## Is logic undoubtable? What can we know for certain?

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• 3.3k
:smile:
• 23
Yes, indeed. Logic defines relations of elements, not elements themselves. You asked me how could logic be invalid but I ask you: why couldn’t it?
The validity of statements always depends on the premises, if I say, for example, that killing is right, and Bob killed John, then Bob did right, ok? Logic cannot define elements, just relations of elements, but, how can we prove right or wrong, if we can, those relations? I know I sound redundant and tautologic but is the validity of logic itself ”knowable”? Can we use logic on logic?
I hope you understand my question, I know it’s a bit odd and that I am not the best ad asking it.
• 23
Well, that’s a good point, and also brings me to the question: since thinking anything relies on logic, how can we think logic? It would be like building an house on another house built on... what exactly? Since we cannot do without logic, is it an absolute truth or rather an instrument relative to the human mind? If it is the latter, since we are fallible and limited, shouldn’it be so?
The fruit of an apple tree cannot be an orange
• 232
Say the subject reports believing some business is located in certain location relative to their home and they draw a map of how to get there. They believe the locations are correct....

As far as I can see, there is no actual contradictory state of affairs in this example. There is the computer and it's program. There are various maps which are drawn differently, and there is the person who drew the maps. None of this is contradictory, is it?

Now, the reason I said "sort of" is because this isn't necessarily a physical contradiction because this is about ones knowledge

Is it right that the idea is that the contradiction lies in what the person who drew the maps believes? That is, he believes both A and Not A. If so, I don't think the example really works. The content of my beliefs is contradictory, but there is still no actual state of affairs that is incoherent, is there? Let's try to make this clear. If you have found a case (instantiated in the real world) where the law of non-contradiction is false, then there must be some proposition you can state, about the world, which is both contradictory and true. What would that be?

That's not really explaining what you mean though. Is conceivability defined in terms of consistency? If so, it's question begging for the LNC. If conceivability is defined in terms of mental pictures, that's not going to work since lots of actual states of affairs cannot be pictured and mathematics has it's own notion of conceivability (basically deduction).

What I had in mind is simple imaginability. If it is at least humanly possible to actually imagine what things would be like if P, then I take it that P is intelligible. I am tempted to think that the mental pictures idea is a little crude, but let's run with it. What's wrong with the mental pictures definition? You say lots of states of affairs cannot be pictured. Could you give an example? I should note that the picturing need not be absolutely precise. I can't really mentally picture what the atoms which compose my laptop are like, but I can at least picture billiard balls interacting in certain ways, and perhaps picture billiard balls that have smaller parts that produce certain effects. I can picture that much, and I know that the atoms in my laptop are a bit like that.

As to the point about mathematics, I don't see why it is relevant. Let mathematicians define conceivability however they like for their purposes - I have no objection. But that they define it one way does not show that there is anything wrong with defining it another way for some other purpose than mathematics.

I suppose my view is just this. When it comes to thinking about the empirical world, if no human being can picture, even in simplified form, what the world would be like if P, then we can have no idea what it would mean for P to be true. In such a situation, we find something (NotP) indubitable - something which cannot be doubted because we have no idea what it even means to doubt it. I don't think there are many of these indubitable truths. There might even be only one of them; the law of non-contradiction.

PA
• 649
Or are you asking the switch to be an inconsistent physical object?

Yes, that's the scenario that is unintelligible.

Mental maps (and beliefs) are abstract representations of the world. We know that representations can be mistaken or inconsistent. But the maps are not the territory.

If we encountered a physical switch that seemed to be both on and off at the same time, we would want an explanation for what was really going on.

This is the case with QM where it seems like the switch is both on and off when you're not looking (due to observed interference effects).
• 762
Is it right that the idea is that the contradiction lies in what the person who drew the maps believes? That is, he believes both A and Not A. If so, I don't think the example really works. The content of my beliefs is contradictory, but there is still no actual state of affairs that is incoherent, is there?

Mental maps (and beliefs) are abstract representations of the world. We know that representations can be mistaken or inconsistent. But the maps are not the territory.

