Kripkes proof shows rules are not objectively true. — Banno

Again. I'm not clear on what it would mean for a rule to be objectively true or false. So, do you mean that Kripke has shown that the idea of objective truth just doesn't apply to rules?

That there is a fact of the matter about what rule is being followed. — Apustimelogist

Oh, OK, I would say that is uncontroversial.

It is a subjective matter because you are appealing to your intuition subjectively and you cannot rule out the other possible rules you can use. — Apustimelogist

Judging from the ordinary understanding of basic arithmetic and logic I would say their results are self-evident to anyone who cares to think about it.

So what, some truths are intuitive and some are unintuitive. Their intuitiveness has nothing to do with objective truth. Intuition is a product of your subjective inclinations. — Apustimelogist

I would say that the only intuitively self-evident truths are logical or mathematical, and I don't see that as being merely a subjective matter.

And just because a rule is unintuitive doesn't refute it being objectively true. — Apustimelogist

I don't know what you mean when you talk about a rule being objectively true.

Of course, applications of "+1" include practical applications. The point is that the rule must be applied to each case; it does not reach out to the future and the possible and apply itself in advance. — Ludwig V

My only point was that the logic of +1 and its concatenations is the conceptual basis of counting and arithmetic, and that its ability to serve practicalities, while alternative stipulated rules cannot show its non-arbitrary nature.

But the fact that we mostly agree is not inevitable, not guaranteed. It is a "brute fact", which is the foundation of logic (and other rules). Bedrock is reached. — Ludwig V

I can't think of any examples of failures of consensus concerning basic arithmetic.

The question of intuition is arbitrary because this is about the notion of objective rules or meanings. Why does intuition matter for objectivity? A putatively objective scientific theory should be true regardless of intuition. The truth of thermodynamics doesnt depend on my cats ability to find it intuitive. — Apustimelogist

The truth of scientific theories is not intuitively self-evident in any way analogous to the truth of basic arithmetical results. So, scientific theories are never proven. That the math involved in thermodynamics is sound may be self-evident, but that doesn't guarantee that it has anything to do with some putatively objective reality.

I think it is arguable that nearly all humans find counting and the basic arithmetical operations intuitive, so it's not arbitrary, Mathematicians have specialized skills that enable them to find things intuitive that the layperson cannot even comprehend because they don't have the requisite training or ability.

It looks like we are going to continue to disagree, but that's OK with me. I believe I would change my mind if given good reason to, but I haven't seen anything approaching such a reason thus far.

I think you can. If you can make up arbitrary rules like quaddition then you can think up infinite many rules which give describe all the same processing ability. — Apustimelogist

But do they yield answers that are pragmatically workable?

To you maybe. It might be totally unintuitive to a different kind of being. — Apustimelogist

Counting is intuitive to humans and apparently some animals. I doubt there are sentient beings which would find it not to be intuitive if they had the ability to count. Of course, there are sentient beings who cannot count, but that would not be a lack of intuitive ability, but simply a lack of the necessary intelligence.

My point here is the forward problem as described earlier. Even though quaddition has particular outcomes, someone can generate all of the behavior of addition and define it, have definitions, without using addition, even if they require a plethora of other concepts to make it work. And again, this all depends on people agreeing with all the necessary concepts which are required to make something like quaddition work. My understanding of all concepts is scaffolded on prior concepts and prior implicit understanding or abilities that have been learned by practise without definitions. — Apustimelogist

I don't think it is true that the same outcomes as addition could be achieved using some other set of rules or concepts "to make it work". I see no reason to think that. Can you stipulate a set of rules and/ or concepts that will always yield the same results as addition? If you cannot, then how could you know it would be possible?

Even if you could come up with something, that wouldn't change the fact that addition is intuitively gettable, while the alternative is just some arbitrary set of rules that happened to work, and which would be parasitic on the gettability of addition in any case.

There is a natural logic of these things. But we had to learn how to do it. It seems natural because it is a) useful and b) ingrained. "Second nature". — Ludwig V

It is natural simply because we can intuitively get the logic once we have our attention drawn to, and become familiar with, its basics. We can apply the rules because they make cognitive sense, so we don't require another set of rules to tell us how to use the rules of counting and addition. We don't even really need to be able to explicitly state the rules, just as it is with grammar in the case of language. The fact that there are several different possible grammatical structures which are exemplified in different languages doesn't change this; the logic remains basically the same, it is only the order that changes.

