Logic is a system that makes it possible for a person who follows the rules and acts in good faith to be reasonably sure he is making sense in a way that should be compelling to any second or third person who also knows the rules and is in acting in good faith.

People who don't know the rues or are not acting in good faith are often - usually - unmoved by appeals to logic.

I believe that logic is a technique for thinking that is hard-wired into our brains and occurs mostly subconsciously. Explicit formal systems of logic are attempts to reverse engineer the way that process works to present it as a system of rules.

According to Charles Sanders Peirce:

• "Logic, regarded from one instructive, though partial and narrow, point of view, is the theory of deliberate thinking. To say that any thinking is deliberate is to imply that it is controlled with a view to making it conform to a purpose or ideal." (CP 1.573; 1906)
• "Logic may be defined as the science of the laws of the stable establishment of beliefs." (CP 3.429; 1896)

Combining and paraphrasing these definitions, logic is the normative science of how one ought to think if one intends to pursue truth; i.e., adopt belief-habits that would never by confounded by subsequent experience.

I think money would be a better example. Because no matter how dumb you're. If it's about your money, you're the world's best calculator. :rofl:

The rules of correct inference...

Logic is an expression of the laws of nature (or the laws of life/existence, however you choose to define the components of reality).

1 + 2 = 3/a bolt of lightning, is not precisely logic. Mathematics is a language that attempts to apply logic to its mode of operation. But, it is only logical in the sense that language is a logical part of communication/expression. For example, an alien unfamiliar with our mathematical language would not know that 1 + 2 = 3 unless the values of the numbers and their association are taught to them. The alien may have their own way of expressing the same relation but it may be a different language than our mathematics. The mode of operation tries to express an already existing relationship (let's call it, 'the process of cumulation') in existence/life. Mathematics didn't invent 1 + 2 = 3, it just realised the validity of it. That validity comes from logic.

I believe that logic is a technique for thinking that is hard-wired into our brains and occurs mostly subconsciously. Explicit formal systems of logic are attempts to reverse engineer the way that process works to present it as a system of rules. — andrewk

Combining and paraphrasing these definitions, logic is the normative science of how one ought to think if one intends to pursue truth; i.e., adopt belief-habits that would never by confounded by subsequent experience. — aletheist

I take these two descriptions of logic as somewhat opposed. Andrewk appears to say that logic is innate, something which we do instinctually, while aletheist seems to say that logic is a behaviour which we learn, as in other cases where we learn how we ought to behave. Or am I missing something here, a principle which may establish compatibility between the two perspectives?

No, I agree that the two definitions are incompatible; @andrewk seems to be saying that logic is the science of how humans do think, while I (following Peirce) hold that logic is the science of how any intelligent beings should think, if their purpose is to arrive at true beliefs by learning from experience. This is similar to the distinction that Peirce drew between logica utens, instinctive and uncritical habits of inference, and logica docens, deliberate and rigorous habits of inference. Logic has to be a normative science if there is good reasoning vs. bad reasoning, which I hope no one in this forum would deny.

The trouble with treating logic as normative is that the claim of normativity requires the use of logic, so it becomes circular. Further, claiming that logic will be useful in the future, as opposed to just observing that it has been useful in the past, runs into Hume's Problem of Induction.

That's part of why I approach logic as something we do, rather than something we ought to do. Like Hume, I ask, 'whence comes the ought'?

The trouble with treating logic as normative is that the claim of normativity requires the use of logic, so it becomes circular. — andrewk

Please elaborate on this assessment.

Further, claiming that logic will be useful in the future, as opposed to just observing that it has been useful in the past, runs into Hume's Problem of Induction. — andrewk

Which is a myth. As Peirce observed, "The validity of Induction consists in the fact that it proceeds according to a method which, though it may give provisional results that are incorrect, will yet, if steadily pursued, eventually correct any such error."

Like Hume, I ask, 'whence comes the ought'? — andrewk

Like I already said, it comes from having the purpose of arriving at true beliefs by learning from experience.

No, I agree that the two definitions are incompatible; andrewk seems to be saying that logic is the science of how humans do think, while I (following Peirce) hold that logic is the science of how any intelligent beings should think, if their purpose is to arrive at true beliefs by learning from experience. — aletheist

There appears to be something confused here. Isn't the point of formal logic to go beyond the limits of experience, to learn about things which we cannot experience? Perhaps we need to differentiate between the logical which comes to us naturally through instinct, and this is where I would class inductive reasoning, from formal logic, which is what we are taught.

