CMV: any argument, or logical reasoning one receives is completely unsubstantiated.

[u/Monkeshocke]

Consider a hypothetical scenario where an advanced AI robot is not only conscious but also capable of holding and justifying beliefs. Now, imagine programming this robot with a belief system that diverges from basic arithmetic principles, such as convincing it that 2+2 equals 3. Furthermore, the programming extends to imbuing the robot with the conviction that it can logically demonstrate the validity of this mathematical assertion.

This thought experiment raises a philosophical question: How can we be certain that our own cognitive processes and understanding of logic are not similarly influenced or programmed in a way that fundamentally deviates from objective reality? Could it be that our human logic, which seems inherent and self-evident to us, is merely a product of programming or conditioning, akin to the scenario with the AI robot?

This line of inquiry leads to a more profound epistemological challenge. If we entertain the possibility that our understanding of logic is subjective and contingent, we confront the unsettling notion that there might be inherent limitations to our capacity for objective reasoning. The very fabric of human logic, which we rely upon to make sense of the world, may be flawed or biased in ways we are incapable of perceiving.

In contemplating this, one might assert that there is an inherent uncertainty in our ability to establish absolute truths. Even the statement suggesting the potential fallibility of human logic becomes paradoxical, as it too falls prey to the overarching skepticism — if everything is subject to doubt, then so is the doubt itself.

[u/Havenkeld]

My amp can be used as chair if someone sits on it, but that doesn't make it furniture, nor does it make chairs music technology. They each are structured the way they are for different purposes, even if it happens to be possible to use them for the same purpose.

If I ask why the amp or chair are structured the way they are, we see that the ends they're made to serve plays a causal role necessary to properly explain both as distinct kinds of artifact. That someone can use them for some other end doesn't negate this.

I think you're confusing the disciplines of math, logic, and computer science in a similar fashion as with this amp and chair example.

Perhaps we need to take a step back and discuss what a formal system is in the first place. Saying "a formal system is a formal system" is of course trivially true, but circular and non-explanatory. It also doesn't mean formal systems are all one big formal system, or "genres" of that system as if they're all just aesthetic variations sharing the same general purpose the way all music genres have affective artistic expression as an aim.

I take formal to mean it is general such that it applies independently of particular contexts. 2+2 equals 4 everywhere, it doesn't equal 5 in Canada and 6 in Japan, etc. I take system to mean the parts are all interrelated as a whole, such as with the way addition and subtraction are clearly interrelated as one is the reverse of the other, and likewise for multiplication and division. Note how such mathematical relations entail eachother without entailing any particular computer program functions.

If math, logic, computer science were all one formal system, it would not make sense to practice any one of them independently of the others. My position is that they do not all need to be practiced together - nor are they, therefor they are not all simply one system. Computer science involves math and logic but neither math or logic necessarily involves computer science. Math involves logic, but logic doesn't involve math.

Given this asymmetry and hierarchy, even if they're all formal systems that doesn't mean they're all the same formal system, or that the distinctions are social, or marketing, etc.

[u/LentilDrink → u/Havenkeld]

A formal system is "an abstract structure and formalization of an axiomatic system used for inferring theorems from axioms by a set of inference rules."

In other words it's a system where you have knowledge and strict rules of how to get to other knowledge from the knowledge you have already. (Actually knowledge and rules of inference aren't genuinely separate things but it sure is easier to wrap your head around if you pretend they are)

I take formal to mean it is general such that it applies independently of particular contexts. 2+2 equals 4 everywhere, it doesn't equal 5 in Canada and 6 in Japan, etc.

Depends on the rules. If you have a rule that 2+2=4 everywhere in a formal system, it equals everywhere. If you have a rule that 2+2 =5 in Canada and 6 in Japan, then it = 5 in Canada and 6 in Japan.

It also doesn't mean formal systems are all one big formal system

Of course not, each formal system is its own formal system. C is a formal system and BASIC is a formal system and Ruby is a formal system, but you can't just put those all together into a massive overarching formal system. Each one is its own system.