There would only be a logic to countermand if there was a sensible definition of these things in the first place which specified the correct behavior without requiring prior understanding... and if rules like quaddition provided different outcomes to addition. — Apustimelogist

Counting makes sense as a genesis of arithmetic. But is doesn't escape from the sceptical question. There is no fact of the matter that determines whether I have counted correctly - except the fact that others will agree with me. — Ludwig V

As stipulated the rules of quaddition do provide different outcomes:

I ask you to add 68+57.

You confidently say "125."

The skeptic asks, "How did you get that answer?"

You say "I used the rules of addition as I have so often before, and I am consistent in my rule following."

The skeptic says, "But wait. You haven't been doing addition. It was quaddition. When you said plus, you meant quus, and: x quus y = x+y for sums less than 57, but over that, the answer is always 5. So you haven't been consistent. If you were consistent, you would have said "5."" — frank

Addition gives "125' and quaddition gives "5". Which one is correct? Imagine there is a wedding, and there are 68 guests from one side of the family and 57 from the other side. Addition tells you to provide food and seating for 125 guests, and quaddition tells you to provide food and seating for 5 guests. Now you tell me which one will turn out to have been correct.

Hard to attain, at times. All we can do is re-state, try again, and all that. I read you as taking an intuitionist stance, as in mathematics is a part of our natural intuition that's even shared with other creatures, and so the skeptic has no basis because the skeptic is framing arithmetic in terms of rule-following when there's more to arithmetic than rule-following, such as the intuitive use of mathematics, whereas the skeptic's use is derivative of that (and so is an illegitimate basis of their skepticism, considering that the skeptic is undermining their own position in the process)

Let me know if that's close or not. — Moliere

I do favour intuitionism in this. If the skeptic could provide different rules of counting and addition which do not consist in infinite iterability and yet can always come up with pragmatically workable solutions as in the simple wedding example above, then it might be time to start taking it seriously. How do you thinking structural engineering would fare if it started using quaddition instead of addition?

When we are riding an ass we feel the ass acting, moving, and we feel the ease or the effort. But to act is not to be carried around by an ass. ...Not even St. Francis' "brother ass"! — Leontiskos

We don't feel the effort or the ease of the ass in the same way we feel our own, but that feeling of our own ease and effort in action or at rest is presumably made possible by neuronal activity that is prior to the feeling, just at when we see or hear things, that seeing or hearing is presumable made possible by antecedent neuronal activity.

So, to reiterate, for me, seeing, hearing, feeling, smelling and tasting seem just as immediate as somatosensory or proprioceptive awareness, but they are all presumably mediated by neuronal activity.

I think what Janus's position amounts to is that there is a kind of fact, namely the familiar rules of arithmetic, which is the natural way to believe a person to be thinking about the question "how many?" — Moliere

I don't believe arithmetic to be merely rule following, but I think it is something we get intuitively on account of its being naturally implicit in cognition. Some animals can do rudimentary counting, which means they must be aware of number.

So, it begins with recognition of difference and similarity, then gestalted objects, then counting of objects, and this basis is elaborated in the functions of addition, subtraction, multiplication and division. Mathematical symbols and the formulation of arithmetical rules then open up the possibility of endless elaboration and complexification.

I hope that makes it clear how I see it. I'm happy for others to disagree, provided they disagree with things I actually think, and not some imagined position based on their misunderstanding.

Sure, when we are aware we feel our body acting, moving and we feel the ease or the effort. We can act and be completely unaware of it, though. When we feel it, it feels immediate, just as it seems immediate when we see others acting, so I'm still not seeing a real difference beyond the difference between feeling and seeing.

You're completely misunderstanding what I'm saying. You're not even close. — Sam26

OK, so what exactly am I misunderstanding?

Yes, I agree with that. We can act without being aware of acting and we can also act with awareness.

I think 'beliefs' which carries the connotation of judgement is a less apt way of talking about the primordial (animal) features of human experience than 'elements'.

