Comments

  • Problem with the view that language is use
    Really? I gleaned it from SoamesMongrel
    Well that explains it, lol

    The first point is that the issue of communication is peripheral at best with respect to the rule-following problem. Secondly, he didn't think that there is anything external that you can add to any rule in order to make it work (like human interaction), rather his point is that we have to radically rethink our philosophical preconceptions about what rules or meaning must be like (such as a picture of a rule that determines its own application all in advance and in a vacuum). So his idea is that once we learn how to look at rules in the right sort of way (that is, not distorted by some philosophical requirements) the ordinary phenomena of rule-following will cease to appear as something mysterious that stands in need for a philosophical explanation (my reading here is mainly due to Cora Diamond and John McDowell - if you wish to read more on this topic).
  • Problem with the view that language is use
    Quine laid out an impressive argument indicating that the ability to apply logic to new situations has to be apriori know-how.Mongrel
    Where did he say this?
  • Problem with the view that language is use
    My understanding is that Witt noticed that rule-following can't account for the entirety of communication because there has to be some source of normativity outside the system of rules. He looked to human interaction to find that source.Mongrel
    I would dispute this interpretation.
  • Problem with the view that language is use
    Yes we can say that "a means b" for an organism if he usually expects b when he sees a, but this is not "meaning" in the symbolic sense like the words of a language (and that was the point I wanted to make).
  • Problem with the view that language is use
    Yep. He's talking about the creative power of language. Duck/rabbit style. We make the stick a standard by comparing stuff to it. See? He's talking about meaning and existence simultaneously.Mongrel
    Yes, but it is a somewhat different issue that has to do with that quote from Plato. I only posted this passage to illustrate one particular idea (that things other than words can belong to language or a symbolic system), but there are some other questions that Wittgenstein wanted to address in this passage.
  • Problem with the view that language is use
    If that's what you're asking, I had no idea. You weren't at all clear about that.Terrapin Station
    I was addressing something that Harry Hindu said (and I assumed that you meant to defend his claim). He said: "the meaning of a yellow banana is that is it ripe. It's blackness means it is rotten. We don't need language to know this", and this is the claim that I was criticizing. Was your story meant to illustrate this or something else?
  • Problem with the view that language is use
    So you're saying we can disregard his use of "means of representation."?Mongrel
    No, that's not what I'm saying. "means of representation" means something like an aid or an instrument of representation, and this is compatible with saying that the stick itself doesn't represent anything.

    Don't you agree he's saying the instrument (whether standard meter or sepia) exists because of its function or role in our language games?Mongrel

    If by that you mean "why did we build the standard meter?" then yes, obviously it was created for this particular purpose.

    Can you explain what he means when he says it is and is not a meter?Mongrel
    Because we can't measure the stick with itself, or at least not in the sense in which we can measure tables with the stick, so it is senseless to say either that it is a meter or that it isn't a meter long because being or not being a meter long is determined by a procedure of comparison with the stick which we cannot apply to the stick itself.
  • Problem with the view that language is use
    Can't you measure the standard meter by other means? Say the time it takes light to traverse that distance, and then compare that to the time it takes light to go other distances? The speed of light isn't something we made up, so it could serve as an absolute standard, like atomic clocks can be an absolute standard of measuring time.Marchesk
    Of course you can measure the meter stick by some other units, but in this case it will be no longer treated as a standard of length.
  • Problem with the view that language is use
    That would entirely depend on whether the monkey has experience with bananas for there to be a good reason, via induction, for him to assume that yellow bananas are correlated to ripeness.

    If he has an extensive history of yellow banana implying "ripe," then he'll likely assume that something unusual is going on with the bananas.
    Terrapin Station

    I think that your story already presupposes that the monkey can understand what 'the banana is ripe' (or that it isn't) mean - but remember, what you are supposed to explain is how the monkey acquires the ability to represent the ripeness of the banana in the first place.

