• Australian politics
    Does anyone care whether the right whingers vote for The National Party or One Nation?

    And this. Hanson has made herself a movie.

    :meh:
  • A new home for TPF
    @Jamal, so how goes it?
  • Direct realism about perception
    You never taste oysters as they are in themselves; your only taste of them is mediated by your tongue...

    :meh:
  • Direct realism about perception
    ↪AmadeusD
    Don't look at the sun directly, kids. It's bad for you. Use a pinhole camera, or a properly filtered telescope.

    :meh:
  • Unfalsifiability, valuation and "warranting belief"
    Nuh. Swans are black. The white ones are foreigners.
  • Direct realism about perception
    The Sun is not what we see when we look at the sun. — AmadeusD

    :meh:
  • Infinity
    Oh, frank. Ok.
  • Infinity
    ↪frank
    And yet they are countable. Look it up.
  • Infinity
    Neither set is countable — frank
    The natural numbers are countable.

    The natural numbers are also a proper subset of the rationals, but they're the same size. — Srap Tasmaner
    As is, there is a bijection between them.
  • Australian politics
    Andrew Hastie and Angus Taylor show how much the Liberal party have learned from their trouncing at the last Fed election by setting aside personal ambition for the good of the party and the nation...
  • Infinity
    But Cantor showed that there is a way to force them through a chute so that you can count them one-at-a-time. It's interesting that it turns out you cannot do this with the real numbers. — Srap Tasmaner
    Interesting metaphor. Does that make the real numbers like a tube of sausage mince? :chin:

    ↪Ludwig V
    Cheers. Interesting chat.
  • Infinity
    ~~
  • Australian politics
    Any chance of Sussan Ley still being Liberal leader in a week?
  • Infinity
    OK. It depends on what you are doing. I was thinking of the point of origin on a graph, but that's not quite the same as counting numbers. — Ludwig V
    I think this is important - see how what we are up to changes what number system we are using?
  • Infinity
    I think many people believe that if something is referred to, it counts as an object. — Ludwig V
    Herein lies much confusion, that can be sorted by looking at quantification.

    Again, it hadn't occurred to me that this would be problematic. It's quite legitimate to move from "7 > 5" to "Something is greater than five", or "There is a thing greater than five". That doesn't commit us to bumping in to fives and sevens along with chairs and tables. Quantification tells us what a grammar ranges over, not what exists as a spatiotemporal object. The confusion here is between differing language games; to think that "object" only means tables and chairs and not 7 or fully incorporated companies.

    Being an object is a role in a language game, not an ontological status.

    Failing to recognise this is what sits behind the confusion of calling things "platonism" hereabouts.
  • Infinity
    Numerals get their identity from roles in activities, not from reference to entities.
    — Banno
    You are not wrong. But now we are getting into trouble with the difference between numerals and numbers. I have a feeling, however, that we may need numbers in order to identify correspondences between numeral systems and perhaps even number systems with different bases.     — Ludwig V

    Again...

    Well, what I was pointing to is the difference between a numeral and a number is in the use to which it is put; one counts with numbers, not numerals. "Numerals get their identity from roles in activities, not from reference to entities" is intended to point this out. The difference between numerals and numbers is not ontological, it is grammatical.
  • Infinity
    But don't we also need 0, as the starting-point? — Ludwig V
    Again, it hadn't occurred to me that this wasn't obvious... do we want natural numbers or counting numbers? It's not needed, as such, unless you have nothing in your pocket.

    That is, which game are you playing?
  • Infinity
    I don't have a problem about the timeless present in the case of constitutive norms. But in relation to procedures, I do. For the obvious reason, that a procedure takes place in time. — Ludwig V
    I was using "procedure" as a generalisation of "function". Where a function will have exactly one result for each input, a procedure need not. I hadn't considered that someone would suppose that logical procedures are somehow temporal. I find that idea quite odd.
  • Infinity
    :wink:
  • Infinity
    You'll find that you can't. — frank
    Why not? I have nothing in my pocket, therefore I have nothing. :meh:
  • Infinity
    I've just been observing the different stances people are taking. — frank
    Yes, you read these threads as people and their interactions rathe than as about ideas.
  • Infinity
    ↪frank
    A no to what? Set your account out. Say something. Do the work.
  • Direct realism about perception
    ↪AmadeusD
    , maybe. But hang on. We do look at a thermometer to see if it is cold. How then is it that thermometers do not measure cold? There's an equivocation here that allows thermometers to both measure and not measure cold.
  • Infinity
    Ok. I don't object to that. I doubt you can do the same thing for ZFC, though. So are you now suspicious that ZFC might be bullshit? — frank
    :roll:
  • Infinity
    ↪frank
    :grin: Enough with your suggestions; say something.

