• bobobor
    12
    Hello everyone,

    It seems to me that many commentators do not appreciate the force of Spinoza's statements about the nature of ultimate reality. According to him, only God exists. God is the only substance. Substance is one, infinite and indivisible. All finite and divisible things are a product of the imagination, which means that plurality, finiteness and divisibility are all illusory. "Measure, time and number are nothing but modes of thinking, or rather of imagining" (Letter to Meyer, 1663).
    It also means, paradoxically, that extension, when truly conceived by the intellect, is at once infinite AND indivisible AND identical with thought (and all the other infinite number of attributes of the one substance).
    It also means, that the everyday world as perceived by the senses - including all the finite moods - is an illusion. Save for the one and only substance, Spinoza is a metaphysical nihilist.
  • Shamshir
    856
    It also means, that the everyday world as perceived by the senses - including all the finite moods - is an illusion. Save for the one and only substance, Spinoza is a metaphysical nihilist.bobobor
    How does this infer nihilism?
    There's nothing that says that the purported illusion doesn't have a purpose.
  • bobobor
    12
    Ontological nihilism is the philosophical position that nothing exists. Spinoza comes very close to it. In its normal use, the meaning of the verb "exist" implies that illusions do not exist. Spinoza says that time, number and measure are merely "modes of thinking", but "modes of thinking" is in the plural, so illusions do not exist because otherwise a plurality of (illusory) entities would exist, which would imply the real existence of number (i.e. a plurality of things).
    Let me add that for some reasons, Spinoza banishes all teleology and purposes from his ontology, so there could be no purpose of anything in it.
    Space and time do not exist in Spinoza's ontology. Substance is aspatial and atemporal. Being infinite, it cannot have finite parts, and being indivisible, it cannot be measured.
    For a different example, see his discussion of "water" in the Ethics (Part I, Note to Prop. XV).
  • Shamshir
    856
    In its normal use, the meaning of the verb "exist" implies that illusions do not exist.bobobor
    What illusions imply are deception and deception is achieved through selective information i.e limited perception. For instance a bottle of vodka actually full of water; you won't know at first glance.

    So, that in tow - how does 'exist' imply that illusions do not exist? Maybe you're implying they don't exist in the sense of being misleading from the whole picture, but then 'exist' wouldn't be the right word.

    Substance is aspatial and atemporal.bobobor
    That's a problem. If there is no space, where's the substance? That's considering that the substance itself comprises its own space or space of self.
    If it's atemporal that could be in due to covering all timeframes, with the inability to shift between them; so it would be temporal but incapable of fluctuation.

    What do you think?

    Being infinite, it cannot have finite parts, and being indivisible, it cannot be measured.bobobor
    I'm not sure how he arrived at that conclusion, but it doesn't really follow.

    Take it as you may, but even infinity is divisible and spells out 'in finity'.
  • 180 Proof
    382
    ... Spinoza's statements about the nature of ultimate reality. According to him, only God exists. God is the only substance. — bobobor

    'Only God is real' - but otherwise correct. Acosmism, not to be confused with the pantheism/pandeism (or panentheism/panendeism for that matter) S still gets dogmatically tagged with by academics despite Maimon & Hegel getting S profoundly right two centuries ago.

    It also means, that the everyday world as perceived by the senses - including all the finite moods - is an illusion. — bobobor

    "The everyday world" (i.e. natura naturata) "is an illusion" only in the sense that it appears ontologically separate from, or independent of, the infinite and eternal Substance (i.e. natura naturans) to finite Modes like us.

    Save for the one and only substance, Spinoza is a metaphysical nihilist. — bobobor

    I think 'metaphysical deflationist' (pace Hume et al) more precisely describes S and his dual-aspect, non-transcendent ontology because, while he argues that only Substance is real (i.e. consists in the essence of existence, that is, The Power to Cause Itself), he also argues that Attributes and their finite/infinite Modes are not real (i.e. consist only in essences lacking existence, or Without The Power to Cause Themselves) merely existing by virtue of being caused, or expressed, by Substance.