    This is because induction requires the ability to form a hypothesis, and then use experience to confirm or disprove it. But to confirm the hypothesis that the ripeness of the banana is correlated with its color by means of repeated observation, you need to know in advance (before you start observing) what it would be for a banana to be either ripe or not ripe (otherwise how could you tell whether your hypothesis was confirmed or not?); but how can you know that from your experience unless you already have some way of symbolically representing the state of the ripeness of the banana?
  • Problem with the view that language is use
    the standard meter in Paris is not considered to be a representation of the concept of a meter. It's a standard. It's also not intended to represent the length of anything. Unless I'm misunderstanding how "representation" is being used here.Mongrel
    But the stick does define what a meter is, or at least this is how it was historically (though nowadays it is defined differently, but that's irrelevant - we can just as well talk about the invented example of the 'standard sepia'). And it doesn't really matter whether you say that the meter stick represents the length of something or not, because the main point is that it is an essential instrument in the game of measuring which Wittgenstein has in mind (in which we do in fact represent the length of objects).

    Wasn't he saying that since we can't measure the standard (because that would require a second standard), it's sort of ordained as the standard in practical use. The reality of the standard is not related to a physical object. It's basis is actually in use. He's going beyond meaning as use, here. It's reality in use.Mongrel
    This is not what he says - there's no sense in measuring the standard because we chose to define it as a standard (or that it has been 'ordained' as you say), and not the other way round.

    And what do you mean by "the reality of the standard is not related to a physical object"?
  • Problem with the view that language is use
    It doesn't really solve the philosophical problem of meaning to say that there are some 'ideas' in your mind. The fact that something is in your mind as opposed to behavior doesn't magically solve everything. It doesn't explain meaning (or rather, it doesn't tell you what meaning is), because if there is a puzzle about how mere words can represent something, there's equally a puzzle about how 'ideas' in someone's head can do the same thing. Thinking that the mind has some magical ability to simply 'mean' things is an illusion.

    I already quoted some passages from Wittgenstein where he gives an argument (especially the sections about the cube picture) against views like yours, but you however completely ignored that argument.
  • Problem with the view that language is use
    If you are interested, when he talks about the existence of the simple elements, he criticizes a view expressed in a passage from Plato which he quoted in section 46: (it's a bit complicated topic)

    46. What lies behind the idea that names really signify simples?--

    Socrates says in the Theaetetus: "If I make no mistake, I have heard some people say this: there is no definition of the primary elements--so to speak--out of which we and everything else are composed; for everything that exists in its own right can only be named, no other determination is possible, neither that it is nor that it is not ... But what exists in its own right has to be ... named without any other determination. In consequence it is impossible to give an account of any primary element; for it, nothing is possible but the bare name; its name is all it has. But just as what consists of these primary elements is itself complex, so the names of the elements become descriptive language by being compounded together. For the essence of speech is the composition of names."

    Both Russell's 'individuals' and my 'objects' (Tractatus Logico-Philosophicus) were such primary elements.
  • Problem with the view that language is use
    Right. Talk about meters is a means of representation. The language game in which we talk about meters is a means of representation. Right?Mongrel

    No, the means of representation is the physical meter stick itself, and W's point is that it can function as such (as "means of representation") only if it is used as a unit of measuring within a 'language game' of measuring things (e.g. where things are compared according to their length for various purposes etc.).
  • Problem with the view that language is use
    Of course. So in the quote you put up, by "our method of representation," he means the language game in play when we talk about fictional things. Where is the representation exactly?Mongrel

    In the quote he talks about representing the length of things via the unit of meter (or colors by a color sample).
  • Problem with the view that language is use
    So by "language game" he meant a method of representation?Mongrel
    No, 'representing' is only one kind of language game (in Wittgenstein's sense) but there could be many others. However if we talk about 'meaning' - in the sense of a word standing for a thing - then I think the question of representation is the central one (but of course language has many other functions other than to represent things).
  • Problem with the view that language is use
    There is more to a banana that just it's color. It also has a shape that isn't the shape of a ball. It also has a particular texture. It's shape, texture and color is what defines it as a banana. We have different senses that allow us to make these distinctions between yellow balls and yellow bananas.Harry Hindu

    Fine, but this is not sufficient to get meaning. Being able to discriminate between objects by their properties is not the same as representing them as being in this way or other. For something to symbolize something else there must exist the possibility of truth and falsehood (that is, of representing something correctly or incorrectly), and that could only make sense within a symbolic system (and again I'm not saying that it must be necessarily verbal).
  • Problem with the view that language is use
    You responded as if we were saying something about the color yellow (in general, regardless of where it occurs) rather than saying something about yellow bananas.Terrapin Station

