Soundness of reason is merely a reference to linguistic convention, and has no significance beyond convention.

Take any example of unreasonable behaviour. Once the behaviour is understood, the unreasonableness disappears. Of course, we might not like a person's behaviour even when we understand it.

Ironically, not only does Johnson's 'refutation' of Berkeley miss the the point, but his non-representational demonstration of the meaning of "real" by actually kicking a rock is a very acceptable definition of "real" for the subjective idealist. Such a demonstrative definition of "real" doesn't by itself lead to the dualistic notion of mental representation of the physical world that haunts realism.

Then the idealist is simply wrong. One can demonstrably conceive of an unconceived object. I can, at least. Why should I believe that anyone else is so different from me in this respect?

I can also predict where this is going to go, and that the idealist will make an error in his or her reasoning here. "But you're conceiving of it!". Yes. Yes I am. — S

Yes, i believe you. And i would even argue that it is obligatory when following the logic of idealism for the idealist to accept any realist claims to the contrary of allegedly "conceiving of an unconceived object", as contradictory as that might sound. For the idealist can always interpret the realist's statements in a way that satisfies idealistic logic.

For example, when a realist is asked to explain himself, he might say "When I say that I am conceiving of an unconceived object, I have this particular image in mind". All that the idealist can say in response is "I wish you wouldn't name that experience "unconceived"!"

Is conception a la idealism a correlative fact in your view, or is it what objects are?

In other words, are you saying that one might be an idealist who allows mind-independent objects, whether they're perceived or not, as long as we correlatively conceive of them, too?

Or is the conception what the objects are? (And then we'd have to figure out how it would make sense posit an unperceived conception, and whether the conception has to be present-to-mind for that or not.) — Terrapin Station

In general I understand George Berkeley and his philosophy of subjective idealism as being a precursor to twentieth century Phenomenalism. For I can only make sense of Berkeley's arguments for Idealism when they are interpreted as grammatical statements that identifies the very meaning of "X exists" with the empirical conditions under which "X" is asserted.

I understand Berkeley's notion of 'ideas' as not referring to conceptual, metaphysical or psychological entities, but much more weakly as referring to acts of observing or thinking.

Of course, looking at an actual object called "X" is not comparable to thinking about "X" when there are no objects present with the same name.

The idealist, who is not concerned with the correlation of thought, language and perception might as well rename his mental image of "X" with the letter "Y" and reserve the use of "X" for exclusive referring to an actually present object named "X". By doing so, he could then forbid the construction of the question "Does X exist when unperceived?" as being nonsensical, in being in violation of his rule for using "X".

He is then free to say "Y exists when unperceived", for it is understood, by definition, as only referring to a thought.



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The question isn't relevant to the idealist. For the question conceives of an unperceived object, which isn't what the idealist is taking issue with.

What the idealist is taking issue with, is the notion that an unconceived object is conceivable. Consequently, your question cannot be constructed in any way acceptable to the idealist, since the idealist will interpret the question as being self-refuting.

The idealist is rebelling against the realist's understanding of an object's existence as transcending the entire space of perceptual and conceptual constructs, as opposed to merely transcending acts of perception.

The realist's central task is therefore to establish whether an idealist is naming objects in terms of particular acts of conception or perception. The realist cannot find such naming conventions useful, for the realist's chief interest is in making experimentally testable speculative inferences about the future and he consequently demands that names convey speculative implications.

In contrast, the idealist whose only concern is to dismiss the idea of mind-independent entities as being incoherent, isn't interested in predicting the future. His use of names therefore does not coincide with the realist's use of names.

"Natural Selection" seems analogous to "Lawless Sequence of Numbers" in arithmetic.

We never see a completed infinite sequence. So "Lawful" only refers to actively using a recipe to generate a sequence or to predict a sequence, say an equation or calculator, whereas "Lawless" refers to merely observing a sequence unfold before us 'without us having an idea or plan'.

But isn't there always uncertainty when using a recipe? Don't we invariably resort to consulting with a calculator? So unless we are platonists, Lawfulness and Lawless aren't terms that describe unfolding sequences in and of themselves. Rather they are merely informal practical designators for how we are using or generating sequences.

Artificial selection is derivable from natural selection, while natural selection is derivable from artificial selection, yet their distinction is merely practical rather than formal or ontological, because this distinction rests upon the notion of an algorithm which is itself a merely intuitive concept, recalling the reason why the Church Turing thesis isn't provable.