It's not just the belief about hands, but a whole system of beliefs that falls into the same category. — Sam26

For me it seems misleading to refer to the background, consisting of those things which are necessarily involved in our everyday lives. like hands, feet, legs, arms, ears, eyes, mouths, hills, valleys, mountains, rivers, lakes, oceans, fish, clouds, sun, stars, moon, human technology in all its forms, architecture, music, painting, poetry, philosophy to name but a few in a list of countless numbers, as a system of beliefs. These things are not beliefs but intimate and inevitable elements of human experience. We know them in the "biblical" sense of familiarity, in an analogous sense as that when it is said that " a man shall know his wife".

Some questions: Do you act? When you act do you know you are acting, or are you not sure whether you are acting? Do you disagree with L'éléphant about his knowledge of walking over to the kitchen? Finally, if you think this knowledge is mediate, then what is it mediated by? — Leontiskos

I think the salient question is not whether you know you are acting, but whether the awareness that you are acting is immediate, or whether it is mediated by processes that give rise to that awareness. Of course, the awareness is, or at least seems to be, from the percipient's point of view, felt immediately. But this is also equally the case when it comes to extrasomatic perceptions.

As I said in my previous post, I think there is an ambiguity in the notions of mediacy and immediacy; so perhaps we are merely arguing about different ways of thinking, ways which cannot meaningfully be opposed because they find their senses in different contexts.

Anything that is an appearance is known mediately,
Action is known only non-mediately
Therefore, action cannot be an appearance.

This makes it clear that the question is whether action is known only non-mediately, and that would seem to be false, which makes the argument as reformulated valid, but unsound.
— Janus

Using this approach, you can get true premises in the following way:

Anything that is an appearance is known only mediately
Action is known non-mediately
Therefore, action cannot be an appearance

(The point is not that action is known only non-mediately, but rather that action is known non-mediately (and mediately), whereas appearance is only known mediately.) — Leontiskos

I'm not convinced those premises are true. I mean I think it is fair to say, thinking about it one way, that nothing is known non-mediately, and from another way of thinking, that everything is known immediately. The first highlights the fact that there are always processes of awareness going on in all kinds of knowing, and the latter highlights that fact that knowing always feels immediate.

I'd say that basic arithmetic's genesis is in abstraction more than counting. But whether that's a good reason or not is up to you. — Moliere

Counting starts with concrete objects and then becomes possible in the abstract with the advent of numerical symbols.

Quaddition seems to arbitrarily countermand the natural logic of counting and addition; the logic that says there is neither hiatus nor terminus.

But not the significance that know-how doesn't give a determinate know-that — Apustimelogist

I don't believe that know-how can always be translated into a determinate know-that. And any such translation will always be an abbreviation, a reductive conceptualization.

Well, if they're not derivable from counting then your argument against quusing isn't really talking about the same kind of thing since you've outlined a procedure for deciding if someone is quusing by pointing out that we can count beyond the quuser. But if it's not counting then that doesn't really demonstrate that a person is adding or quusing. The operations are distinct, rather than reducible to counting. — Moliere

I'm saying that squares are derivable from counting; my point was that the square root of two cannot be instantiated with physical objects (derived from counting) like the rational squares and square roots can. Think about the relationship between the words 'ratio' and 'rational'.

You could come up with a million absurd and arbitrary rules like quusing, and all I can say is "so what?". The logic of counting is inherent in cognition; even animals can do basic counting. And I see no reason not to think that basic arithmetic finds its genesis in counting. Give me a good reason not to think that and I will reconsider.

Right, I also recognize a distinction between knowing-how and knowing-that.

I think the reason no one has challenged the minor is because we all believe that we possess a knowledge of our acts which is not mediated. This is different from our knowledge of the acts of others. — Leontiskos

If all knowledge of action is mediated by neural processes, then we may well all be mistaken in thinking that we possess non-mediated knowledge of our own actions. We "feel" our own actions "from the inside" it seems, and we see, or hear the actions of others, but if feeling as well as seeing and hearing is mediated by prior neuronal activity, the immediacy may be merely phenomenological, which then just be to say that knowledge of our actions seems immediate, which is of course true.