    OK, but I don't think that it really matters whether we talk about yellow as a color, or yellow bananas in particular. I can change my example: suppose a monkey encounters a yellow banana which happens to be rotten, should we say that the monkey infers that he made a mistake about the banana being ripe, or maybe it had the a disjunctive concept that a yellow banana represents either being ripe or rotten? (in which case it didn't made a mistake). Is there a way to decide what the monkey "means" just by knowing its causal history of interactions with bananas?
  • Problem with the view that language is use
    Why would you be mentally bracketing the color yellow as if it's something independent? The idea is yellow bananas versus green or dark brown/black bananas.Terrapin Station
    I'm afraid I don't get your point.
  • Problem with the view that language is use
    Isn't he saying via experience? Via eating a number of bananas, you notice a correlation between the color and the ripeness.Terrapin Station
    But this doesn't make the color yellow itself into a symbol for ripeness. Suppose a monkey comes to expect a banana whenever it sees a yellow object. Would we say that when the monkey sees a yellow ball it believes that the ball is ripe? Or does it believe falsely that the ball is ripe banana? From the example alone it is simply not clear what is supposed to be represented by what.
  • Problem with the view that language is use
    Then how does one get to know and therefore use their first word if we need other words to tell us what another word means?Harry Hindu
    But we don't always need words to tell us what another word means. when a child learns his first language, he is given demonstrative explanations for words - he is shown their use.
  • Problem with the view that language is use
    And if meaning were use, then why are dictionaries full of definitions rather than uses of the word? There are sentences as part of a definition, but they are examples of it's use for that particular definition. If meaning were use then why have dictionaries at all? Any way I use a word would be what it means.Harry Hindu
    What dictionaries do is to replace words which the speaker doesn't know their conventional use, with words that the speaker does know how to use, because if he didn't then the dictionary would be completely useless to him.
  • Problem with the view that language is use
    I think it's worth quoting Wittgenstein once again:

    50. What does it mean to say that we can attribute neither being nor non-being to elements?--One might say: if everything that we call "being" and "non-being" consists in the existence and non-existence of connexions between elements, it makes no sense to speak of an element's being (non-being); just as when everything that we call "destruction" lies in the separation of elements, it makes no sense to speak of the destruction of an element.

    One would, however, like to say: existence cannot be attributed to an element, for if it did not exist, one could not even name it and so one could say nothing at all of it.--But let us consider an analogous case. There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris.--But this is, of course, not to ascribe any extraordinary property to it, but only to mark its peculiar role in the language-game of measuring with a metre-rule.--Let us imagine samples of colour being preserved in Paris like the standard metre. We define: "sepia" means the colour of the standard sepia which is there kept hermetically sealed. Then it will make no sense to say of this sample either that it is of this colour or that it is not.

    We can put it like this: This sample is an instrument of the language used in ascriptions of colour. In this language-game it is not something that is represented, but is a means of representation.--And just this goes for an element in language-game (48) when we name it by uttering the word "R": this gives this object a role in our language-game; it is now a means of representation. And to say "If it did not exist, it could have no name" is to say as much and as little as: if this thing did not exist, we could not use it in our language-game.--What looks as if it had to exist, is part of the language. It is a paradigm in our language-game; something with which comparison is made. And this may be an important observation; but it is none the less an observation concerning our language-game--our method of representation.
  • Problem with the view that language is use
    Are you going to address the "Man with No Words"? He has memories to, but had no words to associate with them.Harry Hindu
    In my first response to you I already said that something can be a symbol without being a word, and I also said that meaning is not just "associating" words with things, so I didn't say that a verbal language is necessary for symbolizing.
  • Problem with the view that language is use
    Why stop there? Nothing would stop you from continuing on to question whether or not you even have a memory of a woman or even a memory of a word and how it is used.Harry Hindu
    Yeah, that's my point - your memory, or a color of something is a symbol or a representation of something else only in its use as a symbol. Something cannot acquire a symbolic meaning just by some act of magic - it can represent only as so far as it belongs to a symbolism (whatever verbal or otherwise).