Consider that the ancient greeks identified numbers with visual geometric constructions obtained using a compass and a straight edge.

If our concept of numbers is derived from geometrical intuition, then any attempt to address Zeno's paradox via appeal to the resulting mathematics is equivalent to trying to make sense of the A series of time via the B series.

Not only does this way of thinking make Zeno's paradox even more bewildering and intractable, it isn't acceptable from the point of view of the intuitionist, who identifies the construction of numbers not with sketches on paper, but with the very phenomenal passage of time.

From this perspective, first-position events are constructed by the very act of starting to count. Zeno's paradox can instead be interpreted as a paradox concerning the conceptual issue of what it means to distinguish spatial positions that represent different times, such as the hands of a clock.

Quantified measurements of position information appeal to machinery, and hence to Computable Analysis that recognizes only a countable set of numbers, namely the computable numbers which represent equivalent-classes of Turing computable total functions.

Computable analysis reveals that the ordering of any two computable numbers is decidable provided the numbers are in fact different. But due to the negative result of the Halting Problem, there is no universal algorithmic test for deciding whether two computable numbers are in fact different or equal. Consequently the very notion of either difference or equality with regards to nearby positions or times is not a mathematically meaningful a priori notion for the constructivist.

The uncertainty principle is derived from the Fourier transform which involves the problem of "the start" (or however you want to call it), in the sense of a time period, which is similar to what Michael is arguing. A time period is defined by frequency, but the shorter the time period, the less accurate is the determination of frequency. The problem is reciprocal, if the time period is too short we can't determine the frequency, if we can't determine the frequency the time period is indefinite. "The start" is the first time period, and the shorter that time period is, the more indefinite any determination made from it is. This is very similar to the problem of acceleration. If a thing is at rest at one moment, then accelerating at the next moment, there must be a time of infinite acceleration. — Metaphysician Undercover

It depends on what you mean by "determine". The mathematics of quantum uncertainty refers, at least according to its most literal interpretation, to the logical inconsistency of two or more propositions, in this case that a particle simultaneously possesses a precise position and a precise momentum.

According to this interpretation, Zeno's paradox is a valid argument, and might even be useful in intuitively explicating some of the principle of quantum mechanics, but nevertheless does not prohibit motion, because Zeno's paradox is understood as referring to the modification of a particle so as for it to have a precise position, at the expense of the precision of it's state of motion.

Personally i don't think appealing to physics or mathematics is ultimately relevant in solving the paradox but that Quantum mechanics complements the vagueness of our phenomenological intuitions in many respects.

When I imagine zeno's paradox, I tend to imagine an arrow travelling for a bit and then I stop it momentarily in my imagination and say to myself "This is now the arrow's position. Now how did it get here?". But of course I am not allowed to mentally stop the arrow from moving, for I would no longer thinking of a moving arrow.

Is it even possible to imagine a moving object that has a precise velocity and/or position? Personally I don't think so. I always find myself either fantasising that I have mentally stopped the arrow in order to measure it's position, or that I am entirely ignoring it's position when thinking about it's motion.

I believe that the overall sentiment expressed by Aristotle's view is vindicated by the Heisenberg Uncertainty principle, which expresses his sentiment by saying that if the position of a moving arrow is determined, then it no longer has a definite state of motion. Hence according to QM, Aristotle is right to distinguish a continuous line from a line divided into intervals.

At any moment in time, try to simultaneously observe both the position and motion of a moving object. In order to maximise one's observational precision of the object's position, one has to pay more attention to features in the visual field that establish the object's position. But this comes at the cost of being less precise when judging the state of the object's motion.

Of course, this experiment when interpreted along classical lines does not demonstrate the uncertainty principle, for it merely demonstrates one's ignorance of the total state of the arrow. But this is an irrelevant argument in the case of Zeno's paradox, for the arguments Zeno presents are phenomenological arguments that appeal only to thought experiments or practical demonstrations in which the motion of the arrow is temporarily ignored while it's position is determined and vice versa. I'm simply saying we have every reason to be phenomenologically suspicious of being able to imagine, or be literally aware of, an arrow's position simultaneous with it's state of motion.