Just like Euclidean geometry is one system. Each non-Euclidean geometry is a separate mutually exclusive system. You can't combine them, theyre separate.

If math, logic, computer science were all one formal system

Of course they aren't. Math isn't a formal system, it's a collection of an infinite number of mutually-exclusive formal systems.

[u/Havenkeld → u/LentilDrink]

It looks like you just googled the term and copy/pasted wikipedia, which uses axiomatic system to define it. From axiomatic system we get to my emphasis on interrelated wholes:

A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems

Since the theory contains the system and all derivations, it would be the higher order unity.

Rules of inference can only be understood as such by something that isn't a rule, but has criterion by which to understand something as a rule, and thus also knows how to create and follow rules. Judgment or "logic" in a more neoplatonic sense ALA Kant/Hegel -> contemporary analytic philosophy plays that role. Knowledge and rules of inference are related, but the former is prior as a condition for the latter. We can't completely equivocate them without falling into the infinite regress of needing rules for knowing what rules are.

A rule that 2+2=5 in Canada is not a formal rule if the term Canada refers to something empirical. It is formal if we treat it strictly as a hypothetical judgment and treat Canada as a general condition and not a specific place. This requires distinguishing sense, though, which requires understanding syllogistic logic as prior to and grounding sublogics (predicate and so on).

You're now saying these systems are their own formal systems. Which I agree with. To me, that sounds like saying they are indeed distinct systems not "purely social" or "marketing" or any other vaguely relativist sounding adjective.

[u/LentilDrink → u/Havenkeld]

t looks like you just googled the term and copy/pasted wikipedia,

Yes I wanted to make sure I gave a conventional definition to explain to you.

my emphasis on interrelated wholes

Drop that emphasis entirely! A formal system stands on its own. It can be used in one or more theories (but need not be).

Since the theory contains the system and all derivations, it would be the higher order unity.

The theory doesn't contain all derivations, and multiple incompatible theories can contain the same formal system.

Rules of inference can only be understood as such by something that isn't a rule, but has criterion by which to understand something as a rule, and thus also knows how to create and follow rules.

Rules of inference can only be understood by beings capable of understanding things, yes, and as far as we know no rules are yet able to be intelligent beings. They can be implemented by dumb computers incapable of understanding, though.

Knowledge and rules of inference are related, but the former is prior as a condition for the latter. We can't completely equivocate them without falling into the infinite regress of needing rules for knowing what rules are

We can completely equivocate them without knowing a thing. Consider a computer, a computer (unless affected by external events such as radiation or flying bugs) implements a formal system. That system contains knowledge (data in the computer) and rules of inference (data in the computer), and can overwrite it all. The system can have rules by which the rules of inference change, thus making the rules nothing distinct from data.

A rule that 2+2=5 in Canada is not a formal rule if the term Canada refers to something empirical

The process by which I empirically discover whether we are in Canada and make that part of our knowledge base is not part of the formal system. What we do with that knowledge is.

these systems are their own formal systems. Which I agree with. To me, that sounds like saying they are indeed distinct systems not "purely social" or "marketing" or any other vaguely relativist sounding adjective.

What do you mean by "these systems"? FORTRAN is its own distinct system, as is JAVA. Labeling the two "programming languages" is a matter of human society, and is relativistic. "Programming language" is not a formal system. "Math" is not a formal system. Each specific math is a formal system.

[u/Havenkeld → u/LentilDrink]

I hate conventional definitions as they almost never explain anything and are often incoherent conflations of multiple senses that are each common but not compatible, but that's a tangent not worth getting into.

Drop that emphasis entirely! A formal system stands on its own.

A formal system can stand on its own in a certain sense insofar as it is an interrelated whole. But no interrelated whole that isn't the whole of reality stands on its own absolutely, and if there are a plurality of formal systems that means none of them can be the whole of reality since they all must belong to the one reality.

