like a required assumption for a physicalist or a monist, but things aren't as straightforward as that. Consider forgery, for instance. Is there any difference between an original painting and a perfect replica? Or between a government-issued banknote and a perfectly executed fake? Chances are that, whatever your metaphysical commitments, you would still say that a replica is a replica and a forged note is a forged note - they are not even equivalent to the original, let alone being one and the same with the original.

    That's because authenticity - and thus identity - of a painting or a banknote is more than its instantaneous physical properties; it is also its diachronic properties - its provenance (at least that's one possible interpretation). So why should we blithely assume that the sufficient conditions for being a particular person is having a particular physical composition associated with that person and nothing else? Note, I am not even denying this premise, I am just pointing out that it cannot be assumed without argument or even mention.

    My advice to you is to shift focus away from the questionable framing, which is just plausible enough to distract people from the philosophical meat of the question. Consider how your predecessors have handled the matter. For example, you may want to look into the prodigious literature on Davidson's Swampman or various teleportation/replication thought experiments.
  • The Meaning of Life
    In other words, it's an objective moral goal of the universe ("ought") enforced by natural selection, which is a fact ("is"). Thus, from this point, the "ought" realm is bridged to the "is" realm. — Chris Liu

    You say "in other words," but what you write then in no way follows from what came before. First, you make this bizarre attribution of moral agency to the universe without explaining how the universe could be a moral agent. Second, you do nothing to meet Hume's challenge - you just double down on your assertion that an ought follows from an is. And finally, you still have to make the leap from the alleged moral goal of the universe (?!) to that of an individual person living in that universe.
  • Why are most people unwilling to admit that they don't know if God does or does not exist?
    You are confusing being agnostic with being an agnostic atheist or an agnostic theist. The difference is that someone who is purely agnostic tends to take a neutral stand regarding whether or not God exists, because they do not want to take either side of the argument when they don't know either way. — Maureen

    The original meaning of agnostic - a term coined by Henry "Darwin's Bulldog" Huxley - is precisely as you say: someone whose position is that they don't know (as opposed to gnostics who do). Of course, Huxley had a lot more to say on the subject than just repeating his thesis over and over and disparaging anyone who might disagree as stubborn, stupid or dishonest.
  • the book "Sapiens" by Noah Harrari and whether or not it has a valid argument
    ↪christian2017
    There has been an interest in "naturalizing" religion - explaining its emergence and perdurance (@Bitter Crank) as a natural phenomenon - going back at least to the late 19th century. Among the earliest and still continuing efforts are anthropological theories, especially ones that cast religion as a social adaptation, which is probably what your author tries to do as well. Later on cognitive scientists and evolutionary biologists joined in.

    At some point a split emerged between "adaptationists" - those who, like Harrari, explain religion as a useful adaptation - and "spandrelists" - those who view it as a byproduct of other developments, in itself adaptationally neutral at best. Among the latter are Scott Atran, Pascal Boyer, Robert McCauley, E. T. Lawson, Harvey Whitehouse - most are cognitive scientists, although the best-known "spandrelists" happen to be evolutionary biologists who are not really experts in this particular field - Richard Dawkins, who went so far as to call religion "a virus of the mind" and Steven Gould, who offered the spandrel metaphor (an architectural element that is not usually build for its own sake).

    Adaptationist theories are advanced by anthropologists and some evolutionary biologists, such as Joseph Bulbulia, Richard Sosis, D. S. Wilson. I find some of the anthropological research such as that of Sosis and Bulbulia, particularly interesting, since it does not just offer tendentious interpretations, but subjects the hypothesis to an empirical test.
  • Is it self-contradictory to state 'there is no objective truth'?
    A statement is either true or false. If it is true that 'there is no objective truth' then that seems like a contradiction. — curiousnewbie

    "No statements are true" would be a self-contradictory statement. "There is no objective truth" or "No statements are objectively true" is not obviously self-contradictory, because the subject is qualified with "objectively" - whatever that means.
  • Why are most people unwilling to admit that they don't know if God does or does not exist?
    ↪Maureen
    tl;dr: Why is that that not everyone is an agnostic like myself? Those people must be stubborn or stupid.
  • Materialism/Physicalism
    What is meant by "materialist"? Usually when people use that word they mean "causal reductionism". — i aM