Imagine if we had taken a video-recording of the object's motion in order to establish a per-frame analysis of the object's positions over time. No per-frame analysis will tell us about the object's motion, since for that we need to look at inter-frame differences which is a feature not present in individual frames. This is again, analagous to the uncertainty principle in that motion and position are estimated, or rather constructed, with respect to incompatible features.

a given situation, to predict a person's motives is to predict their behaviour.
— sime

I must disagree. We may have desires whose satisfaction we choose either to defer or not to satisfy at all. So, while motives and behavior my be correlated, there is no determinate relation between them. — Dfpolis

Yes, in own case I cannot understand my desires in terms my personal behavioural history. But if my attribution of motives to others is considered to be objective , then the motives of others must be describable in terms of behavioural regularity, for the personal feelings I have regarding other people's behaviour is subjective.

So I can accept the reason/cause/motive distinction, but only if the subjective-objective distinction is rejected. Otherwise I cannot see how these distinctions can be maintained.

Isn't the example of Wittgenstein's forms of life and language games, representative of a psychologism tone in his Investigations? — Wallows

I haven't had the time to read the book link you posted, but it is certainly the case, as the author states, that Wittgenstein was an anti-transcendentalist who recognised that the semantics of logic and mathematics was reducible to the application of mathematics in the real world. So there is a case to be made that he didn't support anti-psychologism in the sense of believing that the truth of logic or mathematics (and other language-games) transcends human activities. But that shouldn't be taken to imply support for psychologism either, for the reasons i've previously mentioned.

Any software developer knows that a refusal to test the correctness of their software "because the logic of the software is true for myself, representing as it does my psychological construction of truth" isn't acceptable to the consumer. As Wittgenstein later points out, the notion of truth and falsity is relative to a notion of error. And it is
this conceptual allowance for uncertainty in the correct application of logic that makes logic a meaningful form of communication,whereby the meaning of logical practice is irreducible to any particular application of it's rules or to any particular thoughts and feelings that may occur while practising logic.

Hence the anti-transcendentalist must understand meaning in terms of holistic verification that is irreducible to individual feats of psychology.

Spoken like a true constructivist xD
But seriously, no they're not at all the same. They entertain diametrically opposed worldviews. — NKBJ

If they are diametrically opposite worldviews, constructivism says they cannot be so in the sense of the presence or absence of construction, because constructivism identifies semantics with the process of derivation. Hence constructivism denies the possibility that the semantics of realist conclusions can transcend their logical, phenomenal and behavioural argumentation.

For example, constructivism denies that "This is not a constructed sentence" is not a constructed sentence. Yet it is possible for a realist to apparently accept the sentence's message at face value. The constructivist therefore cannot argue with the realist, rather he must find a way of interpreting the realist's statements so as to make the realist's claims true from a constructivist point of view.

Metaphysics is what everyone denies doing, whilst accusing everyone else of doing it.

I think metaphysical statements are best understood as being speech acts or instructions to think in a certain way. Nobody can avoid doing metaphysics of some sort, even if this consists of refusing to do metaphysics.

I was under the impression that Wittgenstein was advocating an intuitionalist conception of language in the Investigations. You can see it in his famous example of a lion who could speak but we would never understand it. — Wallows

Wittgenstein draws a sharp distinction between understanding how to use a word according to public convention, versus the personal attribution of meaning to a word by private acts of the imagination as part of self-expression or sense-making. And he denied the existence of a necessary relationship between these two sorts of meaning. So he wasn't a "psychologismist" in the sense of believing that the meaning of theoretical terms of public discourse could be semantically reduced to private experiences via a private application of translation rules that map theoretical terms into observation terms - as was briefly considered by the logical positivists during their foray into phenomenalism and verificationism.

Wittgenstein's arguments against private language therefore present a paradox. For he presented thought experiments that supposedly delineate public linguistic semantics from 'a priori' private intuition, yet these arguments only appeal to private intuition... His arguments are like arguing with oneself that one's mental image of Elvis Presley isn't the real Elvis Presley because one can imagine the "real" Elvis entering the room.

Hence in my opinion, Wittgenstein's private language arguments cannot be consistently interpreted as being a proof of ontological claims. Rather, they should be construed more weakly as being a therapeutic construction with only medicinal value - arguments that judging by the confusion of the public, appear to have failed in their intended therapeutic purpose.

Consider the sentence "Animals eat in order to survive". How is this different from saying "survival tends to follow eating"?

In a given situation, to predict a person's motives is to predict their behaviour. And to predict their behaviour involves interpolating memories of that person and the world in general. Teleology should therefore be considered true, or at least meaningless.