    "The everyday world" - nature natured 'sub specie durationis' - is like a wave on the surface of the deep, or an effect, caused by the oceanic Substance - nature naturing 'sub specie aeternitatis'; illustrating, though this analogy is absurdly limited, the perdurance of ephemeral surface waves relative to the long lasting ocean (i.e. Modes of Attributes relative to Substance) and that thereby, however relatively ephemeral surface waves seem, they are not non-existent in the sense S conceives of the difference between existing and the real.
  • bobobor
    12
    "The everyday world" (i.e. natura naturata) "is an illusion" only in the sense that it appears ontologically separate from, or independent of, the infinite and eternal Substance (i.e. natura naturans) to finite Modes like us180 Proof

    I don't agree.The "everyday world" is substance itself perceived in a confused and inadequate way through the senses. But, for Spinoza, even reason is a partially deficient kind of cognition which "regards a number of things at once". The highest kind of cognition is intellectual intuition. Please re-read the passage on water. "water" is a mass noun, but what Spinoza says here must equally apply to all count nouns as well. Water (and anything else denoted by a noun) IS (extension or) substance itself when conceived ("intuited") properly through the intellect.

    the perdurance of ephemeral surface waves relative to the long lasting ocean (i.e. Modes of Attributes relative to Substance)180 Proof

    Several commentators want to interpret Spinoza as holding some "adjectival" theory of modes. I don't see how they can reconcile this with his statement that number (ie. plurality), time and measure only exist in the imagination - which implies that these are inadequate ideas, which Spinoza contrasts with the intellect's (adequate) conception of substance.

    Please also note that Spinoza is a mereological nihilist as he demonstrates in Prop. XII. of Part I that a substance cannot be composed of parts. Therefore, if substance exists and cannot be composed of parts, no ordinary thing (mode) can be composed of parts either, because all modes are included in the attributes and attributes form the essence of substance. As the part-whole composition of ordinary things is illusory, it follows that they don't exist. QED.

    Furthermore, please note that Spinoza writes about causation among finite modes, and the self-causation of the substance. Now, self-causation (causa sui) means that cause and effect coincide. Because in his system true causation is self-causation (this is what we have in our adequate idea of substance), it follows that all other types of causation are untrue, there is inadequacy in their ideas, and their relata do not exist. True causation means that the relata (cause and effect) are identical, which holds only of substance.

    in the sense S conceives of the difference between existing and the real.180 Proof
    Where does Spinoza make that distinction? Sorry, but I cannot find any textual evidence in support of the interpretation that he differentiates between existent and real things.

    how does 'exist' imply that illusions do not exist?Shamshir

    Maybe illusion is not the right word. When I say illusions do not exist, what I have in mind are illusory objects, in effect hallucinations (oasis in the desert). They do not exist by the common usage of the word "illusion" which implies that they are not "out there".


    If there is no space, where's the substance?
    Shamshir

    The question presupposes the existence of space, so it begs the question.
  • tim wood
    3.3k
    God is the only substance. Substance is one, infinite and indivisible. All finite and divisible things are a product of the imagination, which means that plurality, finiteness and divisibility are all illusory. "Measure, time and number are nothing but modes of thinking, or rather of imagining" (Letter to Meyer, 1663).
    It also means, that the everyday world as perceived by the senses - including all the finite moods - is an illusion. Save for the one and only substance, Spinoza is a metaphysical nihilist.
    bobobor

    Pre-Kantian, is how I read it. If I had to render the error in a sentence, it would be confusion of the "how" with the "what." Spinoza, it would seem, is describing a "how" and its consequences. As such, the "what" never comes into it. But we - we being most folks then and now - assign whatness, an error I doubt Spinoza either allowed into print, except as prudential for him, or made in his thinking.

    Metaphor alert: 1) Spinoza built, so-to-speak, an intellectual lever, with fulcrum, arm, load, and force. A machine, then, to realize his arguments and make his points. Subsequent readers confuse the parts, as if to try to lift the fulcrum with the load, and so forth. 2) As a child you imagine your mother loves you. She becomes your saint in your personal hagiography. No harm, serves your purposes - at least until you complete your therapy. But folks generalize the assignment and turn their mothers into real saints - and maybe they're just plain not. But it's not the belief that will bend to the truth, but the truth bent and twisted to fit the agenda.