I think specific forms of logic, like induction come to us naturally, but we are taught not to rely on these types because we have learned of their fallibility. That's why we have developed, and teach forms like mathematics, and deduction, which produce a higher degree of certainty.

Which is a myth. As Peirce observed, "The validity of Induction consists in the fact that it proceeds according to a method which, though it may give provisional results that are incorrect, will yet, if steadily pursued, eventually correct any such error." — aletheist

I agree with andrewk, inductive reasoning is problematic. The solution you state here is nothing more than trial and error. Sure, trial and error works, but it's not a reliable form of logic. "Learning from experience" is trial and error. Formal logic, I believe is grounded in principles not derived from trial and error.

"The trouble with treating logic as normative is that the claim of normativity requires the use of logic, so it becomes circular. "
— andrewk
Please elaborate on this assessment. — aletheist

Try to mount an argument that we ought to use logic if we wish to arrive at true beliefs, without using logic.

I never claimed that we ought to use logic if we wish to arrive at true beliefs, I defined logic as the science of how we ought to think if we wish to arrive at true beliefs. I also acknowledged that we have instinctive and uncritical habits of inference, but distinguished them from our deliberate and rigorous habits of inference. The latter are the subject matter of (normative) logic, which recognizes that there is good reasoning and there is bad reasoning.

I defined logic as the science of how we ought to think if we wish to arrive at true beliefs. — aletheist

I don't understand whether this is referring to discovery of logic or application of logic. Is this referring to
(1) identifying the best way of arriving at true beliefs, or
(2) taking on faith that FOPL is the best way, and for you 'logic' refers to the application of FOPL?

If it's (1) then how can the identification proceed without logic? How can it be determined which method is the best?

If it's (2) then it is simply a declaration of faith in FOPL. That's fine, but faiths are not normative, as we see by looking at religions.

Try to mount an argument that we ought to use logic if we wish to arrive at true beliefs, without using logic. — andrewk

Isn't that what the normative principle amounts to (or something similar)? It's precisely because mounting an argument without the use of logic is impossible by definition that such guiding principles cannot be anything other than normative.

I defined logic as the science of how we ought to think if we wish to arrive at true beliefs. — aletheist

I think that the problem is in how one defines "true beliefs". If we define truth along the lines of "what logic provides us with, then we are just begging the question. If we define truth along the lines of that which experience gives us, then logic is not the provider of true beliefs, memory is.

Aletheist, following Peirce, appears to be trying to conflate these two distinct, and somewhat opposing notions, of what provides us with truth:

while I (following Peirce) hold that logic is the science of how any intelligent beings should think, if their purpose is to arrive at true beliefs by learning from experience. — aletheist

I would caution against following such a principle because premises which are unclear and confused, as this one is, will produce conclusions which are even more confused and unclear.

What is clear, I believe is that we need to distinguish between the products of experience (sensation, memory, etc.), which we know as extremely limited, and highly fallible in any attempt to extrapolate beyond the range of what was immediately sensed, and the products of logic, which give us a broad range of application, with a high degree of certainty. We can place inductive reasoning as intermediary between these two, sharing in the fallibility caused by the extreme restrictions of the empirical, but also giving us a higher degree of certainty than simple memory and sense experience, in application.

The point being that the basic "experience" can only provide us with knowledge of the particulars to which one has been exposed. But in practise we apply this knowledge of what has been experienced, toward the unknown (in the sense of that which has not been experienced). This requires something, "logic", which we must, through effort (and normative means), separate from experience, in order that it may do what it is intended to do, and that is to bring us beyond the limitations of experience.

If it's (1) then how can the identification proceed without logic? How can it be determined which method is the best? — andrewk

I am talking about the study of logic, which is basically your (1), and generally agree with . We employ our instinctive reasoning habits (logica utens) all the time, with varying degrees of success. We develop our deliberate reasoning habits (logica docens) for the purpose of reducing error and ideally (but never actually) arriving at a set of beliefs that would never be confounded by subsequent experience.

If it's (2) then it is simply a declaration of faith in FOPL. — andrewk

I am talking about logic in a much broader sense than FOPL, including not only deductive reasoning, but also retroductive and inductive reasoning. It further encompasses the combination of these that serves as the scientific method - formulating explanatory hypotheses (retroduction), explicating their necessary consequences (deduction), and experimenting to ascertain whether they are falsified by experience (induction). All of this depends on the theory of signs and their relations, which also falls within my (and Peirce's) broad conception of logic.