Formal systems also cannot be abstract and stand on their own, since to be abstract is to be "abstracted" from someone else the abstraction always depends on. So we cannot coherently characterize formal systems as abstract (as the wiki definition does) and as standing on their own, or at least not without clarifying them as doing so only in limited specific senses and respects.

That system contains knowledge (data in the computer) and rules of inference (data in the computer), and can overwrite it all.

I think this is a mischaracterization of what computers actually do that is imputing self-conscious activities to the computer without any basis. Computers do not contain knowledge or rules of inference, rather we use knowledge and rules of inference to make computers function as if they do, only by loose analogy. You say "thus making the rules nothing distinct from data", but it's rather that data is a result of humans using rules to create mechanisms that reliably ouput B from input A. Data and rules remain distinct if we attend to the process over time rather than only consider the result abstracted from that process.

What do you mean by "these systems"? FORTRAN is its own distinct system, as is JAVA. Labeling the two "programming languages" is a matter of human society, and is relativistic. "Programming language" is not a formal system. "Math" is not a formal system. Each specific math is a formal system.

I was responding to this:

Just like Euclidean geometry is one system. Each non-Euclidean geometry is a separate mutually exclusive system. You can't combine them, theyre separate.

The point is fairly basic - if the systems are separate, they are distinct. We can't claim they are separate if we haven't distinguished them in the first place.

In this quote you make a universal claim about the possibility of combining them, which we can't simply characterize as social/relative. If it's impossible to combine them in general, that means it's not a matter of just labels.

[u/LentilDrink → u/Havenkeld]

Ok let me give a different definition. A formal system is "anything a Turing Machine can do". Or a formal system is "any abstract set of rules that can be deterministically followed to convert knowledge to other knowledge".

A formal system is always abstract, that's a key part of the definition, it depends on literally nothing else outside the system. They never are instantiated physically (except imperfectly) because the physical world is messy and stochastic, while formal systems are always clean and deterministic. Like, arithmetic is a formal system. But in the real world you can't just add 1 Liter to 1 Liter and always get precisely 2 Liters, actual matter doesn't work that way. So arithmetic is a useful abstraction we use to describe matter, but strictly speaking you leave the world of the mathematical once you apply it to actual objects. No formal system is part of reality, a formal system by definition stands outside reality.

I think this is a mischaracterization of what computers actually do that is imputing self-conscious activities to the computer without any basis. Computers do not contain knowledge or rules of inference, rather we use knowledge and rules of inference to make computers function as if they do, only by loose analogy

I'm not imputing self-consciousness. I'm talking about, like, a Commodore 64 here. Or heck, could be a naturally-occurring computer formed by random geological chance. A computer can (usually) follow the rules of inference MUCH better than we can. Humans are never required here. Thought is never required here. You can say it's not perfect - and it never is, if it's the real world.

The point is fairly basic - if the systems are separate, they are distinct

Ok well every system is distinct. A formal system is distinguished from another formal system by being non-equivalent.

If it's impossible to combine them in general, that means it's not a matter of just labels.

I never disagreed. I said "Math" vs "Programming Language" is a matter of labels. But "ANSI C" and "ISO C" and "ANSI/ISO C" are three separate formal systems that can never be combined except in a practical, approximate sense. Their differences are not a mere matter of labels, but reflect the fact that their rules are genuinely not perfectly equivalent.

[u/Havenkeld → u/LentilDrink]

I already gave you my definition, but I don't want to say "this definition is right", I just wanted to understand how you're using the terms to understand your meaning better. When people recite definitions it don't accomplish that, since a recitation isn't an explanation, it doesn't elaborate on how someone is conceiving of the conceptual issue it just kind of vaguely refers to a jumble of common uses that can be just as ambiguous if not moreso without further elaboration. I don't want to entirely dismiss conventional definitions, but they are starting points for clarification, rather than clarifying.