    We've shown how quantification can be handled without invoking abstract objects at all — it’s rule-based, normatively grounded, and socially coordinated.
  • Infinity
    An object in your mind is called a mental object. An object in your hand is a physical object. An abstract object is something that isn't physical, but it's not simply mental either. — frank
    :meh: What of quantification?
  • Infinity
    ↪frank
    Perhaps you misunderstood...? Yep, we've moved on to address some of the shortages in structuralism, that it is overly formal, doesn’t explain how humans come to understand or manipulate numbers, what it might be to get a mathematical answer right and how we can still have objects in a structural framework...
  • Donald Trump (All Trump Conversations Here)
    This is at the core of the problems with US politics. — Christoffer
    The elected King? Yes.
  • Infinity
    ↪frank
    Here's me thinking you were following along...
    • Benacerraf’s identification problem
    • Gödel’s incompleteness theorems shows that set theory cannot fully capture all mathematical truths
    • Category theory, topology, homotopy type theory don’t naturally live in the set-theoretic universe
    There aren't a lot of experts in phil of math — frank
    Compare and contrast... https://survey2020.philpeople.org/survey/results/5030?aos=47 ...note change in AOS.

    We could go in to a discussion about whether the view expressed here is structuralism or constructivism, if you like. But none is a majority opinion, even amongst those who study in the area.
  • Infinity
    You have the minority view — frank

    https://survey2020.philpeople.org/survey/results/5030
  • Infinity
    You're trying to have your cake and eat it too. — frank
    That's permitted, under the rules...
  • Donald Trump (All Trump Conversations Here)
    ↪ssu
    In a Westminster system there is effectively another power, the public service. once an independent organ charged with administering policy, they owed allegiance only to other bureaucrats. Of courser this had it's own problems, but being neither elected nor appointed by the president, they were mostly autonomous.

    Not so now.
  • Donald Trump (All Trump Conversations Here)
    ↪ssu
    The US needs an electoral commission. But to do that it would need a public service that is not appointed by the president.
  • Infinity
    There was a lot of strenuous protesting in this thread to the effect that infinity is a thing. Turns out you actually agree with Meta. Numbers aren't things. They're just elements of language games. — frank
    Elements in a language game can be things - because we quantify over them... all these numbers are even, all those numbers are prime.

    So math is just language games, right? — frank
    Drop "just" and you might be getting there.

    Wow! Being productive. :up: — frank
    Despite my obvious addiction, I am still functional. But it's going to be 36℃ today, 42℃ tomorrow, so productivity occurs inside or in the early morning.
  • Infinity
    ↪frank
    nah. I’m at the shops, picking up a few groceries. You are just something to look at while I wait for the check out chick.
  • Infinity
    ↪frank
    you’ve given something a name and a popularity rating.

    Why should I care?
  • Infinity
    ↪frank
    Frege does provide an argument, not just an assertion. His framework addresses the public, objective character of numbers, which Meta simply assumes must be Platonically instantiated. Frege’s “objects” are still abstracta; Wittgenstein and Strawson show how this is overkill: we get public reference without treating numbers as objects at all. Learning to count (Srap) shows how participation in public rule-governed practices secures objectivity and coordination without invoking Platonism.

    And then we have Benacerraf's identification problem. There are multiple equally valid set-theoretic constructions of the natural numbers. If numbers are “objects” in the Fregean or set-theoretic sense, which objects are they? There is no fact of the matter that uniquely picks one construction over another. In contrast, public reference and logical precedence do not require objecthood at all. Benacerraf's argument shows objecthood is doing no work, the Wittgenstinian account offers an alternative.
  • Infinity
    ↪Ludwig V
    Then do we have broad agreement?
  • Donald Trump (All Trump Conversations Here)
    ~
    It is part of the strategy to ensure Trump does not have to leave office. — Questioner
    The insurrection act cannot change the timeline for federal elections. That is down to your congress. The 20th Amendment sets an absolute end to a presidential term on January 20th, with no exceptions for emergencies or ongoing challenges.
  • Direct realism about perception
    I think I explained it quite clearly here: — Michael
    Yes, it's pretty clear. You want to finesse the grammar of cold into cold₁ and cold₂, a contrast which is marked in by differentiating being cold from feeling cold. I would instead draw attention tot he fact of disagreement that makes making the contrast notable.

    No straw man, but a different discussion.

    That's what is behind my

    If “X is cold₂” just means “X causes cold₁ sensations in me”, then:

    *instruments don’t measure cold, only predict feelings
    *disagreements are merely parallel reports
    *learning temperature terms requires introspection
    *correction becomes impossible except as etiquette

    That is not how the language works, and it is not how science or ordinary life proceeds.

    That is orthogonal to the earlier dispute.     — Banno

    as well as:

    If “hot”, “cold”, “painful”, “harmful”, etc. were mere fictions, then safety thresholds, medical advice, engineering tolerances and so on would all lose their point. Science would be answering questions no one had. That John and Jane disagree as to the temperature of the bath is not a fiction; it's something to be explained. This is lost in your account. — Banno
    Collapsing cold₁ and cold₂ renders "cold" impotent.
Home » Banno