Realism is a type of constructivism. For otherwise the statements of realists would not exist. The difference between realists and idealists is in what statements they construct and for what purposes.

The two words are different. Phenomenon implies an experienced thing, whereas change does not imply experience. So two concepts, since it makes sense to speak of non-phenomenal change. — noAxioms

sorry, perhaps i should have been clearer. I'm referring to change within the context of 'phenomenal change' and it's relationship to the A series, as opposed to mathematical representations of change, and arguing that the A series deflates away.

When people say things like "time flows by" they appear to imply that the phenomena of a river is different to the passage of time, something that comes about by first distinguishing phenomena from the A series and then equivocating the A series with the B series to give time an illusion of hidden dimensionality above and beyond what is observed. A flowing river isn't merely a metaphor for time passing, for they are the same thing. "time flows by" just means "the river flows" here. This is entirely consistent with any mathematical description of physical change.

I think those arguments are inane. I don't understand the "if y cannot fail to have x" part of your comment, though.

We're also probably not going to agree on what meaning is. — Terrapin Station

My original point was that I cannot make sense of the notion of unchanging phenomena, so "phenomena changes" is a tautology that says nothing. One might as well have said "phenomena is phenomena" or "change is change".

So to my mind, there isn't room for two concepts, namely that of phenomena and that of temporal change. Furthermore, when we learned the meaning of the words "changing" and "unchanging" we learned it with reference to public semantic conventions, and not directly in relation to immediate experience.

One of those "you can't have x if there is none of x's opposite" arguments? — Terrapin Station

Yes, because if y cannot fail to have x, then x is part of what y means .

"Phenomena is always changing" is analogous to "Every rod has a length"

So just has we can eliminate the concept of length by only referring to rods, we can eliminate the concept of change by only referring to phenomena - where "phenomena" means to refer to the world in general.

Isn't the idea of essential phenomenal change nonsense rather than true of false?

To say "phenomena is always changing" is to assume the meaning of "phenomena could be still". But what exactly is a still experience? For i've never had an intrinsically still experience. Whenever I have ordinarily declared that everything is still, is in relation to performing a task during which I observed things were changing, but not in a way considered important to the task.

So if 'still phenomena' is logically impossible, then to assert the opposite that phenomena is changing is meaningless if interpreted to be an essential statement of experience.

There isn't such a thing as 'physical phenomena', for no physical concept can be given a persistent interpretation in terms of experiential phenomena, as the logical positivists soon realised.

Take for instance Red. It's physical meaning is defined in terms of optical wavelength, not in terms of a sensory impression, and we cannot give an exhaustive description of the context that is necessary such that an application of optical red always produces a "red" sensory impression. Furthermore, the theoretical meaning of "optical wavelength" is holistic, given that it is a property whose meaning and experimental determination rests upon the understanding and application of the rest of physics. Physical red therefore cannot be given a phenomenal definition.

We use our sensory impressions as estimators of our use of physical terms, but they aren't the definitions of our physical terms. On the other hand, we shouldn't forget that our use of physical terms is ultimately determined by the totality of our sensory impressions. So we aren't justified in jumping from semantic holism to physical realism.

(t) transitivity: aRb & bRc => aRc
(s) symmetry: aRb <=> bRa
(r) reflexivity: aRa

(s) & (t) => (r) via substitution of (s) into (t)

Therefore:

(s) => { (t) => (r) } (giving up irreflexivity if transitivity is true)
(s) & Not (r) => Not (t) (giving up transitivity if irreflexivity is true)

He probably wants to argue that a 'worldly referent' is not what adherents have in mind, so your interpretation is sort of cheating, a diversion. — Joshs

But how do we know what adherents have in mind? Isn't the only way to determine this to establish the environmental conditions under which they make their "transcendental" assertions?

Suppose that a christian evangelist insists "God isn't part of the world". If we could determine the environmental and neurological conditions under which he asserts this sentence, then shouldn't we interpret his utterance of "God isn't part of the world" as referring to these conditions?

Their claims do not transcend experience and are, therefore, meaningless! — charles ferraro

Not necessarily. For if transcendent referents are ruled out of semantics, this does not preclude the word "transcendent" being used to refer to things which are not transcendent.

Unless speech is the ultimate cause of itself, all speech must ultimately refer to an external cause, so even "transcendentally referring" speech has worldly referents, even we do not know them.