    Exactly. That is why I mentioned that you need experience in eating yellow and black bananas.Harry Hindu
    This isn't sufficient either. How do you connect between the color of something and your eating it?
  • Problem with the view that language is use
    It's not necessarily a symbol. To know a banana is ripe is to see it as yellow.Harry Hindu
    But you can also see the banana as yellow without knowing that it is ripe (or even knowing that it is something edible). So just seeing the banana is yellow is not sufficient to represent it as ripe.
  • Problem with the view that language is use
    As a memory - how else?Harry Hindu
    How do you know that you have a memory of your mother, and not some other woman that just looks like her? If you consider your memory in isolation from context (or 'use') then by itself it doesn't mean or represent anything.
  • Problem with the view that language is use
    This makes no sense. The meaning of a yellow banana is that is it ripe. It's blackness means it is rotten. We don't need language to know this.Harry Hindu
    If you are using a color of something to represent something else, then the color itself becomes a symbol, you don't even need words for that. I don't see how your example contradicts anything that I said.
  • Problem with the view that language is use
    how is it that your mother pops into your headHarry Hindu

    What does it mean "pops into your head"? Surely she isn't PHYSICALLY in your head like your brain is, so in what sense do you want to say that she is "in" your head?
  • Problem with the view that language is use
    It seems that things other than words and how they are used are imbued with meaning.Harry Hindu
    Wittgenstein would not disagree. See sections 73-74 from the Investigations that I quoted on p.3, which talk about samples: W' repeatedly makes the point that many different things other than words (such as color samples) can belong to language and be part of the symbolism (see also section 50 about the standard meter in Paris).

    What is true though is that for Wittgenstein 'meaning' is not an external relation (e.g. causal) between words and things: if word 'refers' to something then that something belongs to language, or has a symbolic function as much as the word which stands for that thing.
  • Problem with the view that language is use
    I think it could be useful to quote Wittgenstein's himself, and sections 73-74 from the Investigations summarize particularly well what he essentially meant by 'use' - that if we consider 'meaning' as something which could be described in isolation from our actual practices of language use, we simply look in the wrong place.

    73. When someone defines the names of colours for me by pointing to samples and saying "This color is called 'blue', this 'green'....." this case can be compared in many respects to putting a table in my hands, with the words written under the colour-samples.--Though this comparison may mislead in many ways.--One is now inclined to extend the comparison: to have understood the definition means to have in one's mind an idea of the thing defined, and that is a sample or picture. So if I am shown various different leaves and told "This is called a 'leaf'", I get an idea of the shape of a leaf, a picture of it in my mind.--But what does the picture of a leaf look like when it does not show us any particular shape, but 'what is common to all shapes of leaf'? Which shade is the 'sample in my mind' of the color green--the sample of what is common to all shades of green? "But might there not be such 'general' samples? Say a schematic leaf, or a sample of pure green?"--Certainly there might. But for such a schema to be understood as a schema, and not as the shape of a particular leaf, and for a slip of pure green to be understood as a sample of all that is greenish and not as a sample of pure green--this in turn resides in the way the samples are used. Ask yourself: what shape must the sample of the color green be? Should it be rectangular? Or would it then be the sample of a green rectangle?--So should it be 'irregular' in shape? And what is to prevent us then from regarding it--that is, from using it--only as a sample of irregularity of shape?

    74. Here also belongs the idea that if you see this leaf as a sample of 'leaf shape in general' you see it differently from someone who regards it as, say, a sample of this particular shape. Now this might well be so--though it is not so--for it would only be to say that, as a matter of experience, if you see the leaf in a particular way, you use it in such-and-such a way or according to such-and-such rules. Of course, there is such a thing as seeing in this way or that; and there are also cases where whoever sees a sample like this will in general use it in this way, and whoever sees it otherwise in another way. For example, if you see the schematic drawing of a cube as a plane figure consisting of a square and two rhombi you will, perhaps, carry out the order "Bring me something like this" differently from someone who sees the picture three-dimensionally.
  • Problem with the view that language is use
    I'm only using animal communication as a means to critique the notion that meaning is only exclusively it's use.Marchesk

    It seems to me that you don't really understand what W' meant by 'use', since your critique has nothing to do with his actual views (and he certainly wasn't a 'behaviorist' in the usual sense).
  • Problem with the view that language is use
    But how does this explain the difference between animal communication and human?Marchesk
    As I said, it's not a philosophical question and therefore completely irrelevant to philosophical problems about language and meaning. It is not something that you can answer by armchair speculations.
  • Problem with the view that language is use
    I was trying to find a quote from some behaviorist in the past (Watson maybe) that I saw a long time ago. It may have been taken out of context, but it went something like this:

    "I could teach an earthworm English with the right stimui."