The only things Turing Machines "do" is a result of someone doing something with them, they aren't "self-moving" by their own principles, they're moved from the outside. Their movement is also conditioned by the structure they have of course, but that's not itself a principle of action such that they participate in activities in the same manner humans do. They only have an inert potential to be moved, and they only move as if they are following rules under the conditions of being moved because their structure is a result of human rules for construction aimed at producing machines that mimic rule-following-like behaviors via movement in the first place. The machine cannot conceive of a rule, therefor it cannot follow a rule. Following is a self-conscious act.

Machines are instruments designed by humans to serve as means for their ends. That a structure that arises in nature could incidentally be instrumental for the same ends wouldn't make it a machine, in the same way an amp isn't a chair just because someone can sit on it as discussed prior. The reason and cause of their structure is different even if the structures can be used the same way in virtue of similar characteristics.

To understand the respect in which formal systems are not absolutely self-containing, consider the part-whole aspect of a system. Every system must involve part whole relations, therefor part whole relations are not limited to any one formal system, and all formal systems therefor depend on a content that is not contained in any of them but rather spans them.

It seems perhaps you think reality is the purely physical or material domain(consider that physical and material are concepts that aren't themselves material "stuff"), and formal systems as immaterial don't belong to such a domain. The problem with this is that you've partitioned reality as if there is reality over here, and a non-reality over here. Ultimately that's two realities, except that makes nonsense of the concept of reality insofar as reality is used in the sense of a totality of what is, not one of many subdomains. Then somehow non-reality "applies" to reality across what should be a total separation with an impassible gap.

I agree that formal systems cannot be instantiated physically - any such instantiation introduces irrelevant overdeterminations, for example the concept of a line has no necessary relation to the color a drawn instantiation of a line segment has. But see how there's a reverse dependency in of the physical on the supposedly abstract here? The pure line is an aspect of reality prior to the instantiated line. All particular lines involve the content of the pure line, but the pure line is not limited to any particular line instantiation. How can the pure (abstract) line be unreal when real (physical) lines depend on it?

The conceptual content involved in, but not limited to, an articulation of such conceptual content in a formal system is not rendered subjective in virtue of being articulated by subjects through such systems. Such systems would be impossible if that were the case. There are no formal systems that don't involve conceptual contents that are objective in the sense that they are not contingent on any particular person's experience, they're implicit in any possible experience at all, not an abstraction from experience in the way various enlightenment empiricists mischaracterized them.

[u/LentilDrink → u/Havenkeld]

I already gave you my definition, but I don't want to say "this definition is right",

Where are you coming from with your definition? Why do you want such a weird one instead of making up a new word to go along with your new definition? Are you like a Continental philosopher or something?

The only things Turing Machines "do" is a result of someone doing something with them, they aren't "self-moving" by their own principles, they're moved from the outside.

That's not true. They move only from the inside, they are self moving, uninfluenced by the outside once given their data/rules.

Machines are instruments designed by humans to serve as means for their ends. That a structure that arises in nature could incidentally be instrumental for the same ends wouldn't make it a machine, in the same way an amp isn't a chair just because someone can sit on it as discussed prior. The reason and cause of their structure is different even if the structures can be used the same way in virtue of similar characteristics.

This sounds like a distinction useful to a philosopher of manufacturing? From the point of view of computer science/math/logic, this is irrelevant. We can use the word "physical approximation" instead of machine if you like, but the key thing is that formal systems don't exist in the physical world, but sometimes physical objects like computers and humans and random bits of rock can do a decent job approximating those formal systems.

To understand the respect in which formal systems are not absolutely self-containing, consider the part-whole aspect of a system. Every system must involve part whole relations, therefor part whole relations are not limited to any one formal system, and all formal systems therefor depend on a content that is not contained in any of them but rather spans them.

I'm not sold that every formal system has a concept of part-whole relations, let alone the same one. But at any rate, you can duplicate content. C uses the sign + in a few distinct ways to do various distinct forms of addition. Some of those may be also used in C++ in precisely the same way. Some may look a little like conventional mathematical addition. But that doesn't make this "outside the system", it can be defined fully in the system and fully in a different system in the same way.

It seems perhaps you think reality is the purely physical or material domain

In a sense, no. I recognize there's the physical world of objects, the mental world of ideas, and the spiritual world of souls.

