When I was the only one who had brought up or defended the idea of truth-preservation in the entire thread? — Leontiskos
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. — neomac
Do naturalists really speak this way when they are being rigorous and are not engaging in loose and poetic metaphor?
The concept of Logos is problematic not only for its spiritual connotations and connotations of intentionality (the idea that nature is not teleological is a bit of a dogma in naturalism today) but even moreso because it implies that any order in nature is enforced externally, say by eternal "laws of nature," that exist outside nature. This isn't popular due to Hume's "problem of induction" and Kripke's essentialist response. We generally now think that nature has the properties of order that it does because of what nature is, or because of what natural entities are. That is, the "logic" of state progression in nature is intrinsic, not extrinsic. But this in no way means that the order doesn't exist outside the mind, it simply means that such an order is inherit to nature because of what nature is. — Count Timothy von Icarus
3. Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted. — Count Timothy von Icarus
I was dipping back into the Routledge handbook of metaphysics and it made me think of something. For folks who don't like thinking of logic in terms of naturalism, or logic as "out there," "in the world, sans mind," do you embrace realism towards propositions, states of affairs, facts, and events? — Count Timothy von Icarus
I suppose a thoroughgoing nominalism that takes logic to be solely a property of mind doesn't have this problem. But to my mind such ontological commitments seem to threaten a fall into radical skepticism and solipsism. — Count Timothy von Icarus
So, on the one hand I see a bridge between all three "types" of logic laid out in the initial definitions that comes from naturalism. Humans are natural systems and our minds formed by nature and our systems are formed by our minds. Thus there seems to be a way in which our minds and representational systems should map to things present in the world and be shaped by any patterns therein. — Count Timothy von Icarus
Everything is possible until it is necessary, and both these concepts are contingent on the concept of negation, and negation contingent on the disjunction of plurality of experience, as in derived a posteriori. Logic precedes that of which there is formal systems, or of which there are the field of "Logic" the same way physics precedes everything ever thought in the field of physics — Julian August
Without revealing too much of my own framework, this is my description of logic:
Hilbert said, "Mathematics is the art of giving the same name to different things." This applies to all of logic, as does its opposite. For logic is also the art of giving different names to the same things, and in a sense, these two actions are the same.
For my definition of logic, you'll have to wait for my magnum opus, if it ever comes. — Ø implies everything
Of course, sometimes when we talk about logic we want to refer to the logic of the external world, not just thought. For example, we can talk about an organelle being shaped by "the logic of natural selection." In this case, "the logic of natural selection," might be described by numerous formal systems, but it is not the formal description itself we are talking about, but rather the way the series of causal events that appears to conform to the more general logic. That is, the formal system is itself merely an encoding of the principle we want to refer to. — Count Timothy von Icarus
Formal logic and Symbolic logic are not able to deal with the real world phenomenon and states very well. — Corvus
Hilbert said, "Mathematics is the art of giving the same name to different things." — Ø implies everything
Formal logic and Symbolic logic are not able to deal with the real world phenomenon and states very well.
— Corvus
They are at the very heart of the development of digital computers, such as the one you're reading right now. — TonesInDeepFreeze
Above point tells us Logic is not just simple symbolic formula manipulation.
Sure, logic must be the working engines of all the computers and even AI agents suppose. But there would also some custom logics they set up, and embed into the programs in the devices depending on what they are used for. It wouldn't be just the plain classic symbolic logics only in use.They are at the very heart of the development of digital computers, such as the one you're reading right now. — TonesInDeepFreeze
Yeah, that was written sometime ago, when I knew little about logic. Since then I have read a few different logic textbooks, which totally changed my ideas and views on logic.Above point tells us Logic is not just simple symbolic formula manipulation.
I'm a bit more cautious about that. It seems like the die is already cast on logic generally referring to formal systems in philosophy. I was searching around for a good term to refer to the idea of "what we use logic to describe in nature," but I haven't thought of a catchy one. — Count Timothy von Icarus
The traditional classic logic wouldn't be able to deal with the dynamic and unpredictable nature of the real world. From quite some time ago, various types of non classic logics seem to have been implemented, and used such as Temporal Logic, Description Logic, Fuzzy Logic, Epistemic Logic, Many-Valued Logic, Probability Logic, Topological Logic, Assertion Logic, Deontic Logic ... etc to deal with the dynamics of the real world.What Corvus should have said is that they are not very good at cognizing in the way living systems do, as Hubert Dreyfus famously showed 60 years ago with his ‘What Computers Can’t Do’ and his more recent update ‘What Computers still can’t do’. Of course they are a part of the real world. — Joshs
It wouldn't be just the plain classic symbolic logics only in use. — Corvus
various types of non classic logics seem to have been implemented, and used such as Temporal Logic, Description Logic, Fuzzy Logic, Epistemic Logic, Many-Valued Logic, Probability Logic, Topological Logic, Assertion Logic, Deontic Logic — Corvus
Math is a subset of logic that deals exclusively with relationships of quantity. — Kaiser Basileus
Good point. Yes, I agree with that. Classic logic is very useful in checking out logical validity and soundness in the spoken languages and written documents. It is also the foundation of all the other non-classic logic too. One must learn classic logic first in order to understand all the non-classical logics.Classical logic is useful, even just in its sentential component, which is the Boolean logic used in ordinary computing, and further as classical logic is the logic for the ordinary mathematics for the sciences and for the study of recursive functions and the theory or computability that are at the very heart of the invention and development of the digital computer. And, while predicate logic cannot account for all forms of inference, predicate logic is usually prerequisite for study of the more advanced logics. — TonesInDeepFreeze
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