    There is no one thing that is meant by "materialism." "Materialism" is a rather dated term, more often used in derogative contexts nowadays, with "physicalism" and "naturalism" being more favored by proponents, but there is no one meaning for those terms either. If you set yourself the task of nailing down these terms once and for all, you will almost certainly fail. It's better to examine specific claims and positions than to argue over isms.
  • The Meaning of Life
    Darwin's discovery of evolution — Chris Liu

    So every life should strive for ever better form of continuation in order to achieve the goal of perdure, forever. That's the only meaning of life, if any. — Chris Liu

    What philosophical tradition these thoughts are related or belongs to?
    Has anyone proposed similar ideas to the public? Who if yes?
    What flaws do you see in this essay?     — Chris Liu

    Broadly speaking, as
    ↪Banno
    pointed out, what you are trying to do is to deduce the meaning of life from a description of its natural history and dynamics - an ought from an is. Hume argued persuasively that the is-ought gap is unbridgeable (this is sometimes referred to as Hume's law), and his argument has impressed many since, but not everyone. Some, like the pop-philosopher Sam Harris, simply don't know better, but as naturalistic philosophy has become more popular in the latter half of the 20th century there have been conscious attempts at eroding the walls between nature and those domains that have traditionally been thought to be separate: epistemology and axiology (value and ethics) - and, for that matter, eroding the walls between epistemology and axiology as well.

    If you want to learn more about this, look into naturalized epistemology and ethics.
  • Beginners question on deductive conclusions/analytic propositions
    Thanks for the reply, my confusion arose after reading the following on the deductive reasoning page of wikipedia.
    "Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true".     — Hume1739

    "Necessarily" is used here informally, as an amplification. This should not be confused with necessity in modal logic (which does not figure in this context). All this means is that given the truth of the premises the conclusion of a valid argument cannot be anything but true. This doesn't make the conclusion unconditionally necessary - the italicized condition still applies.
  • Psychiatry’s Incurable Hubris
    ↪unenlightened
    I was responding directly to your own summary of your position. If you think that summary was inadequate, you could try again, instead of shooting the messenger.

    Perhaps we can talk about 'the medical model' - behaviour understood as illness. — unenlightened

    Perhaps. That would be an improvement over criticizing "the biological neuro-physical materialist objective approach" because it did not reduce all questions of medicine and psychology to simple, bite-sized physical explanations like bug, gene or chemical deficiency.
  • Psychiatry’s Incurable Hubris
    There is no bug, no gene, no chemical deficiency, no physical property at all that unequivocally marks out any psychological illness — unenlightened

    the biological neuro-physical materialist objective approach has not been successful — unenlightened

    So your complaint is that mental illnesses are not reducible to simple underlying physical causes? That's what makes psychology and psychiatry "unscientific" in your assessment?
  • Does philosophy bring out those that are mentally unbalanced?
    So, I say all that to say is am I wrong for thinking this way meaning, are there some really disturbed individuals that tend to gravitate these types of discussion boards? — Anaxagoras

    Your opening post doesn't necessarily describe "really disturbed individuals" - it applies to a much wider range of people who are not skilled at writing and expressing their thoughts, or just don't put much effort into their posts.

    If I'm reading something that is hard to follow and the focus of what their writing is seems to go in all directions with no direction, I'd chalk this up as maybe the individual would not have a firm grip on the basics of writing. — Anaxagoras

    Yes, exactly.

    But as to your question, that has been my observation as well. To put it crudely, a forum with "philosophy" in its title tends to attract the loons in more than average numbers.
  • Anecdotal evidence and probability theory
    It's my best guess. — coolguy8472

    Some people? What do you think? What are your reasons? Isn't this why you opened a discussion on a philosophy forum?