    Which is impossible because the earthworm has no such cognitive capacity to learn English, let alone lacking any sort of body that could communicate words.

    I mention that because it ties back to how animals generally lack certain linguistic features that human languages possess, and this is biologically based. Behavior can't bootstrap an ant colony to English, unfortunately, because that would be fascinating. (Did read a scifi story were wasp colonies were intelligent and figured out how to go online and tell us about it. They may have been genetically enhanced, though).
    Marchesk
    Well but that's not a philosophical question but a scientific one (about the psychological conditions under which some organism is capable of learning a human-like language). This was not the kind of question which interested Wittgenstein, and therefore it wasn't the question that he tried to answer when he talked about meaning and use (therefore the topic of this whole tread simply misses its target). What interested Wittgenstein were the logical features of language that make it function as a language, not the psychological conditions which allow some creature but not another to learn language - that has nothing to do with philosophy according to W'.
  • Problem with the view that language is use
    Sort of, but I think at this point one would invoke Kant, because this seems rather Humean and empirical. And Kant argued persuasively that you need categories of thought to get the empirical endeavor off the ground, otherwise you just have a meaningless jumble of sensory impressions.

    Similarly, you need cognition to make language work, otherwise, you just have a bunch of meaningless behavior.
    Marchesk
    Yes you can say that there is a Kantian ring to Wittgenstein's philosophy, but it has nothing to do with 'cognition' (whatever it means) as you say. Again, the point here is not that we have to look into the realm of psychology (as opposed to behavior) to understand language, rather I think that both Kant and Wittgenstein argued that you have to look at logic or norms, that is how we use the logical/normative system of language in our dealing with the world (or experience in Kant's case).
  • Problem with the view that language is use
    Wittgenstein was aiming for a radical redefinition of meaning, not merely pointing out that words acquire meaning by how they're used. Everyone knows that already. Wittgenstein's approach is behavioral, not cognitive, and I take issue with that.

    You must have the cognitive (thought) prior to behavior, or there are no language games. Language games can't get off the ground without cognition.
    Marchesk

    But Wittgenstein's argument is that 'cognition' by itself can't do anything magical that is over and above what behavior can, as far as language or meaning are concerned. If you are puzzled about the possibility of meaning, postulating some magical inner mechanisms in the mind is not going to solve the problem. This is because the philosophical questions about symbolism (i.e. representation of reality through language or though) is going to arise about inner mental states as much as it arises for written signs on paper, or behaviors. You are not going to get meaning out of something just by assuming that it is something 'cognitive', 'mental', 'inner' or whatever. And this is because you can't understand a symbolic system (whether it is language or thinking) just by inspecting the physical or mental properties of the symbols themselves (i.e., the words on the page or inner mental states).

    So for example take sections 139 -142 in Philosophical Investigations, where Wittgenstein illustrates this point by showing that a mere existence of some mental state like a mental picture (in his example it is a picture of a cube) cannot by itself determine a unique meaning or use for the word (or concept) 'cube', because the picture can be interpreted in countless different ways as standing for completely different things. And the mere fact that the picture is 'mental' can't force on you just one unique interpretation which will somehow make you understand the picture as a 3d picture of a cube, and not say as a bunch of 2d rectangles (and similar considerations apply to 'interpretations' as mental entities which accompany the picture). (see also sections 73-4 where he makes a parallel point about a sample of a leaf - for something to be a sample for something else - and this is connected to your question about universals - it is not enough to consider the sample by itself, rather you must look at its use; you must consider the technique of comparing the sample with the things which it is a sample of, e.g, what circumstances are we going to count as something that 'fits' the sample (or doesn't), and what practical purpose it serves)