We employ our instinctive reasoning habits (logica utens) all the time, with varying degrees of success. We develop our deliberate reasoning habits (logica docens) for the purpose of reducing error and ideally (but never actually) arriving at a set of beliefs that would never be confounded by subsequent experience. — aletheist

Would the following be a reasonable representation of your claim?

We ought to use logic if we wish to acquire true beliefs because, reasoning according to my instinctive reasoning habits, which I believe to also be the instinctive reasoning habits of almost all humans, leads me to conclude that it is the only reliable way to develop true beliefs.

Again, normative logic is not something that we use, it is the study of how we ought to think if we wish to acquire true beliefs - i.e., how we can deliberately improve on our instinctive reasoning habits, which is all that we have at our disposal initially. Peirce recognized four specific methods of inquiry - tenacity, authority, a priori, and science. Each can and does lead to true beliefs under the right circumstances, but only the method of science - consisting of retroduction, deduction, and induction, in that order - has self-correction built into it. It is not the only reliable way to develop true beliefs, but it is the most reliable way, given our inescapable fallibility.

Isn't that what the normative principle amounts to (or something similar)? — SophistiCat

Good question. I have never had a clear idea of what people mean by normative, and looking up definitions doesn't seem to help. The definitions don't seem to align with the many, varied ways in which people use the term. The only common feature seems to be that there's always an 'ought' in a normative belief, but the ought could be instrumental (we ought to do X if we want to achieve Y) or absolute (we ought to do X, full stop).

What seems like a likely candidate for a common accepted meaning is that a belief is normative if we belief that almost everybody holds it. This has the troubling consequence that a belief that slavery is wrong - something that seems so important and fundamental to us now - is not normative because in so many cultures slavery has been unquestioningly accepted.

Perhaps something a bit stronger. We could say a belief is normative if we believe that nearly all people, in nearly all practically likely circumstances, would hold that belief. With that definition, I think we could say that a belief that logic is the best way to arrive at true beliefs is normative, but we couldn't say that a belief either in the acceptability or unacceptability of slavery is normative. Further, it doesn't seem to be too much of a stretch from that to say that people 'ought' to hold that belief, if one's prepared to take a pragmatic sidestep of Hume's 'ought vs is' guillotine. Indeed, the 'ought' becomes a simple observation of what we believe to be the case.

What do you think?

As should be clear from my previous comments, when discussing logic as a normative science, I mean it in the instrumental sense - we ought to think in a certain way if we want to adopt true beliefs. Going a step farther, I suggest that we ought to adopt true beliefs if we want to avoid unpleasant surprises in our future experiences.

As should be clear from my previous comments, when discussing logic as a normative science, I mean it in the instrumental sense - we ought to think in a certain way if we want to adopt true beliefs. — aletheist

It was never in question that that was your belief. What I am interested in is what you mean by the 'ought'. My current hypothesis, based on my immediately previous post, is that you:

believe that nearly all people, in nearly all practically likely circumstances, would hold that belief [that logic is the best way of reliably obtaining true beliefs] — andrewk

Does that correctly reflect your position?

Not quite; more like: If an infinite community were to engage in infinite inquiry, using any and every method along the way, their ultimate consensus would be that the scientific one - retroduction, deduction, induction - is the most reliable way to arrive at true beliefs.

I find a lot of what has been said interesting, some I think is correct but incomplete, or else a little off the truth.

I (following Peirce) hold that logic is the science of how any intelligent beings should think, if their purpose is to arrive at true beliefs by learning from experience. This is similar to the distinction that Peirce drew between logica utens, instinctive and uncritical habits of inference, and logica docens, deliberate and rigorous habits of inference. Logic has to be a normative science if there is good reasoning vs. bad reasoning, which I hope no one in this forum would deny. — aletheist

His distinctions are fine, but incomplete. My take is that there are three especially interesting aspects of logic (I'm ignoring the aspect of how logic is taught and folding that into the norms logic for simplicity):

Normativity of logic: How ought we reason?/What are the correct rules for reasoning. The views of what are the correct logical norms have demonstrably over time (e.g. Classical logic invalidates some of Aristotelian logic and adds what the old logic lacked). This isn't very surprising.

Logical Consequence: Given a set of axioms and inference rules, what theorems can be derived? This is, essentially, what's meant by "logical possibility", it's relative to whatever formal system you're using.

World Logic: Following Pierce, you might call this logica ens, logic itself. It's somewhat hazy but basically it's the logic of the world. It's related to logical consequence, but it's really about the underlying mathematical structure of the world which could be mapped to some specified logic. Sometimes you'll see logicians say something like "In a world governed by Intuintionistic logic, x, y, z would be the case". It's that, what actually follows from what in the actual world.

