If you say in the latter statement that there can be many formalisms mapping on the same rules, then formalism is distinct from rules. And surely, by formalism, you could mean to refer to the logic rules as you also stated. But were this the case the following claim of yours “1. Logic is a set of formal systems; it is defined by the formalism” would equate to “1. Logic is a set of logic rules; it is defined by the logic rules” which sounds, if not tautological yet, very little informative.
Sure, it's tautological. That was the position of Russell and the Vienna Circle. Moreover, by this view, all of mathematics is itself tautological. — Count Timothy von Icarus
Certain logic formulas are tautologies e.g. "( P ⇒ Q ) ⇔ ( ¬ P ∨ Q )" in the sense of being always true whatever is the truth value of the variables P and Q. However not all logic formulas are tautologies (e.g. P ⇒ Q). The idea that logic (and mathematics to the extent it is reducible to logic) is tautological basically comes from the idea that logic theorems can prove only tautological formulas. And this is in line with what I also said about deductive reasoning “from premises to conclusions we are manipulating our own representations so that, semantically speaking, there is no more truth in the conclusion than there is in the premises, there is no more information in the conclusion than there is in the premises.“
But your statement “Logic is a set of formal systems; it is
defined by the formalism” (which is neither a logic formula nor a logic tautology) seemed to offer a definition for “Logic”. And valid definitions should not be tautological in the sense that what is to be defined should not occur in what is defining. Yet your other claims made your definition of “logic” look tautological (even claiming “Logic is all about tautologies” would sound tautological if it equates to “Logic is all about logic”).
The rules define what the system is. And per deflationary theories of truth, that tend to go along with this sort of view, truth is itself simply something defined in terms of such systems. That is, truth is "neither metaphysically substantive nor explanatory. For example, according to deflationary accounts, to say that ‘snow is white’ is true, or that it is true that snow is white, is in some sense strongly equivalent to saying simply that snow is white, and this, according to the deflationary approach, is all that can be said significantly about the truth of ‘snow is white.” — Count Timothy von Icarus
I’m not persuaded by the deflationary theories of truth so I can’t share your assumption. The most intuitive objection I can make against it is that, asserting p doesn’t mean nor implies that p is true.
the general idea is that logic is about abstract systems, not thought and certainly not the world or metaphysics.Logic might inform our metaphysics, but our metaphysics (or philosophy of mind) should not inform our consideration of logic. — Count Timothy von Icarus
Notice that “abstract” in “abstract systems” may also have a metaphysical connotation: namely, being out of space and time. And this understanding would lead us to a form of platonism about logic (which is also a metaphysical view). However “abstract” can simply refer to the result of a cognitive task by which we are focusing on certain set of characteristics or type of information while ignoring others. So “abstract systems“ refers to the possibile result of such cognitive task. I guess that’s the understanding suggested by your claim, right?
Independently from the merits of Tarski’s semantic theory of truth for formal systems, if the price for it is to relativize the notion of truth to a given (object) language, my problem with it is: what does “if and only if” in the T-condition mean? If the be-conditional requires the notion of “True” to be understood as a logic operator, but the notion of true can not be applied at the same language level in which the bi-conditional is expressed, then what does that bi-conditional even mean? Besides asserting p (in the most basic object language and since it’s a language it can offer just representations of facts not facts themselves) doesn’t mean that p is true.
Right. Or what does it mean to "describe things" at all in a language we are pretending is completely divorced from anything else in reality? At a certain point, when you get into very deflationary views, you're no longer describing "things." All you can say is that "a system can produce descriptions.” — Count Timothy von Icarus
Indeed, I’m not even sure that such views would even justify anybody saying “a system can produce descriptions”, since the notion of “description” to me conceptually implies the idea that representations of states of affairs are distinct from the states of affairs in the world as the former refers to the latter (not the other way around), and the idea that the former can correctly or incorrectly apply to the latter (hence the distinction between “true” and “false”).
But most philosophers are naturalists, so it doesn't seem too outlandish. — Count Timothy von Icarus
If you mean that this thread is specifically about naturalist views of logic, then I didn’t get it but I will take it into account from now on. On the other side, if you mean that this thread is about views on logic and your views on logic are grounded on popular naturalist assumptions, then I’ll confirm what I said that I do not share such popular views and I’m open to discussing them.
What you may be tempted to say instead is that if there are representational tools that can successfully represent the world, then the world must be such that our representational tools can succeed in representing it. But this claim does very much sound like claiming that we can represent the world that we can represent, doesn’t it?
It sounds similar; I don't think it's identical. First, if we posit that any intelligibility we find in the world is hallucinatory, something we project onto a world that lacks it, I don't see how this doesn't slide into the territory of radical skepticism. The steps to get us to "how do you know cause and effect exist? Maybe your mind creates all such relationships," seem like they should also get us to "why do you think other minds exist?" Or "why should we think an external world exists outside of our perceptions?" Afterall, don't we suppose that others have minds because of how those minds seem to effect their behaviors?
The fact that animism is pretty much universal in early human cultures (e.g., "the river floods because it wants to"), and that children tend to provide intentional explanations for natural phenomena ("the clouds came because the sky is sad") seems to show we can "hallucinate" other minds to some degree. But if we think all of the intelligibility we find in the world is simply projected, then I'm not sure how solipsism isn't a problem.