All utterances have been used at least once, and hence all utterances have meaning, even if that meaning is indecipherable.

It doesn't make sense for the presentist to think of the past as being immutable, for the presentist does not interpret his memories as referring to anything transcendent of his volatile world of experience, and he surely appreciates that his memories change over time.

And if the presentist also denies the second law of thermodynamics as constituting a direction or orientation of the present, then time-travel into the past or future could be seen as being nonsensical in virtue of experience not being linearly ordered.

I'm not sure how you get the impression that the later Wittgenstein believed in psychologism. For he rejected the "picture theory" of meaning, arguing against the reduction of linguistic understanding to mental states or immanent experience.

But since his methodology was solipsistic, one shouldn't to go so far as to say that he believed linguistic meaning transcended experience, only that semantics cannot be given a constructive universal definition in terms of immanent experience.

Lets think of a specific example, for example let's imagine a god who created the universe and who exists outside of space and time.

Now in one sense this is a meaningless and impossible thing to do, but in another sense this is perfectly possible. After all, we can imagine anything and associate it with a sentence.

Also consider the fact that religious people who purportedly make transcendent claims teach the meaning of their claims and think about them. But this would not make sense or be possible unless their claims were in fact not transcendent of experience.

So my way of thinking is this: propositions concerning the supposedly transcendent are in fact ordinary propositions concerning the world, but in disguise. The only difference between a transcendental proposition and an ordinary proposition, is that the former is irreducible to a particular public worldly referent.

linguistic reference is only demonstrable within a language-game.

Wittgenstein made the therapeutic suggestion to include percepts and actions in the definition of "language", because concepts such as linguistic reference can only be made sense of within the broader concept of a language-game. Whereas if "Language" is used to only refer to the verbal part of the language-game, your philosophical puzzlement arises.

Yes memories have content, in the same way that a digital image has pixel values, but it is a vacuous tautology to say that information is intrinsically past-referring. unless that content is related to other content in a particular way.

Consider false memories and deep-fake photographs. What does it mean to say that they are false, in the sense of having no referent in the past? In a causal sense all phenomena could be said to represent the past, whether the phenomena is considered to be genuine or fake, and whether the phenomena is recalled into mind or externally perceived in the world.

In practice, we verify the truth of memories and photographs and it is our process of verification that decides whether the memory is "true" or "false". Orthodox opinion interprets past-contingent propositions as being intrinsically past-referring and purely by the force of their expressed content and independently of the process of their verification. In contrast, I'm saying it is the process by which a proposition is verified that determines whether the content of the proposition is past, present or future referring.

I cannot fathom a hard distinction between memories and present experience, for i cannot see much of a distinction between memories and photographs. And in the case of a photograph, in order for it to 'refer' to the past, it must be used in a certain way.

For example the photograph must be compared to another photograph, or inspire a personal recollection from a person and so on. As with photographs, it doesn't make sense to say that the content of individual memories are past-referring in and of themselves . Rather the concept of the past is actively constructed out of memories , together with reason, current observations and experimentation, without being reducible to memories themselves. But this implies that the past is also uncertain and changing, and not merely in a dead epistemological sense but in a living sense. Therefore the psychological past and the psychological future appear to be heavily overlapping concepts that cannot be ordered using cartesian coordinates.

In my opinion, the objective of science is the simulation of behaviour, with the aim of inventing efficient and understandable languages with which to communicate the body of results of simulation experiments, for purposes of engineering.

By the most pragmatic interpretation of that aim, any invented language and method of simulation suffices as a scientific method provided it achieves its goals of behavioural replication to the level of precision deemed necessary for a given engineering application.

Aren't tastes and personal preferences also truth-apt?

For isn't it possible to doubt our own tastes and preferences?

Don't we often say that we want something, but regret having done it? Don't we often say we prefer something but regularly do the opposite? And aren't we sometimes glad to have been forced to do something that we wouldn't have done voluntarily?

I've noticed for instance, that when I am depressed I will insist that I don't want to do something, say go for a walk, but when forced to do it I actually enjoy the walk.

So if a person's verbally expressed tastes and preferences are understood to convey information about their future behaviour, then they are falsifiable and hence truth apt. Perhaps society does know what is best for each of us.