    Or in sum, to read any thinker accurately requires first shedding or suspending or "bracketing" one's own preconceptions as much a possible, to take the writer on, on his own terms.
  • Janus
    8.6k
    :up: I agree with your interpretation of Spinoza. Puts me in mind of Rovelli too, who I have been reading recently.

    https://www.amazon.com/s?k=rovelli&i=stripbooks&crid=HNGAMPQKM3MV&sprefix=rovelli%2Caps%2C399&ref=nb_sb_ss_c_3_7
  • Janus
    8.6k
    But, for Spinoza, even reason is a partially deficient kind of cognition which "regards a number of things at once". The highest kind of cognition is intellectual intuition. Please re-read the passage on water.bobobor

    Assuming your interpretation all and any kinds of cognition and intellectual intuition would simply be emergent illusory phenomena like all the rest.
  • Wayfarer
    8.8k
    'For 17th c philosophy, at the very deepest level the universe contains only two kinds or categories of entity: substances and modes. Generally speaking, modes are ways that things are; thus shape (for example, being a rectangle), color (for example, redness), and size (for example, length) are paradigm modes. As 'a way a thing is', a mode stands in a special relationship with that of which it is a way.

    Following a tradition reaching back to Aristotle’s Categories, modes are said to exist in, or inhere in, a subject. Similarly, a subject is said to have or bear modes. Thus we might say that a door is the subject in which the mode of rectangularity inheres. One mode might exist in another mode (a color might have a particular hue, for example), but ultimately all modes exist in something which is not itself a mode, that is, in a substance. A substance, then, is an ultimate subject.

    Independence and Priority

    The new philosophers of the 17th century follow tradition in associating inherence with dependence. They all agree that the existence of a mode is dependent in a way that the existence of a substance is not. The idea is that modes, as the ways that things are, depend for their existence on that of which they are modes, e.g. there is no mode of ‘being 8’0 long’ without there being a subject that is 8’0 long. Put otherwise, the view is that the existence of a mode ultimately requires or presupposes the existence of a substance. This point is sometimes put by saying that substances, as subjects, are metaphysically prior to modes.

    Degrees of Reality

    In contrast to contemporary philosophers, most 17th century philosophers held that reality comes in degrees—that some things that exist are more or less real than other things that exist. At least part of what dictates a being’s reality, according to these philosophers, is the extent to which its existence is dependent on other things: the less dependent a thing is on other things for its existence, the more real it is. Given that there are only substances and modes, and that modes depend on substances for their existence, it follows that substances are the most real constituents of reality.'

    Further down in the same article, we read:

    'Spinoza concludes that substance “will be the cause of itself…it pertains to the nature of a substance to exist”. This is analogous, I think, to Aristotle's 'unmoved mover' or first principle, as in that which is self-begetting, not begotten by something else.

    17th Century theories of substance, IETP

    The notion of 'degrees of reality' is significant, I feel. It denotes 'ontological proximity to the first cause'. I would aver that there is no equivalent concept in modern philosophy, although happy to be proven incorrect.
  • Wayfarer
    8.8k
    I entered the above in part because of the equivocation of the term 'substance' in philosophical and ordinary language, In philosophical texts 'substance' is not what we would consider substance in day-to-day language. I think most people believe that 'form and substance' is like a jelly mould, where the jelly is the substance and the mould is the form. But the meaning of substance in classical and early modern philosophy is nothing like that.
  • 180 Proof
    382

    :cool: I'm on my 3rd reading of Order of Time now.

    Or in sum, to read any thinker accurately requires first shedding or suspending or "bracketing" one's own preconceptions as much a possible, to take the writer on, on his own terms. — tim wood

    I couldn't agree more. Well put.

    I don't agree.The "everyday world" is substance itself perceived in a confused and inadequate way through the senses. — bobobor

    No. That's like saying 'tables & chairs, rainbows & kittens' are identical to the fundamental physical laws constitutive of them.

    Only natura naturata, Modes like "the everyday world", appear to natura naturata, Modes like us, sub specie durationis which S distinguishes from Substance, or natura naturans sub specie aeternitatis.