States if affairs or physical objects cannot be either coherent or incoherent. It is beliefs, mental maps, or what have you, that can have such a quality as coherency.
• 20
Logic is sometimes a stable way to go. Except for things like...
Stealing money (\$5) from parents for food when I was 8 years old.
Logical, I was hungry and there was the coin jar filled with coins and now I could eat.
Emotionally it is bad because people worked for it and it’s wrong.
So...do I just not take the money due to emotion instead of logically needing to eat?
It’s a tough question to answer.
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As far as I can see, there is no actual contradictory state of affairs in this example. There is the computer and it's program. There are various maps which are drawn differently, and there is the person who drew the maps. None of this is contradictory, is it?

The person's set of beliefs are, and beliefs are part of the mind. This would make minds the sort of objects that can have contradictory properties, no?

The content of my beliefs is contradictory, but there is still no actual state of affairs that is incoherent, is there? Let's try to make this clear. If you have found a case (instantiated in the real world) where the law of non-contradiction is false, then there must be some proposition you can state, about the world, which is both contradictory and true. What would that be?

Are your beliefs not part of the world? It would seem strange to regard one's set of beliefs as a fundamentally different type of collection than other sets. Whether dualist or otherwise.

What's wrong with the mental pictures definition? You say lots of states of affairs cannot be pictured. Could you give an example? I should note that the picturing need not be absolutely precise. I can't really mentally picture what the atoms which compose my laptop are like, but I can at least picture billiard balls interacting in certain ways, and perhaps picture billiard balls that have smaller parts that produce certain effects. I can picture that much, and I know that the atoms in my laptop are a bit like that.

I think you're trying to have it both ways here. You say it need not be precise but then what you're saying implies some unimaginable things can still exist despite not being properly conceived of. Conceiving of a useful alternate picture isn't really conceiving of the thing itself, just an analogue that suffices for some explanations but fails others. Examples could include any example of unobservables in scinetific theories, fields, geometric objects that are of infinite size (like a Euclidean plane), huge distances (can one really picture the expanse between Earth and the Sun???), etc.

As to the point about mathematics, I don't see why it is relevant. Let mathematicians define conceivability however they like for their purposes - I have no objection. But that they define it one way does not show that there is anything wrong with defining it another way for some other purpose than mathematics.

Well the point is there's no real way (even in principle) to conceive of nearly anything large or strange in mathematics. Infinite sets? Nope. Or just large numbers, even (say 10^10^10 amount of anything at all, totally indistinguishable pictorally from 10^10^11 of something else). Or weird algebraic objects like groups or rings. Conceivability in math is really about have a way to construct or prove things about these objects by means of formally established rules of proof. The mental picturing theory just can't work for anything outside of everyday finite counting and even then it hits a limit. To me conceivability needs to include this otherwise it's fundamentally incomplete a view, so the inconsistent objects do make it on if standard mathematics does.
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Yes, that's the scenario that is unintelligible.

Then in that case I don't think it can exist. As I said, i doubt inconsistent physical objects can exist (though I'm unclear how to regard the mind), but this seems distinct from the abstract objects I mentioned previously.
• 5.3k
Logic defines relations of elements, not elements themselves.

But...

names, variables, and so on can be given an interpretation. So logic does define its elements.

As is validity.

The validity of a logical argument refers to whether or not the conclusion follows logically from the premises, i.e., whether it is possible to deduce the conclusion from the premises and the allowable syllogisms of the logical system being used. If it is possible to do so, the argument is said to be valid; otherwise it is invalid. (Wolfram mathworld)

...of the logical system being used. My bolding. Logic defines validity.
• 23
I think we might have a bit of problem because of the language differences, but what defines logic?
If logic defines validity, what defines logic? Experience of events maybe? I still can't get it, how do we understand that logic is valid?
• 5.3k
how do we understand that logic is valid?

Because sorting out what is valid and what is not valid is what logic does.
• 13

I suppose where ever it is not supported by empiricism, as ultimately even mathematics is merely theory/philosophy in the language of math until it can be proven as applicable to reality. We know 1+1=2 because of all the situations we have observed where this is true; not because we figured it out logically. True we may have come to the conclusion using logic-- but logic that is based on empiricism and must be shown to be empirically true before it can be considered as logically sound AND true in practice.

