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From the SEP article on negation:

In Hintikka’s (1973) game-theoretical semantics, negation is modeled by a role-switch between two players in a semantic game (cf. the entry on logic and games). A geometrical intuition of negation as inversion can be found in a paper by Ramsey, who suggested that

[w]e might, for instance, express negation not by inserting a word “not”, but by writing what we negate upside down. Such a symbolism is only inconvenient because we are not trained to perceive complicated symmetry about a horizontal axis, and if we adopted it, we should be rid of the redundant “not-not”, for the result of negating the sentence “p” twice would be simply the sentence “p” itself. (F.P. Ramsey 1927, 161–2)

The idea of negation as the inversion of arrangements of truth values, such as truth value polygons, has been developed in Varzi and Warglien 2003, see also Shramko and Wansing 2011 for negation as order-inversion in a logic of generalized truth values.

Then, regarding the words "electron" and "positron" as "negative" and "positive" respectively:

"Charge" is a property of objects. The total amount of charge and the charge distribution of an object determine its behavior in electromagnetic fields. "positive" and "negative" are (historical) conventions, just like "rose" and "tulip". If we would swap these terms, we could still tell the charges (and the flowers) apart. In that sense there is no absolute meaning to either. The much more important fact is that there are two different polarities of charges which exist in equal numbers [[quotation of a comment]]. ... If we re-designate all positive electric charges as negative and vice versa, while keeping their absolute value, the resulting physics would be the same. So exact choice is merely a matter of convention [[quotation from an answer]].

Is the naming convention for those leptons an example of (subconsciously? presuppositionally?) adopting the inversion "model" of negation? Or is the convention "evidence for" that "model"?

Clarification (edit): so one definition (of some sort) that I've seen for negation is a string like, "A → ⊥" (read along the lines of, "Some proposition A maps to the False"). Then in Paoli[19] the truth-vale lattice has t and f along with ⊤ and ⊥, the former two of which could be represented as i and -i in the metaphor of numerical truth-values. But if it is conventional/arbitrary, which of the two square roots of -1 is itself negatively signed, then... Except then I wonder about ⊤ and ⊥, however, for in the given metaphor, they go with 1 and -1, which are not positive and negative in such a conventional/arbitrary way. Per the idea of a truth-value multiset whose items are all copies of ⊤, it would be more "conventional," which copies get designated as the top and bottom elements of the corresponding lattice, but we would seem to have to generalize the negation-as-inversion beyond the mapping specifically to ⊥, but would have negation as a relation between certain pairs of ⊤-copies (the ⊤-and-⊥ pairing, the t-and-f pairing). But even if we come up with something here that clearly mirrors the conventionalism about lepton signage, wouldn't we have to find a more meaningful correlation between {positrons, electrons} and {i, -i} or else the mirroring is just a coincidence?

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    The direction of "conventional current" is a historic accident, see e.g. here: electronics.stackexchange.com/a/302806 May 15 at 16:14
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    There are two different Boolean structures: the discrete structure lets 0 and 1 swap, but the poset structure always has an arrow 0 -> 1 and no inverse. Electrons are the former, but constructive logic is the latter. Note that it's not possible to mess up the latter because there are no functions from the singleton set to the empty set! A deep dive is available on nLab as "negative thinking".
    – Corbin
    May 15 at 18:14
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    Electrons are called electrons because amber (elektrum) rubbed with cloth gets a static charge. It's a historical accident that we don't call them hairbrush-ons...
    – g s
    May 15 at 18:31
  • that is an impressive illustration of the difference between philosophical intuitions, how we have to choose between what we want (an expansive intuition) and what is more difficult. thanks!
    – andrós
    May 15 at 19:11
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    Positron is not the negation of electron, just as polar opposite of a property, when it makes sense, is not the negation of the property generally. Black is not non-white and negative is not non-positive, which includes neutral. Ramsey's "inversion model" of notation would work for any involution, it does not indicate any relation to negation specifically, and intuitionists hold that negation is not even an involution.
    – Conifold
    May 15 at 23:52

3 Answers 3

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Isn't that all just a matter of context and perspective?