    Where does Spinoza make that distinction? Sorry, but I cannot find any textual evidence in support of the interpretation that he differentiates between existent and real things. — bobobor

    Where does S state he is, as we seem to agree, an "acosmist" rather than a "pantheist" (or vice versa)? C'mon, bob, (closely but charitably) read, interpret, extrapolate, reflect --

    S makes the distinction sub specie aeternitatis between Natura Naturans (i.e. Substance) and Natura Naturata (i.e. Modes): the latter Non-Necessarily Existessences do not contain existence - and only are caused to exist only by the former which - its very essence contains existence - Necessarily Exists. Modes are 'unreal because they may or may not exist'; uniquely, however, Substance is Real because it cannot not (or be conceived of not to) exist. The Definitions & Axioms at the start of The Ethics Part 1 Of God stipulate this distinction which S promptly proceeds to elaborate on (i.e. demonstrate) methodically throughout the progression of Propositions, Scholia, etc that follow.

    Is 'chapter & verse' really necessary? 
  • bobobor
    12
    S makes the distinction sub specie aeternitatis between Natura Naturans (i.e. Substance) and Natura Naturata (i.e. Modes): the latter Non-Necessarily Exist - essences do not contain existence - and only are caused to exist only by the former which - its very essence contains existence - Necessarily Exists.180 Proof

    Modes, according to Spinoza, are "God considered as affected". So it is all about "aspect-seeing", if you wish.
    Let me return to the water example. Spinoza asserts several inconsistent propositions about water, each involving contradictory properties like "divisible-indivisible" "having separate parts - inseparable", "produced - not produced", "corrupted - incorruptible" and so on, according to the different aspects under which it is conceived - imagination (sense-perception) and intellectual intuition, respectively. To repeat, the very same water is seen as "a chunk of ordinary matter" (which is illusory) and "extended substance itself" (which is real). And it is very plausible to suppose that what Spinoza says about water must generalize to all physical entities, mass and count alike.
    Unless you want to interpret him as someone who subscribed to dialetheism, you must resolve these contradictions. One property from the above opposing pairs must go - the question is, which one is to go? Clearly, the one that is conceived at a lower level of cognition, ie. sense-perception (imagination).

    [
    Where does S state he is, as we seem to agree, an "acosmist" rather than a "pantheist180 Proof

    Your comparison seems to me unfair. I requested textual evidence for his distinction between reality and existence - you gave none. My label "acosmist" is just my rephrasing a sentence quoted from Spinoza, in which he says that "measure to determine quantity" does not exist outside the imagination it is only an "aid to the imagination", which means that nothing - not even space - can be measured. Immeasurable space - that would be a real contradiction, wouldn't it? So does the cosmos as we know it exist in Spinoza's ontology?

    all and any kinds of cognition and intellectual intuition would simply be emergent illusory phenomena like all the rest.Janus

    No. Intellectual intuition - the only non-illusory kind of cognition - can be said to be God's self-intuition. As you rightly pointed out, all the rest are illusory phenomena.
  • tim wood
    3.3k
    you must resolve these contradictions.bobobor
    Maybe I'm out-of-court in this part of the discussion, but why must they be? Or more sharply, what, exactly, is meant by "resolve?" Or perhaps even, what, exactly, qualifies the contradiction that the diathelist allows. It cannot be all of them.

    The problem with contradiction - the law of non-contradiction (LNC) - is that rarer than hen's teeth is a real appreciation and discussion of it; it's just taken for granted. But its expression in Aristotle is at a time of maximum tension between rhetoric and logic - Aristotle, following Plato, ultimately favoring logic. But at the same time he clearly understood that rhetoric and logic were different, about different kinds of things, though equally clearly, related. That is, Aristotle, with Plato, would have liked everything to be subject to the LNC, but at the same time, he knew that isn't the case. And rhetoric is the sphere, the place, the forms and arguments, that allow for contradictories, for the purposes of realizing the purpose of rhetoric, usually, a decision as to some action.

    The question, then, becomes, if you cannot (under)stand what you suppose to be Spinoza's contradictions, then, do you understand Spinoza?
  • Fooloso4
    1.1k
    All finite and divisible things are a product of the imagination, which means that plurality, finiteness and divisibility are all illusory.bobobor

    Does Spinoza say this? In the quote from the letter to Meyer Spinoza is not talking about things in the world but measure, duration, and how many. It does not follow that the things that measured and counted are products of the imagination.