Ultimately logic in itself does not prove truth, valid logic does. This is why in math class we are expected to show our work--to prove our conclusions are not only correct but were reached following valid logic and not merely by luck. Logic is only universal if it can be empirically shown.
• 13

Whose logic? Suppose my logic tells me differently than yours, thus leaving us in a situation where we both claim logic but do not agree? If logic establishes validity shouldn't our logic align as say our senses of sight and touch often do when we agree on the color and firmness of a rock? It seems that disagreements on objective reality presupposes invalid logic on one end or the other unless truth and validity are meaningless.

The sheer fact of having to show your logic to prove it brings it into the realm of empiricism--in that you are making your logic experienceable to another being using written or spoken media--in my opinion. Unobservable logic from you is nothing more than thought to me, so how can you prove your logic as valid without providing the experience of proof of it's validity?

What separates logic from opinion? (Hint validity)

In a nutshell I am saying that sorting out what is valid from what is invalid is what PROOF does, and something being logical to either you or me does not constitute proof that our logic is based on valid premises, or we would never have different conclusions on a matter such as whether logic can deduce the facts of reality from that which is untrue.
• 5.3k
Suppose my logic tells me differently than yours,

For example...
• 763
Whose logic? Suppose my logic tells me differently than yours, thus leaving us in a situation where we both claim logic but do not agree?

Then you're using a different logic and will have to determine which logic is to be applied. But outside very deep disagreements in technical math and philosophy the difference in what arguments are considered valid aren't going to have an impact in everyday life. Classical logicians and constructivist logicians are going to agree on basically everything outside mathematical logic discussions, for example.

If logic establishes validity shouldn't our logic align as say our senses of sight and touch often do when we agree on the color and firmness of a rock? It seems that disagreements on objective reality presupposes invalid logic on one end or the other unless truth and validity are meaningless.

Um, a logic establishes the validity of an argument given a set of axioms and inference rules, it says nothing of our experience in the world being correct or not. If I see a color and say it looks more red than orange, and my brother says it looks more orange than red, we have surely not therefore made a fundamental disagreement about logic.
• 23
Yes, yes indeed, that's the core of my question, we cannot rely on logic to prove logic valid, so what do we do? We "trust" it because experience suggests its validity?
Yet experience may not always be reliable, not to mention that experience itself may not exist.
You say that logic determines validity but remember that if a camera is broken the photographs too will be flawed.
I "trust" logic, Syllogistic logic on top, and I understand that without logic we can't really think, so taking out logic isn't really gonna get us far, not to mention that, technically, the only answer to my question would need to be illogical, since saving logic with logic is tautologic (it is like saying "that it is because it is") but I'd reject an illogical answer.
• 5.3k
we cannot rely on logic to prove logic valid,

I think you are missing something extraordinary. Not just validity, but proof, is dependent on logic. Logic is the structure of validity and proof.

Even your doubting logic assumes a logical structure.
• 649
States if affairs or physical objects cannot be either coherent or incoherent.

The switch being on and off is an example of an inconsistent state of affairs. The SEP entry for States of Affairs gives the example of Paul's having squared the circle.

Also paraconsistent logicians accept or at least consider the existence of inconsistent physical objects.

What kinds of objects are we considering (only mathematical objects or do we include physical objects as well)?
...
[Priest's] proposal seems to be committed to ‘inconsistent objects’ in the physical world: the objects to which our inconsistent but true physical theories refer.
...
Whether the world is indeed ‘inconsistent’ — assuming there is a sensible formulation of this claim — is something we would rather be agnostic about. Just as empiricists (such as van Fraassen [van Fraassen, 1980]) are agnostic about the existence of unobservable
entities in science, we are agnostic about the existence of true contradictions in nature.
— Paraconsistent Logics and Paraconsistency - da Costa, Krause, Bueno
• 762
What separates logic from opinion? (Hint validity)

As @MindForged already told you, you are misusing the term "validity." A valid conclusion is a conclusion that is reached by following (some) rules of logic. Logic itself cannot be valid or invalid.
• 2.5k
We know 1+1=2 because of all the situations we have observed where this is true;
All this runs deeper than casual thinking can get to. We may well "know" that 1+1=2 from observation. But that leaves a problem with "know" that Hume excavated. That is, we observe it.