    Double and triple hearsay is a persuasive enough topic for courts to at least discuss the issue before rejecting the idea of it being valid persuasive evidence. — coolguy8472

    Look up what "hearsay" means. "Double hearsay" would be something like "My cousin heard from her hairdresser that X won the lottery." Your case is completely different.
  • Anecdotal evidence and probability theory
    My guess is that that in a lottery where the odds are 1 in a billion:
    P(Person 1 won the lottery given they claimed "I won the lottery, my friend saw the ticket and can confirm") = 1%
    P(Person 2 won the lottery given they claimed "I won the lottery, my friend saw the ticket and can confirm") = 1.01%     — coolguy8472

    Unless this really is a completely random guess, can you give any reason for your numbers, or for the difference between them? What does make the second uncorroborated claim more probable (however slightly) than the first uncorroborated claim?
  • Is it or isn't it?
    ↪Frank Apisa
    You may think that you are supporting the OP by claiming that 2+2 equals 4 by definition, but you are actually doing the opposite. If it is nothing more than a definition, then it is just an arbitrary convention, like naming. 2+2 could just as soon equal 5, if we agreed to define it that way.

    In a way, this is true. Of course, no one literally defines the result of 2+2 - it can be rather easily proven from the axioms of arithmetic - but the axioms of arithmetic are themselves conventional in the sense that there is no completely a priori justification for adopting them. Indeed, there are any number of alternative algebras, some of which have been found to be useful or at least interesting.

    However, there must be a good reason for why conventional arithmetic is so important for us - and that could be a topic for a philosophical discussion, except that the OP doesn't seem to be interested in such a discussion.
  • Is it or isn't it?
    Make of this what you will — tim wood

    I am at a loss as to what to make of your thread. The topic that you coyly avoid naming is Is 2 + 2 = 4 universally true? - which, of course, poses the exact same question as you do here. What was the point of duplication?
  • Is it or isn't it?
    ↪tim wood
    Is this going to be another endless thread where loose terms like "absolute" are introduced but never explained, and then people proceed to talk past each other ad nauseum?
  • Top Hybridization-Geneticist suggests we're a Pig-Chimp Hybrid.
    The nutters are out if force today. I blame Mercury in retrograde!
  • How to interpret this mathematical assignment
    Not sure what this means. How to interpret ≡? — Ulrik

    It just means equality here. I wrote ≡ to emphasize that the equality holds unconditionally.

    For example, in the standard arithmetic p×1 = p for any p other than 0. This equality is axiomatic. But in an alternative algebra it could be axiomatically true that p×q = p for any p and q. In this algebra

    a + (bc) = a + b = (a + b)(a + b)
  • Brexit
    ↪Bitter Crank
    The sad thing with Brexit is that, as with Trump in the US, a massively skewed opinion on this forum is not representative of opinions among the general public. UK citizens are still closely divided over the issue, and polarization is such as hasn't been seen on any issue in recent times - perhaps the closest comparison would be Jacobite conflicts three hundred years ago, except that divisions then were more in line with preexisting regional and religious divisions, whereas now the Brexit controversy is tearing apart colleagues, friends and families.
  • Is 2 + 2 = 4 universally true?
    What I am suggesting is that "2+2=4" or any other correct mathematical expression like it where two expressions on opposite sides of an equals sign are in fact equal is perhaps regardable as an instance of this law. — petrichor

    I think the question at issue is whether it is a fact. As others have explained, it doesn't have to be. It depends on your starting assumptions.
  • Proof that something can never come from nothing
    Let's define nothingness as the conjunctions of negations of any possibly or actually existing things: ~p1 & ~p2 & ~p3 & .... From that definition is follows trivially that no object can exist out of nothingness. — Pippen

    So, dispensing with the unnecessary formalism, what you have stated is that if nothing can possibly exist, then there isn't a possibility of anything existing.

    Color me impressed.
  • The Foolishness Of Political Correctness
    ↪Fooloso4
    Apologies, I mistook carelessness for plagiarism.

    The irony here is that I actually read the article and quoted relevant points. You on the other hand seem not to have read the Wiki article you linked to. If you had you would know that the history of the term is not one of simply mockery and derision. — Fooloso4

    Yes, I know that the term had a complicated history, but as can be seen from the Wiki precis, throughout most of that history it was used ironically and disparagingly.
  • The Foolishness Of Political Correctness
    The proponents of political correctness like to portray anyone who takes objection to political correctness as a bigot or a neanderthal. Any expression containing even a hint of anger brings on that response. I am responding now to political correctness in a manner that is fully reasoned and that cannot be portrayed credibly as any such thing. — Ilya B Shambat

    One person's political correctness is another's basic good manners.