    From the letter to Meyer:

    The modifications of substance I call modes. Their definition, in so far as it is not identical with that of substance, cannot involve any existence. Hence, we can conceive them as non-existent. From this it follows, that, when we are regarding only the essence of modes, and not the order of the whole of nature, we cannot conclude from their present existence, that they will exist or not exist in the future, or that they have existed or not existed in the past; whence it is abundantly clear, that we conceive the existence of substance as entirely different from the existence of modes.
  • Wayfarer
    8.8k
    I'd be interested in any comments on the passage I quoted above (and the article it comes from). I think the notion that there are 'degrees of reality' is important in this, because it allows for the conception of things that are more and less real. Whereas, for us, 'existence' is univocal, something either exists or doesn't.
  • Janus
    8.6k
    I think the question of reality has to do, in Spinoza's mind, with the question of necessity/ contingency. Something is Real for Spinoza if its existence does not depend on anything but itself. Since the modes are dependent on God they are not Real in this sense of necessarily existing "in themselves"; but they are not "illusory" either. If Spinoza thought they were illusory, he would be an idealist.

    For Spinoza, who is a determinist, all phenomena are necessary manifestations of substance (God), so they cannot be illusions. So, phenomena are both necessary manifestations of substance and contingent upon substance. You might say they are real but not Real, although Spinoza does not use this language. he uses the terms natura naturata and natura naturans respectively to make the distinction between what we might call the necessary necessary and the contingent necessary.
  • Valentinus
    589


    A while back, fdrake made a helpful comment showing one way to understand the "infinite extension" component.

    As a matter of causality, Spinoza is not defining anything that comes from something other than itself to be an illusion. Our existence depends upon not being so wrong about that sort of thing that our ignorance kills us. Humans have to frame the world as means to ends. Spinoza is telling his Christian brothers that they are anthropomorphising the Creator. In addition, he was exiled from his Jewish community for expressing such views. The approach amounts to starting with one's experiences as authentic information that other people want to fool with.

    I am hard pressed to imagine something further removed from nihilism.
  • Wayfarer
    8.8k
    all phenomena are necessary manifestations of substanceJanus

    I would read it as 'necessary manifestations of being' It's also not exactly correct, but 'substance' is just too close to 'matter' in my reading.
  • Fooloso4
    1.1k
    ↪Fooloso4 I'd be interested in any comments on the passage I quoted above (and the article it comes from). I think the notion that there are 'degrees of reality' is important in this, because it allows for the conception of things that are more and less real. Whereas, for us, 'existence' is univocal, something either exists or doesn't.Wayfarer

    I thought it was very good. I almost cited it in my response. As to degrees of reality, I think it is important for understanding the ontology of those who make use of it, but it is not a concept that I agree with.
  • Terrapin Station
    13.8k
    It seems to me that many commentators do not appreciate the force of Spinoza's statements about the nature of ultimate reality. According to him, only God exists. God is the only substance. Substance is one, infinite and indivisible. All finite and divisible things are a product of the imagination, which means that plurality, finiteness and divisibility are all illusory. "Measure, time and number are nothing but modes of thinking, or rather of imagining"bobobor

    How would I appreciate the "force" of it when it just seems arbitrary and nonsensical to me?
  • 180 Proof
    382
    To repeat, [ ... ]
    Unless you want to interpret him as someone who subscribed to dialetheism, you must resolve these contradictions.
    — bobobor

    No, bobo, don't. I assumed you'd studied, not merely read/skimmed, The Ethics (at least the entirety of Part 1 Of God). My bad.

    Your comparison seems to me unfair. — bobobor

    Of course it does.

    So does the cosmos as we know it exist in Spinoza's ontology? — bobobor

    Yeah, "the cosmos" (i.e. Natura Naturata) exists (vide Einstein re: Spinoza) but only exists non-necessarily (i.e. contingently), that is, "the cosmos as we know it" can be conceived of not existing, and therefore, in Spinoza's sense sub specie aeternitatis, is unReal.
  • Wayfarer
    8.8k
    As to degrees of reality, I think it is important for understanding the ontology of those who make use of it, but it is not a concept that I agree with.Fooloso4

    Well, I think it might help to make sense of the distinction between 'necessary' and 'contingent' being. The former exists necessarily, the latter as only derivative from the former. It allows us to say that the cosmos 'as we know it' exists, but is not real. Whereas the current philosophical lexicon rarely allows for this distinction.
  • Fooloso4
    1.1k
    Well, I think it might help to make sense of the distinction between 'necessary' and 'contingent' being.Wayfarer

    Yes, I agree, but that is not a distinction I find helpful unless when reading those who make use of it. One must accept the notion of a necessary being.