Like "negation" literally just means "to say no". Now what it means in practical terms to "say no to something" or to "deny it", depends on the thing that you say no to. Like if it's a binary choice, denying 1 only leaves 0. So negation fixes the value to be "the other". While if you broaden the choices to idk the natural numbers, denying 5 could mean "anything but 5". Or if you look at it with respect to specific properties it could refer to a particular number, for example for additive properties you might place a dividing line at the neutral element of 0 and argue that the negation is the inverse or opposite (that's what's on the other side), i.e. -5. Though if you were to look at multiplicative properties instead, the neutral element would be 1 and the inverse 1/5

So the properties of a "negative" can vary based on what you say no to and why. Like if you use negative as antonym for positive (to put something), you kinda already imply that the negative is the absence of (something being put somewhere). Though if you look at "polar opposites" you look at opposite ends of a 1-d spectra or things that are "diametrically opposed" (points on the edge of a circle with the distance of a diameter (which can be expressed as 1-d spectrum).

Now physics has used and continues to use many different perspectives when looking at electrons.

Like in the beginning the observation was of 2 charges that attract each other and repel itself, as well as attracting neutral material. They were distinguishable and polar opposites with respect to one property but not all (different relation to each other and itself, same relation to neutral stuff).

So within electrostatics they are opposites of each other in terms of asserting forces on each other and themselves, but there's no reason why one would be called positive or negative or whether they should be treated as negations of one another. As g s has mentioned electron just refers to the method of creating that electrostatic charge i.e. rubbing amber, while the other charge was produced by rubbing glass.

So at this point you could have literally named them "roses" and "tulips" as their names just served to distinction between each other but encoded no further information (thought they usually named them by the means by which they were produced i.e. amber).

Then discussions emerged as to whether it's actually 2 "fluids" or whether it's just 1 and the 2 phenomena are just the presence (positive) or absence (negative) of 1 entity.

So with the advent of electrodynamics and moving charges it was supposed that it's the "real"/"positive" charge that moves while the other charge is just an absence of that and which was suspected to be the "glass-charge". Turns out it was exactly the opposite and it's the amber-charge that moves. Another explanation for the positive/negative might be the aesthetics of Lichtenberg figures: https://www.capturedlightning.com/frames/lichtenbergs.html

Also once you have a movement you can also define arbitrary coordinate systems in which one direction is positive and the other is negative. And where again you have polar opposites and diametrical opposition.

That being said electronic engineers still consider current to move in the wrong direction and physics is still treating it as one or 2 substances depending on what is needed or in some domains even thinks of "holes" (absences of electrons) moving.

And yet another domain emerged when anti-particles where hypothesized and found, where negation as cancellation joined the equation. Like technically the proton is already an opposite of the electron, having the opposite charge. While the positron is the anti-particle to the electron, which has not just the opposite charge but is an electron except for the charge, unlike the proton which is for example much heavier. So when positron and electron collide they can annihilate into radiation.

Also the positron or (positive electron) is technically weirdly named, because apart from it's stability in vacuum it's usually the electron that is considered positive while a wild positron would annihilate rapidly and not be present.

So there are a lot of these theories of negation in use in the physics of electrons and the naming convention are often just historic accidents and misnomers that sometimes enlighten and sometimes confuse.

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    I think this is the best answer offered because it goes into detail about electrons and positrons specifically, showing that it is not quite a matter of "evidence for" the negation-as-inversion thesis so much as a slight example of when negation is inversion (such that negation can be other things, too). May 16 at 19:44
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It seems to me that your question proper is not about physics, but rather notations of representations used in artificial languages. Logic, for instance, has several ways to represent negation. A horizontal bar above a proposition, the use of the tilde, the negation symbol. Logic also includes the use of inversion: for a tautology and for contradiction (top and bottom informally in typesetting).