    You will need to be more specific about what form of political correctness you object to - giving examples - if a useful discussion is to occur.     — andrewk

    There are no good forms of political correctness. "Political correctness" - as the very history of the phrase indicates, is a term of mockery and derision. I hate it when people ask "What do you think about political correctness?" - because that is like asking "What do you think about assholes?" The phrase is so loaded that there is simply no way to discuss it "in a manner that is fully reasoned." When people launch into a discussion of "political correctness," you already know where they stand before they even complete the first sentence.

    Rather than addressing "proponents of political correctness" (there are hardly any) it would be more productive to examine what it is that opponents of PC (that is, everyone who uses that phrase) find objectionable. An uncharitable view is that they simply resent being called out for bad behavior. They insist that their behavior must be socially acceptable, and when instead they are met with disapprobation, that is when the accusation of "political correctness" is leveled.

    Not every behavior in a society can or should be governed by institutionalized regulations, such as criminal law. Part of society's self-regulation is social opprobrium. Society's attitudes shift; some forms of behavior become so odious that no one would dare flaunt them in public any more (like calling a dark-skinned student "the black spot"). And when such blatant transgressions of social norms do occur, no one thinks of deriding the inevitable backlash as "political correctness."

    The PC phenomenon arises in cases where there is no overwhelming consensus; it is an artifact of "culture wars." A part of society seeks to deprecate some attitudes and behaviors - with a view of eventually suppressing them, the way homosexuality was and is suppressed in parts of the world, or the way blatant bigotry is suppressed elsewhere. The rhetoric of "political correctness" is a weapon with which the other part of society resists the attitude shift.


    That's a great post, thank you. — fdrake

    @Fooloso4's post - a catalog of American liberal grievances with a tenuous relationship to the OP - was a careless copy-paste job from various online articles. I am pretty sure that not a word of it is original.
  • Mathjax Tutorial (Typeset Logic Neatly So That People Read Your Posts)
    ↪fdrake
    Nice. I hardly know any latex, so thanks for the convenient tutorial.
  • Definitions Of Reality
    This parses with the quantum mechanics, in which observing the phenomenon changes it - and we, through our actions, impact the world. We most certainly have influence on reality. Once again, both the man-made and non-made reality is real. What is reality? Reality is what is. We can then – measure it, study it, observe it, and of course contribute to it as well. — Ilya B Shambat

    You don't need to appeal to quantum mechanics in order to conclude that we "have influence on reality." If you are an agent, then you are influencing reality - that is what it means to be an agent!

    Anyway, there is a sense in which what we believe about a subject is what makes the subject what it is. Does, for example, logic exist - is it a part of reality? Ultimately, the answer depends on how we want to define reality in the particular context. There is no fact of the matter here, other than the fact of how we construct meaning. We can construct the meaning of the word reality so that it includes things like logic - or not: it is completely up to us.
  • Proving a mathematical theorem about even numbers
    So we can just take this and generalize our findings to represent any number? — Ulrik

    If I understand you correctly, the question that you are asking is "How can we know that any number can be given a decimal representation?" (Because the expression d0 + d1(10^1) + ... is just what the decimal representation stands for.)

    This is a good question. Note that in order to ask this question, you must first acknowledge that a number - a natural number in this case - is a mathematical entity that exists independently of its representation. So it is at least a priori conceivable that there may be a number that cannot be represented in decimal notation.

    Natural numbers are usually formalized by Peano axioms. Any set of entities that satisfy these axioms represent natural numbers. So if we can prove that the set of decimal numbers satisfy Peano axioms, then we have proven that decimal numbers represent natural numbers - in other words, any natural number has a decimal representation. (Now, of course, every decimal number is a natural number, but what is in question is whether every natural number is also a decimal number.)