    Added: That is, one must accept the notion of a necessary being in order to make such distinctions. I do not.
  • Janus
    8.6k
    Matter is not what Spinoza means by substance. According to Spinoza matter/form (substance extended or res extensa) and mind (substance thinking or res cogitans) are just two of the infinite attributes of substance.
  • StreetlightX
    4.3k
    E1D3: "By substance I understand that which exists in itself and is conceived through, or by means of, itself; i.e. the conception of which does not require for its formation the conception of anything else."
  • bobobor
    12
    "the cosmos" (i.e. Natura Naturata) exists (vide Einstein re: Spinoza) but only exists non-necessarily (i.e. contingently)180 Proof

    No. All contingent existence is illusory. If you don't want to interpret Spinoza as contradicting himself, you must acknowledge this.

    To see why, here is a challenge, an argument based on textual evidence. I use only three "premises", if you wish (although not in a strict logical form).

    1) In Part I of Ethics, Spinoza explicitly asserts in its definition that a mode is "IN ANOTHER" ("By mode I understand the affections of a substance, or that which is in another through which it is also conceived.)

    2) In the same definition, he also asserts that a mode is conceived through that "another" (so it depends on it notionally).

    Thus, supposing that that "another" is substance (via its attributes), it means that all modes (if they
    existed) 1. would be IN the substance 2. They would DEPEND on the substance notionally.

    By notional dependence I mean that modes cannot be understood without understanding what the substance is (i.e. without understanding the attributes that form its essence).

    3) BUT Spinoza must deny that modes inhere in the substance ("are in another") as parts in a whole. Why? Because, if they would, then substance would have parts. But Spinoza demonstrates that no substance can have finite parts. (Ethics, Part I, Prop XIII.)

    Let me recap the main points: All Modes would be 1) "IN the substance", 2) would "DEPEND on the substance notionally" and yet they would 3) NOT be parts of the substance.

    And here's the challenge: explain the following situation, preferably by giving an example of something (let us call it X) and another thing (let us call it Y) that meets all the three requirements below (of course, substituting "mode" for X and "substance" for Y would beg the question):

    1) X is in Y.
    2) X depends notionally on Y (X cannot be understood without reference to what Y is).
    3) X is not a part of Y.

    To me, this is sheer conceptual confusion. Yet, 1), 2) and 3) should be true of all finite modes if they existed. So you better admit that no finite modes exist, on pain of contradiction.
  • Janus
    8.6k
    Your argument relies on equivocating between "affection" and "part". My affections are not a constitutive part of myself, they are activities, but they are real nonetheless.
  • StreetlightX
    4.3k
    :up: The whole effort of Spinoza's metaphysics - the very essence of its radicality - consists of contesting the subject-predicate Aristotelian model of relations that the OP is working with. Perhaps the best way I've heard it put is that the modes have an adverbial nature, rather than a substantival one - they expresses not “what” but “how” being is.
  • TheWillowOfDarkness
    1.9k
    1) X is in Y.
    2) X depends notionally on Y (X cannot be understood without reference to what Y is).
    3) X is not a part of Y.

    To me, this is sheer conceptual confusion. Yet, 1), 2) and 3) should be true of all finite modes if they existed. So you better admit that no finite modes exist, on pain of contradiction.
    — bobobor

    Spinoza's distinction between substance and modes is precisely understand all those three are true of all finite modes.

    Finites modes (X) are of the singular unity substance (Y ).

    Any finite mode, notionally, depends on Y (substance) because no finite modes occur outside its unity. (for there were modes outside substance, there would not be the unity which is of all modes). It's not because substance is some kind of being which is making the modes exists, but rather simply because anything which does exist is of the unity.

    Finite modes are not part of substance at all. For that to be the case, substance would be rendered just another contingent being, present only on account of these specific modes. The unity of substance requires it be beyond any of its modes, since it is not given by any particular mode.

    We can seen this in how an identification of substance gives no insight into which modes are present. If I mention how there is substance, I fail to describe anything about which finites modes exist. Similarly, if i mention there is a finite mode, I fail to speak about the unity of substance. If I describe Spinoza's Ethics exists on my shelf, I failed to identify substance.

    No conceptual confusion, 1), 2) and 3) are all true of existing finite modes.
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