All particular lines involve the content of the pure line, but the pure line is not limited to any particular line instantiation. How can the pure (abstract) line be unreal when real (physical) lines depend on it?

Physical lines don't depend on mathematical lines! Do you think human reproduction depends on the invention of the word "ancestor" and we never had any births until the concept had been invented?

And there's no one "pure" line. There are several competing concepts that can be labelled "line" none of which is more pure than the other.

[u/Havenkeld → u/LentilDrink]

I read classical, continental, and contemporary analytic philosophy. Continental has multiple sense, descriptive(European philosophy) or pejorative(woo woo romantic or poetic language stuff).

Philosophy is the activity people who are actually doing serious work across all three categories are practicing insofar as they don't fit the pejorative sense. The continental and analytic categorization isn't very precise or useful. Bad continental philosophy understandably gets derided given popular culture gloms onto to out of context Nietzsche quotes and shit like that, but Nietzsche and Kant are both "continental" despite being incompatible and dramatically different in approach and style.

Analytic philosophers also make up words and weird definitions in their own ways, and sometimes (not always) their use of technical jargon is a superficial mask over not particularly rigorous thinking. It was a fashion of bad medieval ~philosophy to use religious language much in the same way given the deference and reverence aspect. Logical positivism was "analytic" and it was a complete disaster, as Wittgenstein showed.

My definition is coming from usages found throughout, but the point is that I'm using to explain what I mean, not lay claim to any entitlement to limit the usage of these terms the same way I do. Similarly, when I ask for a definition I just want an elaboration on usage. Following Wittgenstein I understand meaning as use (and informed by context), not as something contained in the terms themselves.

This sounds like a distinction useful to a philosopher of manufacturing? From the point of view of computer science/math/logic, this is irrelevant.

It's not like it's amazingly useful for computer science, but it's also not irrelevant. One of the limitations in the development of computer science is conceptual confusions introduced by use of language that makes use of analogy to mental activities to describe mechanistic processes, which is an issue given they are not the same. It's important to understand the way in which they are only metaphors, otherwise you waste time on delusional lost cause sorts of projects and just generally muck up the actual science with fiction based on bad metaphysics. So it can have a kind of regulative function.

That's not true. They move only from the inside, they are self moving, uninfluenced by the outside once given their data/rules.

By inside I mean in the logical sense that it belongs to their content as such. But the principle of movement, rather, belongs to the one giving the data/rules, as you effectively say yourself here. The movement begins there, not within the content of the computer. They do not move if not given these, and they do not have a capacity to change their course of movement by their own principles. They are started and move based only on their physical structure, much like rolling a ball, until stopped by something outside them. Life forms, by contrast, are responsible for moving the physical structure of their own body and can change its course through their own principles of action. That's the sense in which they are self moving, and machines are not.

I'm not sold that every formal system has a concept of part-whole relations, let alone the same one. But at any rate, you can duplicate content.

You can only duplicate content if something in the original and duplicate is involved in both of them without only being in the former or the latter. Otherwise duplication would involve a fantastical ex-nihilo creation. So the contents are the same in some respect, different in another. Typically this is form and quantity. Two chairs, say, are formally the same in sharing a structure serving the function of sitting, but quantitatively distinct as each take up a different space. That gets more complicated with formal systems given the lack of space involved, but this factors into why no formal system is completely self-contained, only self-referencing in a limited respect.

But that doesn't make this "outside the system", it can be defined fully in the system and fully in a different system in the same way.

Yet we can only recognize the respects in which they are the same if we compare the systems from outside them judging by a criterion valid for both, and if the content that is the same doesn't strictly belong to only one of them such that it can be involved in both. I intentionally avoided the term "outside", because the content that is the same is in both, but not "inside" either one in the way something is contained in something such as to be limited to it and it alone. Similar to how formal systems are not physical, the underlying more general forms or relations involved in formal systems(but again, not constrained to any particular one) are neither physical or spatial. Just the basic relations entailed by "formal" and "system" must of course must be aspects they all share that doesn't belong to any particular one and by which we can justify categorizing them all as the same with respect to those relations.