    If you take a look at the Peano axioms, you will see that decimal numbers automatically satisfy most of them, since every decimal number is a natural number. The one that is not obviously true is the postulate that says that natural numbers are closed under succession, i.e. the successor of every natural number is also a natural number. Is the successor of every decimal number a decimal number? In other words, does always have a decimal representation?

    We can prove this by induction. First we can easily show that the postulate holds for every single-digit decimal number: d + 1 is either another single-digit decimal number or 10. Then we assume that any n-digit decimal number has a decimal successor, and using this assumption we can prove that any (n+1)-digit decimal number has a decimal successor...
  • How to interpret this mathematical assignment
    ↪Ulrik
    It's hard to tell without a context, but if we don't assume the standard notation and the standard arithmetic, and instead assume some algebra with unknown axioms and notation, then consider an algebra where the following axiom holds:

    For any p and q, pq ≡ p
  • Theory of Natural Eternal Consciousness
    What do you guys think? — simmerdown

    At first glance this sounds really stupid. Considering that the author's previous article was published in a crackpot open-access "Journal of Consciousness Exploration & Research," I'll save myself the effort of looking further into this.
  • Why the Greeks?
    ↪Moliere
    Why let facts get in the way of a half-assed "theory"?
  • Why the Greeks?
    What makes these episodes enduring is that they get transmitted to succeeding cultures. Had the Greeks been swamped by some horse-riding horde indifferent to Greek culture, we probably wouldn't be talking about Aristotle. — Bitter Crank

    Yes, this is an important point. We don't even know what was lost without a trace - the Greek civilization was very fortunate in that respect. Babylonian civilization was influential too, and it left behind lots of very durable clay tablets (most still waiting to be analyzed), and the Babylonian script was deciphered, so at least now we can take stock of their achievements. Minoan civilization was also highly advanced, but it was more isolated, and Minoan script still hasn't been deciphered. Other civilizations were even less fortunate in what they transmitted and what they left behind.
  • Why the Greeks?
    Generally I find such pop-culturology totally without merit. The usual procedure is to pick two stereotypes about a culture - or an entire civilization, as in this case - and weave a thin ad hoc narrative to "explain" one in terms of the other.
  • Why the Greeks?
    ↪Jacob-B
    Babylonian mathematics is said to have been more advanced than Greek mathematics ever was in some respects. Not only did they come up with some advanced practical techniques, like solving quadratic and cubic equations, but their numerical concepts were generally more advanced (Greeks mostly busied themselves with geometry). Some of the Babylonian knowledge reached Greece and influenced Greek astronomy and mathematics, but ideas didn't spread as readily then as they do now, so many of these impressive advances were forgotten and are only known now thanks to archeological discoveries and deciphering of clay tablets.
  • Counterexemple to Hume's Law?
    he disjunction AvB is either an "is" statement or an "ought" statement. — Nicholas Ferreira

    Like @unenlightened said, there is no reason to accept this.

    "It is raining outside or I should have bought some milk."

    Is this an "is" statement or an "ought" statement?

    I think it's just a nonsense statement.
  • Brexit
    I lived in France for a few years.One of the historic differences is the revolution. It may seem extravagant, but the class divisions in England especially play an important role. Most of the government went to the same school, and the same university. That's only slightly an exaggeration. — unenlightened

    I am not sure that the differences in class consciousness that you perceived have much to do with the French revolution. Here is Proust writing at the turn of the (last) century:

    ... middle-class people in those days took what was almost a Hindu view of society, which they held to consist of sharply defined castes, so that everyone at his birth found himself called to that station in life which his parents already occupied, and from which nothing, save the accident of an exceptional career or of a “good” marriage, could extract you and translate you to a superior caste. M. Swann the elder had been a stockbroker; and so “young Swann” found himself immured for life in a caste whose members’ fortunes, as in a category of tax-payers, varied between such and such limits of income. One knew the people with whom his father had associated, and so one knew his own associates, the people with whom he was “in a position” to mix. — Marcel Proust, Swann's Way
  • Donald Trump (All General Trump Conversations Here)
    "I don't care. I believe Putin."

    That's what President Trump is alleged to have said in a discussion with U.S. intelligence regarding information he was given about North Korean intercontinental missiles and whether they could reach the United States.     — CBS
Home » SophistiCat