If memory serves, the original convention for the flow of electrical charge is the opposite as it is understood today. The notation of drawing arrows in electrical schematics points away from the cathode towards the anode, though contemporary understanding is that electrons, and thus current, moves in the other direction. This would be an example where inversion of the arrow in schematics (the notation) would have no impact on the actual flow of electrons. (Might make it easier to remember charge flow. (Interestingly, in linguistics, negation is described by the term polarity begging the question if a conceptual metaphor is at play.)

Your question seems to be terminological, and it looks like there might be two ways to understand 'inversion'. On one, like the use of top and bottom, it seems the inversion is a literal description of literally inverting one symbol to another. But swapping two players in a game-theoretic structure doesn't seem to be a literal use of the term. It seems more like the reversal in electrical notation that would simply realign the notation with the conceptual underpinnings of the flow of electrons. (Though this Veritasium video on the flow of current (YT) seems to muddy the waters on the analogy of the flow of electrons like water molecules in a pipe.)

A review of the SEP article you posted starts off with the universality of negation in natural language. In Japanese, inversion is not used to indicate negation with affirmation in two unrelated lexemes: です for affirmation and ありません for negation. English adds a lexeme 'not'. I guess turning symbols upside down would suffer from the hassle of trying to figure which way to read a document if we imagine every sentence and all phrases in English with negative polarity written upside down. It also catalogs what looks like to be a number of subtle differences of negation in different contexts. But it seems to me that your question simply centers around the literal rotation of symbols 180 degrees to indicate notation. In this case, electrons use a negative, and both positrons and protons use a plus symbol, which wouldn't be the literal inversion of notation, though e- and e+ would seem to lend themselves to the same idea that the negative or positive sign is arbitrary and could be used in the opposite fashion without any real difference to how physics is done. In this way, it's an arbitrary convention.

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    There's this hypothesis about the matter/antimatter imbalance that postulates that most antimatter does indeed travel backwards in time, in a way, but that the timeline they travel down is actually reflected around the axis of symmetry of the Big Bang C. So a (hypothetical!) graph of the forward and backward universes together would seem to have a sort of "rotation" of most matter and antimatter clumps into "opposite temporal positions." May 15 at 16:33
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    @KristianBerry The obsession over the asymmetry of time is real. For me, once I got to the realization that the model of time in our heads relies on a presumed external objective notion of the flow of time, it placed me in a double bind in regards to instrumentalism and realism. If the asymmetric flow of time is simply an instrument for understanding time, it would seem there might be some possible world in which time doesn't behave like we understand it. But that time functions in any other way realistically would mean that we couldn't have the simple sequence of inferences. What's that about
    – J D
    May 15 at 17:10
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  • The choice of the sign of leptons is convention. Apparently there is no law of nature that the electron charge is to be considered negative.

  • That the electrodynamic interaction is invariant under charge conjugation is a deep result from physics. The same invariance also holds for the strong interaction, but is violated for weak interaction. For further information see C-symmetry.

  • To me it seems: Connecting these laws of charge conjugation and charge violation with logical negation, and invoking Hintikka and the other authors from your post, including your own thoughts about possible subconscious or “presuppositional” processes – does not bring more clarity.

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  • The obvious point is that if charge negation is conventional per symmetry in physics, and if the negation-as-inversion thesis says that even logical negation is conventional per symmetry in logic, and if we sought to ground our logic in physics to some extent, then we might count the conventionalism about negative charges as evidence for conventionalism about negation simpliciter, i.e. we would be finding support for the position spelled out in the SEP article. May 15 at 18:39
  • @KrisitanBerry And what about violation of charge symmetry by weak interaction ...?
    – Jo Wehler
    May 15 at 18:44
  • Besides not really knowing how much that's relevant, I should note that there is the so-far stable postulate of CPT-symmetry with the T being for "time reversal," of all things. At any rate, if the negation concept is applied conventionally for leptons but less conventionally for some other type of charge carriers, we still would have a relativity of the concept of negation to different subdomains of discourse, so there would be a higher-level conventionalism in play (regarding the use of the word "negation" more generally, here). May 15 at 18:48

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