But logic certainly isn't just normative and to think so is contrary to most of the professional work done in mathematical logic. Sometimes I just want to explore the derivations of some logical consequence relationship. That does not entail I'm asserting we ought to in general reason according to the principles of the logic I'm exploring. That's just mistaking practical reasoning advice with a mathematical calculation.

But logic certainly isn't just normative and to think so is contrary to most of the professional work done in mathematical logic. — MindForged

I agree, but I can see how I might have given a different impression above. Charles Peirce, following his father Benjamin - one of the most accomplished American mathematicians of the 19th century - defined mathematics as the science of reasoning necessarily about hypothetical states of affairs. As such, it includes mathematical logic as distinct from and more fundamental than normative logic. However, deductively ascertaining the consequences of a particular set of postulates does not reveal anything about reality, unless those postulates turn out to be consistent with reality - something that we cannot properly investigate without normative logic.

Charles Peirce, following his father Benjamin - one of the most accomplished American mathematicians of the 19th century - defined mathematics as the science of reasoning necessarily about hypothetical states of affairs. As such, it includes mathematical logic as distinct from and more fundamental than normative logic

But I don't think that's right. If I take some arbitrary logical system and work out what follows from what in that system, I am not reasoning about hypothetical states of affairs. I'm simply investigating the properties of the relationship between particular abstract objects. I mean, just take fuzzy logic. I personally don't care for it, but if I were taking a look at the formalism and just did proofs for shits and giggles, that wouldn't be reasoning about hypothetical states of affairs because I don't think the idea of "fuzzy" states of affairs would be coherent in a metaphysics regarding the physical world. I'm just doing math at that point.

If you're defining logic principally as normative, that cannot include mathematical logic as it is easily possible to divorce that entirely from how one thinks one ought to reason. Reasoning can be made more rigorous by adopting a logical formalism, by adhering to a logic, but that doesn't mean the two are the same. Doing logic is not to pick out a type of reasoning as the correct kind.

Simple: Logic = correct reasoning, that's what it's about, period.

... that wouldn't be reasoning about hypothetical states of affairs because I don't think the idea of "fuzzy" states of affairs would be coherent in a metaphysics regarding the physical world. I'm just doing math at that point. — MindForged

That is precisely what Peirce and I mean by "hypothetical states of affairs" as the subject matter of pure mathematics - there is no connection (purported or otherwise) with reality as the subject matter of metaphysics.

Doing logic is not to pick out a type of reasoning as the correct kind. — MindForged

That depends entirely on what we mean by "doing logic."

That is precisely what Peirce and I mean by "hypothetical states of affairs" as the subject matter of pure mathematics - there is no connection (purported or otherwise) with reality as the subject matter of metaphysics. — aletheist

OK then I think referring to them as "states of affairs" is inappropriate then because that term is generally used to refer to various aspects of reality, not to the relations of abstract objects. It would sound very... queer to talk about the "state of affairs of the number 2".

That depends entirely on what we mean by "doing logic." — aletheist

Just doing logical derivations, exploring some specified consequence relation. Doesn't commit you to thinking the rules guiding those derivations ought to be the same rules you adhere to when you reason.

Good question. I have never had a clear idea of what people mean by normative, and looking up definitions doesn't seem to help. — andrewk

I would define a normative belief as one that directly justifies and urges or inhibits action or conduct. It says "You should do this," "This is the right way" or "That is the wrong way." A normative principle is a generalization of such beliefs. When I say "directly" I mean that the normative belief does not acquire its normative status in virtue of something else. It doesn't tell you that you should do this or that for reasons, because if there are other reasons, then they are in turn the source of normativity. Normative beliefs are where reasons bottom out.

The condition that a normative principle applies not just to oneself, but to everyone is a contingent, non-essential property of normative principles, I think. Normative principles are often, but not always universal. Moral relativists typically believe that the force of moral principles is limited to a particular culture or community. Jews believe that their religious strictures apply only to Jews (there are a few Biblical prescriptions applicable to gentiles as well, known as Noahide laws). Personal obligations and vows have force only for one particular person.

I realize that all this is somewhat vague and squishy, and will fray and crumble at the edges when subjected to scrutiny, as analytical philosophers especially like to do. But that just means that the concept of normativity is not simple, clean and sharp-edged, which is to be expected for a concept whose nature is psychosocial.