I think in many ways reflecting on experience is just that though. I feel like people can have radically different views of what experiences are, what feelings are, what they actually perceive, and how do people make something of their perceptions other than by intuition? — Apustimelogist

I have been talking specifically about synthetic a priori knowledge of what is intrinsic to embodied experience: spatiotemporality, differentiation and the other attributes I mentioned.

Hmm, thinking about it, I think it might be difficult if your intuitions are set on counting rather that quounting. But maybe a quonter would find no problem with it. — Apustimelogist

Maybe...I remain unconvinced.

I think ultimately what is "natural" just boils down to something like an impelled preference and I don't see that as a valid way of arguing that something is somehow unique, correct or objective. — Apustimelogist

Well, we see things very differently, and for that I would say, there is no antidote. You keep mentioning objectivity, which has nothing to do with what I've been arguing.

I don't really see how phenomenology is not another form of armchair speculation in a similar way. — Apustimelogist

It's not mere speculation because experience is something we can reflect on and analyze. Metaphysics is not based on experience at all but on imaginative hypothesizing.

The relevance for what? Its simply the issue of whether the descriptions you ascribe to behavior is uniquely determined as opposed to underdetemined or indeterminate. — Apustimelogist

Some descriptions of some behaviors are more determinate than others, obviously.

I can demonstrate quus with objects just as well as I can with addition. — Apustimelogist

I don't believe you can.

You are not presenting any arguments, just baseless objections, it seems, so the conversation is going nowhere.

Neither do I see a real significance in the distinction between "natural"and "artificial" concepts. — Apustimelogist

Natural concepts are those which inevitably evolve out of experience like space, time, number, difference, similarity, causation, constitution, form, material, change, grammar, logic and so on. Artificial concepts are those which are purely derived from stipulating arbitrary sets of rules. The latter are parasitic on the former.

I don't see the phenomenological dimension of philosophy as "armchair speculation", but rather as reflection on what we actually do.
— Janus

Well thats more or less what I mean. — Apustimelogist

Well, it's not what I mean. Armchair speculation I would class as metaphysics, not phenomenology.

As I have already said, the quus issue has no relevance or consequence for people's ability to do things but I think if you are interested in notions of realism or whether we can have objective characterizations, problems like this are very interesting and central. — Apustimelogist

I don't see the relevance at all, and no one seems to be able to explain clearly what it is, so...

I think if you consider that quantitative abilities and counting might be primitive processes we cannot non-circularly decine then I would say actually, yes we are blind to these. — Apustimelogist

We are not blind to considering how counting and the basic arithmetical operations can be instantiated using actual objects. This is not the case with quus.

If you can't derive addition from counting then how are you proving you are doing addition? — Apustimelogist

You can derive addition from counting. Counting basically is addition.

I keep harping on the square root of 2 — Moliere

I'm not sure how much the symbolic language matters. — Moliere

If you have four piles of four objects then you have sixteen objects, three piles of three objects then you have nine, two piles of two objects you have four. This obviously cannot work with two objects, so I'm not seeing the relevance to deciding whether addition, subtraction, multiplication and division are basically derivable from counting operations.

Without the symbolic language of numerals the irrational nature of the square root of two would not have been discovered.

There can be no doubt that all our cognition begins with experience...But even though all our cognitions starts with experience, that does not mean that all of it arises from experience — Kant

This is the passage from Kant I am familair with"

In respect of time, therefore, no knowledge of ours is antecedent to experience, but begins with it. But, though all our knowledge begins with experience, it by no means follows that all arises out of experience.

So, it addresses knowledge, not cognition. How do we arrive at a priori knowledge? It is not given directly in sensory or somatosensory experience, but I think it is gained by reflecting on sensory and somatosensory experience, and I don't understand the Kant quote to contradict that or to be suggesting any other source for synthetic a priori knowledge.

Talking about the nature of the self is does not really have an impact on what I mean when I say we construct concepts, at least not in this context from the way I see it. — Apustimelogist

My point in making that distinction was that some concepts, like counting and addition come naturally, and other concepts like quaddition are arbitrary artificial constructs.