    And so when Wittgenstein talks about 'use', what he means by that (among other things) is that you have to look at the use of symbols within a system or a praxis to understand their meaning, and this means that you have to consider how the symbols (to put it in a Tractarian way) are compared with reality: e.g., under what circumstances do we say that such and such is the case, what kinds of other propositions can we logically infer from it, and what sorts of language techniques ('language games') we need in order to make the talk about this or that subject matter intelligible (and there is a host of many pother questions that need to be answered).
  • Problem with the view that language is use
    What does it mean "language is use"?
  • Compositionality & Frege's context principle
    As Srap Tasmaner suggested, it's better not to use the word 'meaning' here, or any of its cognates, to describe what you say since it will only cause confusion. It doesn't show that "it's semantics all the way down" as you claimed.
  • Compositionality & Frege's context principle
    When I say "meaningless" I mean semantic content, and save few rare exceptions (such as 'a' like in "a man"), letters don't have any semantic function analogous to words. If we put aside ambiguity (and a couple of other complications), then when you have two sentences with the same word, you know the word has the same semantic function (i.e., it's not a coincidence that we use the same word both in "the cat is on the sofa" and "I have a cat" etc.). Whereas if you have sentences with the same letters it tells you absolutely nothing about the meaning of the sentences since it's a pure coincidence that in English e.g., 'cat' and 'car' have two letters in common, and therefore from this you can't infer anything about their semantic content (it would be absurd to infer that 'cat' and 'car' must mean similar things because they share some letters - what about other languages where they don't?).

    About the meaning of words, as I said in another post, it's a bit of a terminological dispute. The really interesting question is in what sense words have "meaning" and what is the relation between the meaning of words and the meaning of sentences, and which one is more basic. We can talk about the meaning of words in some sense, but on my view (as someone who takes the context principle seriously) the meaning of words is parasitic on the meaning of sentences, and that means that atomistic semantic theories (that try to explain the meaning of sentences on the basis of the meanings of their words) are false.
  • Compositionality & Frege's context principle
    You either analyse sentences into components or you don't. If only sentences have meaning, then their components are meaningless. You can't have your cake and eat it too. Your contextualist who notices "structural similarities" among sentences would be like the guy who reasons that "ball" and "balk" and "balm" must have similar meanings. If you don't get to use components, all you have is truth conditions.Srap Tasmaner

    It can't be right that if something is composed of meaningless parts, then it itself must be meaningless (if this is what you meant). Surely, the letters of the alphabet from which words are composed are semantically meaningless, and yet the compositionalist claims that words are meaningful (and the same applies to sentences, they are also composed of meaningless letters). So if you are right, then even on the compositionalist view all words (and therefore sentences) are meaningless - and that can't be right.

    The same applies to what you said about logical connectives.
  • Compositionality & Frege's context principle
    The past tense thing was just meant as a proxy for all the stuff we learn to talk about where we cannot directly check that the relevant truth conditions obtain. I think you hit a wall pretty quickly if all you have to go on is the truth and falsehood of statements.Srap Tasmaner

    Sorry I don't get your point. On my account you don't have to know the truth or falsehood of this or that particular sentence, only understand the truth conditions of some sentences (which is of course not the same as knowing whether they actually obtain).

    Even the natural next step is blocked, which is recursively generating complex statements from simple ones using the logical constants. (And similarly for understanding such statements by analysing then into simple statements so coupled.) I don't see how you get the logical constants going at all.Srap Tasmaner

    Again, I don't see your point here... If as you say logical constants recursively generate sentences by combining other sentences, then how is the question about the meaning of single words supposed to arise here? I think that on the contrary, truth functional logic seems to be very congenial to the contextualist.

    If forced to choose, I'm saying the word is the basic semantic unit, not the sentence, so long as it's understood that the meaning of a word is the semantic contribution it makes to a sentence in which it is used. The statement is the unit of judgment, though, so "semantic" up there is really the wrong word. The word is the smallest unit of meaning.Srap Tasmaner

    Perhaps there is a sense in which this whole debate is terminological. You could say that words have individual "meanings" on my account, but only if by "meaning" we understand something other than saying, e.g., that the meaning of the word 'cat' is cats (that is, that meaning can be explained by sub-sentential relation between words and things in the world (such as reference)). Rather knowing the "meaning" of a word is to know its logical function in different sentences, or seeing what is in common between different sentences that contain the same word (and I have in mind here Wittgenstein's "propositional variables" in the Tractatus, and it can be argued that Frege's object/concept/function distinction is a similar idea). So perhaps the real issue here is explanatory priority between words and sentences, rather than the question about the meaning of individual words (which can be understood in all sorts of different ways).