• Benj96
    20
    We've all come across a paradox or two during our lifetimes, be it the grandfather paradox made famous by several iconic films, the liar paradox, paradox of free will, Russells, the list of examples is seemingly endless and spans all range of disciplines from science and mathematics to philosophy and linguistics. Even chemistry and biology have several between them.

    So why on earth would paradoxes be built into the universe? Are contradictions fundamentally necessary? Do paradoxes somehow govern the laws of nature or obey some true laws of nature we have yet to discover? Or are they merely generated by false assumptions regarding the subject of the paradox - A fallacy in the understanding of how time works for example. Or where the self ends and begins. Or the meaning of language?

    Perhaps the universe has no paradoxes only assumptions. And those assumptions when combined correctly contradict eachother just as one persons belief or lifestyle may contradict anothers only if they were to encounter one another. Could paradoxes simply be a by-product of conscious awareness. A necessary boundary to allow limitless imagination, speculation and query in a universe that otherwise may just have determined laws and strict defined regulation that would not permit the fluidity or plasticity of thought and combination of ideas that the mind can and does generate.

    Is argument itself not the ultimate paradox? Should you ever consider an idea or hold a belief you will inadvertently encounter opposition. Why is there rarely unanimity of thought between conscious beings? Is the sensation of self, of ego, of ones success in a limited existence paradoxic to anothers? Ones wealth, anothers poverty. Ones authority, anothers submission.

    If there is any ultimate truth out there it certainly would demonstrate the contradictory nature of its pursuit. The transience of agreement and the overwhelming lack of logic to many aspects of experience. What do you think a paradox is and why it exists? Is there anything in common that links paradoxes together? Could it be one simple rule that manifests as a different contradiction when applied to different disciplines? All views encouraged and welcome :)
  • tim wood
    4.4k
    Consider the substrate of any paradox. That's the "wherein" of it. And once that's identified correctly, often the paradox becomes uninteresting. All (correction welcome) arise from language/communication. Well, language allows for paradox. But if they're to be resolved, it must be in and on the ground from which they came and not so much the content they refer to, although as, e.g., with Zeno, content can be useful. Zeno argues the impossibility of certain events, the paradox being that the events in general happen all the time (Achilleus overtaking the tortoise). In this example, the content, the "that" which occurs, stands as a check for any discussion: in the world Achilleus always has and always will overtake the tortoise.
  • EnPassant
    213
    So why on earth would paradoxes be built into the universe?Benj96

    I don't believe they are. I think paradoxes are superficial. They are limitations on language and defects in human thinking. In Russell's Paradox the statement is:

    "The set of all sets that are not members of themselves." Immediately we have a problem because the statement assumes that this entity is a set, but it is not, as the paradox shows.

    It needs to be restated as:

    "All sets that are not members of themselves."

    Now we can ask the question What is this entity if it is not a set? See my entry on R.Paradox. in the mathematics thread.
  • jgill
    547
    But if they're to be resolved, it must be in and on the ground from which they came . . .tim wood

    One of the weirdest is Banach-Tarski, and that one arises if one assumes the Axiom of Choice. Discard the AOC and it goes away. Another, the Diagonal Paradox, is simply a matter of perspective and magnification.
  • tim wood
    4.4k
    I think I understand the statement of the B-T paradox - break a sphere into pieces of the right sort and then make two spheres from the parts. But this isn't physics, rather it's how certain things are defined and understood - or not understood. That is, the interest of the statement devolves to the particulars, and they're of a different kind and level of interest.

    Btw, if one sphere can make two spheres, then why not N spheres - or even an uncountably infinite number of spheres?
  • jgill
    547
    B-T depends upon the Axiom of Choice. This shows how "dangerous" it is to simply add new axioms to ZF. One would think that AOC is obvious and of little consequence, but not so. It takes one away from the world in which we actually live and plunks us down in another universe.

    For a more palatable paradox, there is Braess' Paradox (which has been employed in a number of major cities):

    For each point of a road network, let there be given the number of cars starting from it and the destination of the cars. Under these conditions, one wishes to estimate the distribution of traffic flow. Whether one street is preferable to another depends not only on the quality of the road, but also on the density of the flow. If every driver takes the path that looks most favourable to them, the resultant running times need not be minimal. Furthermore, it is indicated by an example that an extension of the road network may cause a redistribution of the traffic that results in longer individual running times
  • Banno
    7.8k
    Paradoxes are not built into the world. Rather they are the result of not saying things well. They are errors in the grammar we chose. They may be dissolved when we choose a different grammar.
  • frank
    5.1k
    Paradoxes are not built into the world. Rather they are the result of not saying things well. They are errors in the grammar we chose. They may be dissolved when we choose a different grammBanno

    What a weird thing to assert.
  • Banno
    7.8k
    It's how it works. You gota problem?
  • frank
    5.1k
    It's how it works.Banno

    How do you know that?
  • Banno
    7.8k
    Philosophical investigations.

    Is this another discussion where you start to be interesting and then disappear?
  • frank
    5.1k
    I come here for sanity breaks. I'm not trying accomplish anything big. You?
  • tim wood
    4.4k
    I come here for sanity breaks.frank

    Yikes! Where do you live - so I can plan never to go there!
  • jgill
    547
    Banach-Tarski is merely the result of bad grammar? :roll:

    Maybe by "grammar" you mean math here, and the AOC is "bad grammar"
  • Banno
    7.8k
    Banach-Tarski is merely the result of bad grammar?jgill

    Well, yes; a grammar that accepts AOC as against a grammar that does not.
  • StreetlightX
    5.3k
    With the caveat that grammars are neither good nor bad as they stand; only that they are better and worse for some purposes, and not others. But yes - paradoxes are grammar - techniques - pushed to where they ought not go.
  • TheMadFool
    5.8k
    What's the difference between being in the wilderness without a compass and being in the wilderness with a broken compass?
  • Banno
    7.8k
    You might be able to fix the broken compass.
  • TheMadFool
    5.8k
    You might be able to fix the broken compassBanno

    How would you know if the compass is fixed?
  • Becky
    17
    Mathematical paradox is defined “ In any instant, a moving object is indistinguishable from a nonmoving object: Thus motion is impossible.” we are trapped by time.
  • frank
    5.1k
    Philosophical investigations.Banno

    I'm just suspicious about going from a little reasoning to a statement about how the world works.

    An experiment that shows the truth of what you're saying would be better.
  • Banno
    7.8k
    ...a little reasoning..."frank
    ...over two hundred pages; and thousands more in secondary literature.
  • frank
    5.1k

    The Summa Theologica has 3020 pages in the hard cover edition.
  • Banno
    7.8k
    Yes, indeed; quantity does not equate to quality.

    What's this conversation about? What do you want?
  • Banno
    7.8k
    A summary in ten words or less?

    Read PI. Or @Sam26's notes. I'm sure not motivated by you to put in the effort.
  • frank
    5.1k


    You're missing my point. Reasoning gives you a hypothesis. And maybe you meant that, you just left out "My favorite hypothesis is..."
  • Banno
    7.8k
    You're missing my point.frank

    yep.
  • Marchesk
    3.3k
    The double slit and various related experiments do come close to suggesting the universe likes paradox. But probably we just don't understand what's going on.
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