And my point ia you are doing this with pretty much every conversation you are having about philosophy. Philosophy is an armchair science so a huge amount of its arguments rely on this same kind of conceivability of what seems correct, what seems possible, logical, metaphysical or otherwise. — Apustimelogist

I don't see the phenomenological dimension of philosophy as "armchair speculation", but rather as reflection on what we actually do.

I don't think there can be a fact of the matter independent of human experience and even within experience, people find themselves unable to determine a solution to issues like this quus one. Its chronically underdetermined, there is no objective way to see it that can definitely rule out all of the others. Thats the vision that makes most sense to me anyway. — Apustimelogist

Well, there certainly cannot be an ascertainable fact of the matter, which is independent of human experience, I'll grant you that much. I see the quus issue as not merely under-determined, but trivial and of no significance, and I wonder why people waste their time worrying about such irrelevancies; but maybe I'm too stupid to see the issue, in which case perhaps someone can show me that I'm missing something.

You said earlier that you don't even really know the causes of your thoughts or how they arise. So you know the causes of your understanding of addition? Or quantity itself? — Apustimelogist

The causes of our thoughts are presumably neuronal processes which have been caused by sensory interactions; my point was only that we are (in real time at least) "blind" to that whole process. I don't believe we are phenomenologically blind to activities like counting and addition and I think it is a plausible inference to the best explanation to say that these activities naturally evolved from dealing with real objects. I'm not claiming to be certain about that, just that it seems the most plausible explanation to me.

Basically I'd say that arithmetic is more complicated than counting. — Moliere

Of course I agree that arithmetic is more complicated than counting, all I've been saying is that it is basically counting. It is the symbolic language of mathematics that allows for the elaborations (complications) of basic principles.

And I would also argue that it all finds its basis, its genesis, in dealing with actual objects, Thinking in terms of fractions, for example, probably started with materials that could be divided.

so it is not we who construct, but we who are constructed from moment to moment
— Janus

Semantics really, isn't it? — Apustimelogist

Not really, I think it is literally true that we are being created moment by moment—until we are not. We do not create ourselves. We don't even know what causes the thoughts we have to arise in awareness.

Well you start to get into a slippery slope here because modality is something we make use of all the time whether in daily life, intellectual discussion, conceptualizations etc. This kind of skepticism, while very fair, is also I think is an argument against all your thinking, not just in this discussion. — Apustimelogist

I don't see a slippery slope, but rather a phenomenological fact that we make a conceptual distinction between what is merely logically possible and what might be actually, physically or metaphysically, possible. We don't know what the real impossibilities are, but we inevitably imagine, whether correctly or incorrectly, that there are real, not merely logical, limitations on possibility.

Yes, and what is in question is whether there is a fact of the matter about who is correct. — Apustimelogist

I think we mostly do assume that there is a fact of the matter, but of course we have no way of knowing that for sure or of knowing what a "fact of the matter" that was completely independent of human existence could even be.

Similarly we can count marks, or we might know the the arabic numerals, but we may not know how to solve an addition problem without some sort of knowledge of figuring sums. — Moliere

If you wanted to count a hundred objects you could put them in a pile, and move them one by one to another pile, making a mark for each move. Then if you wanted to add another pile of, say, thirty-seven objects you just move those onto the pile of one hundred objects, again marking each move. And then simply count all the objects or marks. I don't see why we should think that all the basic operations of addition, subtraction, division and multiplication cannot be treated this way. We really don't even need to make marks if we have names for all the numbers and we can remember the sum totals.

Depends on what you mean by arbitrary. There is a reason we tend to label things in a certain way and its to do with how our labelling and descriptions are literally physically, mechanically caused by a complicated brain that has evolved to infer statistical structures in our sensory inputs and learn. — Apustimelogist

Yes, and there can be no disembodied brain, or brain in isolation from environment. We are blind to the worldly process of construction, so it is not we who construct, but we who are constructed from moment to moment.

We are all more or less similar, and animals too, so there will be similarities and differences. Our concepts could have been otherwise, if we were. Could we have been otherwise? Of course, it is, logically speaking, possible; but that means no more than that imagining ourselves having been different involves no contradiction. How can we find out if it is really possible?