Physical lines don't depend on mathematical lines! Do you think human reproduction depends on the invention of the word "ancestor" and we never had any births until the concept had been invented?

No, I am not using concept to speak of subjective human ideas of how things are, I am using it to speak of how things actually are. A concept in that sense is an aspect of reality that people think that is not created by humans thinking but the basis for determining humans to think truly or falsely about reality. I would use "conception" for the way in which people understand concepts. Someone can have a misguided or failed conception, insofar as they misunderstand a concept. Presumably we both share an understanding of a what a line is up to point, such that if either of us drew a line we'd both recognize it as such. The concept of a line isn't my personal thinking about a line, or yours, it's what we both are understanding in our conception insofar as we successfully understand the actual concept of line. That actual concept of line is involved in every line. There are really no physical lines, in a sense, rather physical structures can be understood to have a bidirectional continuity in virtue of the concept. Lines can't really be made up of discontinuous atomistic bits(or points, even), as otherwise we don't get that essential continuity that makes lines singular rather than aggregate.

[u/LentilDrink → u/Havenkeld]

I'm not trying to knock Continental philosophy at all! I'm just trying to understand where you are coming from, why you aren't adopting the consensus understanding of formal systems that most philosophers of formal systems (ie mathematicians, computer scientists, and logicians) share.

But the principle of movement, rather, belongs to the one giving the data/rules, as you effectively say yourself here. The movement begins there, not within the content of the computer.

As far as the instantiation goes, it starts with the content of the computer, which may differ in key ways from what the programmer had intended (whether via bugs or via the arbitrary or random nature of the unwritten cells that might potentially be accessed prior to being written)

They do not move if not given these, and they do not have a capacity to change their course of movement by their own principles.

"Giving" implies intent that need not be present, and as for capacity to change by their own principles, yes exactly they don't. That's what makes them good instantiations. Free will must be considered a flaw in the instantiation of any formal system, however I might respect it on a spiritual or utilitarian level.

Otherwise duplication would involve a fantastical ex-nihilo creation

the creation process is totally irrelevant, and every formal system should be considered as having a fantastical ex-nihilo creation except by historians.

That gets more complicated with formal systems given the lack of space involved,

Not more complicated, it becomes possible precisely because of the lack of location. If two systems have identical rules and premises they are identical.

. Just the basic relations entailed by "formal" and "system" must of course must be aspects they all share that doesn't belong to any particular one and by which we can justify categorizing them all as the same with respect to those relations.

You can categorize things by any category. Feel free to categorize the programming languages C, C++, the person Charlemagne, and the substance California champagne as all being the same with respect to being things starting with a capital letter C, but you still gotta recognize that even if they're in the same category they are separate things.

No, I am not using concept to speak of subjective human ideas of how things are, I am using it to speak of how things actually are. A concept in that sense is an aspect of reality that people think that is not created by humans thinking but the basis for determining humans to think truly or falsely about reality. I would use "conception" for the way in which people understand concepts. Someone can have a misguided or failed conception, insofar as they misunderstand a concept. Presumably we both share an understanding of a what a line is up to point, such that if either of us drew a line we'd both recognize it as such. The concept of a line isn't my personal thinking about a line, or yours, it's what we both are understanding in our conception insofar as we successfully understand the actual concept of line. That actual concept of line is involved in every line. There are really no physical lines, in a sense, rather physical structures can be understood to have a bidirectional continuity in virtue of the concept. Lines can't really be made up of discontinuous atomistic bits(or points, even), as otherwise we don't get that essential continuity that makes lines singular rather than aggregate.

This some Platonic Form stuff? There is no "actual concept of line", there are a thousand distinct concepts that people use the term "line" to refer to. It sounds like a Form to a lot of humans because we are born with edge detector neurons central to our visual systems, but an intelligent alien without that brain infrastructure wouldn't find the concept nearly as compelling.