Most philosophers are naturalists though, and most think the natural sciences are one of the best sources of information we have about how the world is though. And if we accept we are formed by natural selection, then it is prima facie unreasonable to think how we "make the world intelligible" has nothing to do with how the world is.
Second, what is the point of positing aspects of reality that we cannot ever, even in principle, experience? To be sure, people have experiences all the time that they say they cannot put into words. That makes perfect sense; we do more than just use language. But aspects of reality we can never know? They are like Penrose's invisible fire breathing dragon who is flying around our heads and not interacting with anything. We can imagine an infinity of such entities. But as long as they are, in principle, forever unobservable, their being or not being seems identical. When we move to the existence of that which cannot even be thought it seems even weirder. It's the inverse of radical skepticism, instead of seeing a way to doubt everything, now we can posit anything (so long as we can never know of it). — Count Timothy von Icarus
I’m not positing “that any intelligibility we find in the world is hallucinatory”, I’m not a radical skeptic, I’m not a solipsist. My point is more that we have a network of concepts (like representation, world, truth, fact, possible fact, logic/semantic inference) that enable us to talk meaningfully and reflectively about our own cognition. Since they are mostly primitive concepts they can not be questioned or explained away without ending up into some nonsense or implicitly reintroducing them. To me “realism” about the existence of the external world (that can be experienced or referred to by other minds beside mine) is matter of conditions to talk meaningfully about the external world, so any attempt to question the existence of the external world sounds nonsensical to me as much as any attempt to demonstrate it, because one needs demonstration were things can be questioned meaningfully.
On the other side, our representations of the world may not correspond to what is the case, and may refer to mind dependent facts (as human linguistic conventions or social institutions). Unfortunately we may hold more false beliefs than we are able to detect or wish to admit. And human representations and logic/semantic inferences may serve human biological extinction as much as they can serve human biological survival.
Logic rules allow us to infer some conclusions from some premises. Such rules ensure that if the premises are true, then the conclusion is true. And that’s possible because from premises to conclusions we are manipulating our own representations so that, semantically speaking, there is no more truth in the conclusion than there is in the premises, there is no more information in the conclusion than there is in the premises. The mapping to the world can be done by the premises. But logic would work even without any such mapping. E.g. Premise 1: squares are triangles; Premise 2: triangles are circles; Conclusion: squares are circles.
This gets to the "Scandal of Deduction." If in all valid deductive arguments all information in the conclusion is contained in the premises, what exactly is the point of deduction? It tells us nothing. So why does deduction seem so useful? Why can't we memorize Euclid's axioms and then immediately solve every relevant geometry problem we come across?
This is probably the best example I know of where thinking of logic as completely abstract runs into problems. A lot of ink has been spilled trying to figure out some sort of formal solution to the Scandal, because the idea is that any solution has to lie within the scope of the abstract systems themselves.
I don't think this works. Floridi and D'Agostino put a lot of work into their conception of virtual information, trying to figure out how it is that at least some inference rules introduce new information in an analysis. But it seems like such a project is doomed. As both they and Hintikka agree, Aristotelian syllogisms only deal with surface information, information explicit in the premises. The problem is that we can still find this type of analysis informative, just as we can not know the answers to very simple arithmetic problems until we pull out a pencil and start computing.
Naturalist approaches have no problem here. We don't see things and immediately know what they entail because thought is a complex process involving a ton of physical interactions, all of which occur over time-- simple as that. — Count Timothy von Icarus
Concerning the "Scandal of Deduction", even though I do not share your naturalist assumptions, my way out is somehow similar to yours. We do not have the full list of valid representations of the world in our mind simultanously. We process them progressively according to some logic/semantic rules. And we may also fail in doing it.
It’s not the world that satisfies such rules, but our representations of the world. While we can represent and logically process representations of state of affairs that do not map into reality and do not correspond to facts, are there real states of affairs that we can not represent ? But how can we answer such question without possibly representing such state of affairs? What are we picking with the notion “state of affairs“ for whatever goes beyond our means of representation (so including the notion of "state of affairs" itself)?
Not everything can be put into words. I'm not sure if it makes sense to posit things that can be known in any way though. — Count Timothy von Icarus
Sure we may be unable to describe many of our experiences to any arbitrary degree of detail. For example there are many varieties of “red” and yet we can refer to all of them simply as “red”. That’s not the point, the point is that in order to talk meaningfully about experiences we can’t put into words, we still need to apply correctly a sufficiently rich set of notions and make inferences accordingly: e.g. that the varieties of red are not varieties of grey, they are colors and not sounds, that they are phenomenal experiences and not subatomic particles, that one normally needs functioning eyes and not functioning ears to experience them, etc.
Anyhow, would you agree that the world has an influence on how we represent it? — Count Timothy von Icarus
The term “influence” may express an ontological notion of causality, but I find this notion problematic for certain reasons. On the other side, if we talk in terms of nomological regularities, surely I do believe that certain external facts (e.g. the light reaching our retina) correlate with visual experiences which then we have learned to classify in certain ways. That would be enough for me to talk about “influence” but at the place of ontological causal links, there are just nomological correlations plus a rule-based cognitive performance.