It seems obvious we can interpret what we observe in different ways; that is different people can. Or one person may be able to imagine other possibilities than those which are simply found to be the case.

We can come up with arbitrary, even ridiculous, ideas like quus, to be sure; language even enables us to speak of round squares and many other absurdities. Language can even make the mind seem as though it is disembodied, a free-floating locus of identity. We are the locus-eaters, reifiers of myriad concepts, generators of nuclear identities. Poetry is a great benefit.

Right. I'm not sure about "constructed" because it seems to carry an implication of arbitraryness. The formulation of rules seems to be motivated by and follow what we actually observe.

You don't have to answer the question if you don't want to or can't find anything to say.

I do hope you disagree with me. — Christopher Burke

Thankfully I think I do disagree with you on some points, or at least feel the need to point out that we seem to be talking about different things or about things from different angles.

I know what you mean here. One can imagine that sensorium level representations (empirical ones) are 'sort of' veridical. Vision is almost ubiquitously used as the exemplar of this. It is highly implausible to assume that our extero-sensations and the percepts formed from them do not correspond with our environment, otherwise our ancestors and ourselves wouldn't have survived. But one still cannot check that directly of course. — Christopher Burke

I agree with you in thinking that our perceptions are most plausibly thought to be telling us something about the extra-human environment, or at least about the interactions between us and the environment, and this is borne out by the obvious everyday fact that we humans see the same things in the environment, right down to very precise and specific features of the things we find in the environment.

And I am saying we can check if it is raining, or if the cow over there is mooing, or if the creek has dried up due to lack of rain, or if my house was burned down in a bushfire, and so on and so on. This is just a claim about the collective representation we call "the empirical world", and not a claim about what it is that might give rise to that collective representation. Within the empirical world correspondence between statements and actualities rules.

We are less beguiled with other senses. It is easier to accept that, for instance, sweetness is our reaction to something rather than being a quality of the sugar cube per se. — Christopher Burke

Sweetness is what we experience when we interact with certain substances. Whether we are to say the sweetness is in the substance, in the interaction between tongue and substance or in the tongue, or more radically, in the mind, I think comes down to preferences for one or another of several different imaginable ways of thinking about the experience.

If I say "this apple is very sweet" and I offer it to others to try, I can expect a fair degree of agreement from the others. There may be the odd person whose plate does not register sweetness, but reliable general agreement can be expected.

Standard truth statements like you give ('p' is true iff p) always make me slightly uneasy.
- 'p' is a representation (a linguistic statement) supposedly justified by p (its extramental representatum). But how do you know p? Well of course it's by having a another representation of p. For instance, the sentence 'there is a tree' is justified by simultaneously having a percept of a tree. All you have is parallel representations, one linguistic and the other iconic. Truth statements like those seem to me to pretend to have direct access to extramental reality per se as their justification.
- Mischievously: Is '('p' is true iff p)' only true iff ('p' is true iff p)? Representation is always a 'hall of mirrors'! — Christopher Burke

Note I am claiming only that correspondence is checkable within the collective representation, the empirical world. So, I am not saying there is anything more that we can be completely certain of regarding the assertion "there is a tree" than that we all see a tree there. We don't really know what it is that gives rise to us all seeing a tree there, other than there is "something going on" that reliably produces the perception of a tree there. Even the cat sees it; we see her climbing it, trying to catch the birds that apparently also see it and perch in it.

Perhaps the most parsimonious conclusion is that there is actually a tree there, but we can't be sure; the tree might be a projection of a universal mind. But then if it were a projection of a universal mind and not a mind-independent concrete existent, would it not still be the case that there is a tree there that is independent of my mind and of any and all other minds apart from the universal one?

It seems to me these are the only imaginable possibilities: concrete mind-independent existent, or projection of a universal mind. can you think of any others? In any case, it seems this is an unanswerable question; people may have their preferences: idealism or materialism, but there seems to be no possibility of a definitive answer. This is where correspondence fails. Problem is coherence seems to be a matter of taste.

:up:

I think it would be huge philosophically. — frank

What difference would it make to philosophy in your view?

Someday humans and bananas will be hybridized and will share 100 percent dna. — Merkwurdichliebe

I believe it has already happened in some enclaves.