Namely, as mentioned in the OP, if we reduce matters of what gives one meaning in life or purpose to a matter of taste or personal whim, then haven't we idiotized the issue of what gives one meaning in life to a simple matter of what I like best or dislike most? — Wallows

Only if epistemology is premised upon a hard object-subject distinction. Or put equivalently, that one's epistemology is based upon the correspondence theory of truth, or alternatively, that pre-existing truth is interpreted as being discovered rather than presently constructed by the observer, whereby their preferences and decision-making are considered irrelevant to the truth they obtained.

Once the correspondence theory of truth is rejected, epistemological scepticism is transformed into ethical and aesthetic preferences.

For example, consider the so called epistemological problem of other minds. According to the correspondence theory of truth, either other minds exist or other minds do not exist and their ontological status is independent of the way human behaviour is judged by an observer. This leads to sceptical doubt , the problem of individuality, the hard-problem of consciousness etc.

On the other hand, suppose the "truth maker" concerning the existence of other minds, is viewed more holistically as being as much a function of an observer's perceptual relationship to the entity he is observing. According to this anti-realist account, an observer's conception of other minds is as much an account of his personal preferences that guide his perceptual and cognitive actions than it is the behavioural data he is viewing.

So in short, if correspondence theory is rejected, then preferences are epistemologically relevant.

Necessary statements are commands or policies, i.e. speech acts, whose origin of force is the intentions of the speaker or institution who asserted them. This includes metaphysical assertions, ethical assertions and all universally quantified 'propositions' over infinite domains in science and mathematics.

So "Bachelors are unmarried men", when interpreted as expressing a necessary truth, is to declare a policy allowing the substitution of the former as a synonym for the latter without exception. Hence the image of it holding in "all possible worlds".

However, when interpreted as expressing a publicly verifiable proposition "Bachelors are unmarried men" is both contingent and under-determined.

Anyway, doesn't the semantic under-determination of the word "determinism" render the question meaningless?

Consider the following circular definition, which nevertheless has intuitive meaning.

Determinism is the thesis that the state of the universe at any given time, together with the laws of nature, fixes (determines) the states of the universe at all other times. — SophistiCat

But this definition is also fulfilled by taking determinism to refer only to the fixing of an arbitrary finite number of states. And no amount of protest against this non-standard interpretation of "determinism" is able to eliminate it.

So it isn't clear in my mind, as to how the original question can be sufficiently represented.

I don't think that Quantum mechanics is helpful or useful in this sort of discussion, because of it's many conflicting interpretations that parallel the philosophical disputes that already existed in classical mechanics in relation to probability, time and counterfactual reasoning.

In my constructivist opinion, what is impossible cannot even be thought. Impossibility refers to the sentences of a language that have no application in a given language-game.

So, i interpret special relativity as saying that an object of positive mass accelerating to c isn't a meaningful proposition of relativity, i.e. that it isn't even wrong, because it cannot be constructed from the application of the postulates of special relativity.

Recall Wittgenstein's analogy for verbal definitions in terms of occasional sign-posts that are placed to guide walkers along a route. The sign-posts tend to be laid down only at the points where they are useful, namely at the places where walkers frequently become lost or confused.

The route is analogous to the implicit conventional use of a word, whereas the sign-posts are analogous to the explicit conventional definition of the word. Needless to say, individual walkers will walk idiosyncratically , regardless of whatever the sign posts say.

And is it necessarily the case that a walker who frequently follows the route could give an accurate verbal account of it without him actually following it?

Interestingly Lewis Carroll's paradox concerning the meaning of logical deduction in "What the Tortoise said to Achilles" came 50 years earlier than Wittgenstein's remarks concerning the relationship between rule-based definitions and language use.

https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles

Whilst this is slightly jumping the gun, later on in PI Wittgenstein expresses a similar logical refutation of the idea that the use of language can be grounded in rule-based definitions or explicitly expressed conventions, because in a nutshell the very meaning of rules and conventions is grounded in their use! - For otherwise our definitions lead to infinite regress.
As an example, just try to define the logical operators non circularly.

Also, regarding the question of 'exactness' with respect to the specification of rules, Wittgenstein had questioned earlier in his career (i think during his middle period in Philosophical Grammar), whether the notions of exactness, identicalness etc were a priori in the sense of being phenomenological aspects of experience. The significance being whether or not exactness is empirically reducible. For if it isn't, then the notion of exactness is well, inexact, it's meaning only being demonstrable as a family resemblance of uses across different language-games.