In the land of the rigid designators where reigns the Great God Krapke there shall be no acknowledgement of the roles of description, definite or otherwise.

I think we mostly are in agreement, so I'll just address this:

By gaining coherence, we hope to also gain correspondence between our theory and its referent extramental states of affairs, but we can't check that directly. So coherence is our only yardstick for truth: to seriously doubt its reliability is the road to madness and damnation! A little fly in the ointment here is that at bottom, coherence relies on logic and any formal system suffers Gödelian incompleteness. But if anyone judges coherence to be unreliable, just try incoherence! — Christopher Burke

It seems to me that when it comes to simple empirical observations, the truth of statements is a matter of correspondence. 'it is raining' is true iff it is raining, 'that tree is taller than this tree' is true iff that tree is taller than this tree, 'my wife is having an affair' is true iff my wife is having an affair, and so on.

Of those examples the first two are perhaps much easier to check than the third; it obviously depends on how discreet my wife is. Basic science consists in just such ordinary empirical observations, and observations augmented by equipment such as the telescope and microscope.

When it comes to the explanatory phase, though, the theories that serve as explanations cannot be verified to be true, and even falsification has its issues, so I think we do assess the plausibility of such explanations according to how well they cohere with the whole body of such theoretical explanation.

I'm not sure about the applicability of Gödel's Incompleteness Theorem to anything beyond Peano arithmetic, but in saying that I'm only parroting what I remember reading; I haven't looked into it much.

If correspondence is thought as applying to the world as it in itself, an absolute context-independent reality, and not merely to the world as it is experienced and understood by humans, a contingent, relational, contextual reality, then of course it is out of its depth.

It's what happens to the sense data immediately after the instant of interaction which differs. — Christopher Burke

I agree. With humans, as soon as the sense data reaches awareness it is always already imbued with meaning. With machines it simply never reaches awareness unless it is ours or some other animal's.

I actually think and write about philosophical issues because I desire that theoretical coherence. It feels more comfortable than cognitive dissonance ... for a philosopher anyway. (Generally, alas, people seem to have a very high tolerance of cognitive dissonance: cf politics and religion!) — Christopher Burke

Coherent theories can be wrong; most probably are. Or if not wrong then under-determined. For those who like thinking rationally consistency is important. I don't think those who think little experience cognitive dissonance, because consistency is not important to them, or they don't think enough to see that there are inconsistencies between their different thoughts or beliefs.

Yes, maybe I was a bit careless there. The trouble here is that we are paddling around at the bottom of the epistemic well. There are no sub-concepts to fall back on, so we end up swapping synonyms. So 'sentient', 'aware', 'conscious', 'what it's like to be' are interchangeable, although some philosophers discern subtle differences. — Christopher Burke

I think terms find their meanings, their senses, in relation to contexts, to associative networks of understanding. That's why any term will mean more or less differently to different people.

When we reach epistemic "bottom", so to speak, I think we confront our basic (rationally) groundless presuppositions. I don't see this as the place to find certainty, self-evidence, but rather the place that lets us see other possibilities. other basic presuppositions, other perspectives, and the basic groundlessness of all perspectives.

Of course, this won't satisfy those who are uncomfortable with uncertainty.

Rather, rules are post-hoc classifications and inferences we impose on our own behavior. — Apustimelogist

I don't think rules are imposed, they describe behaviors which are entrenched and replete with their own logic.

I think I'd respond by saying you're doing counting, which is neither addition nor quaddition. — Moliere

Addition, subtraction, multiplication and division are all, as far as i can see, basically counting, and counting is basically naming different quantities. Think about the abacus.

Draw 57 tally marks. Ask the skeptic how many there are. If the answer is "57", draw 68 more. Have the skeptic count them all. That should be a good enough answer for him. — RogueAI

See this comment I made in this thread 25 days ago:

You lay out 68 marbles and then you lay out 57 marbles in a separate row, then you ask the other "what are the names of the numbers of marbles in the two rows". Then you push them together and ask the other to count all the marbles and say what the name for that number of marbles is. — Janus

As far as I can see this solution dissolves the supposed problem. Much ado about nothing...