Very well then, we observe it; all we get from that is the observation that at a certain time and place it was observed that 1 apple (or sheep - whatever) plus 1 apple equals 2 apples. The observation doesn't tell us anything about next time. So what, in this context, does "know" mean?

To solve this, you develop logic; you invent it. And you work it in such a way that its conclusions are certain. In itself and by itself it is useless. But then you might notice that arithmetic conforms to your logic, and logic conforms to your arithmetic. You work on that and find that the two mirror and reflect each other to the extent that the certainty of the one translates to the other. Voila! Now you know 1+1=2.

but logic that is based on empiricism and must be shown to be empirically true before it can be considered as logically sound AND true in practice.
In consideration of the above, no. And by the way, a "logic that is based on empiricism" is an oxymoron: it is just no logic at all. Empiricism is just that, empiricism. To call it logic is akin to creationists calling creationism a science. Attempting with a word to claim assets and a status to which it is not entitled.
• 762
The switch being on and off is an example of an inconsistent state of affairs. The SEP entry for States of Affairs gives the example of Paul's having squared the circle.

Also paraconsistent logicians accept or at least consider the existence of inconsistent physical objects.

See, we can say what it means for a sentence (for example) to be inconsistent. I don't think it is possible to say what it means for an object or a state of affairs to be inconsistent - without looping back to the language that we use to describe that object/state of affairs. So yes, you can sort of attribute inconsistency to things, but that attribution will be parasitic upon language, thought, reason. Of course, things and talk of things are hard to separate anyway, except that if we are realist to any extent, we accept that there is a one-to-many relationship between them. That is, there is one thing, but our relationship to it is through thinking/talking about it, and there can be more than one way to do the latter - including dialetheic ways.

Take the superposition state in quantum mechanics, for example. One way to talk about it is through the use of the quantum mechanical formalism, and there is nothing inconsistent about that - it's just straightforward linear algebra. But sometimes people feel that the mathematical formalism doesn't give us the feel, the intuitive understanding of what the thing is, and they try to accommodate it in more familiar, human-scale classical terms. Or they are actually committed to the view that, at least for macroscopic things like cats, such terms should always apply, quantum formalism be damned. One way or another, they can end up talking about the superposition state using a deliberately inconsistent model. Does it make the subject of their description itself inconsistent? Yes, as long as they are talking about it in that particular way, and with the understanding that the inconsistency awes itself to that particular conceptualization.
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And by the way........

A tip of the pointy hat from the back of the room.
• 649
See, we can say what it means for a sentence (for example) to be inconsistent. I don't think it is possible to say what it means for an object or a state of affairs to be inconsistent - without looping back to the language that we use to describe that object/state of affairs. So yes, you can sort of attribute inconsistency to things, but that attribution will be parasitic upon language, thought, reason.

That seems equally true when attributing any state to things, such as that the switch is on. Do switches really have state or is that just a conceptual projection by humans onto a world that has no intrinsic structure?

Of course, things and talk of things are hard to separate anyway, except that if we are realist to any extent, we accept that there is a one-to-many relationship between them. That is, there is one thing, but our relationship to it is through thinking/talking about it, and there can be more than one way to do the latter - including dialetheic ways.

Yes, though dialetheic realism would seem unintelligible. It's worth noting that Aristotle's main version of the LNC was about the nature of the world and not propositions (i.e., it is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect [Metaph IV 3 1005b19–20]).

One way or another, they can end up talking about the superposition state using a deliberately inconsistent model. Does it make the subject of their description itself inconsistent? Yes, as long as they are talking about it in that particular way, and with the understanding that the inconsistency awes itself to that particular conceptualization.

Do you mean the person-on-the-street's mistaken intuitions about QM? Even if so, people don't usually think of themselves as referring to their own conceptual models. The subject of ordinary discourse, as with physics discourse, is the world itself (albeit with the understanding that claims are provisional).

Conversely, Bohr's famous quote may be apt here: "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature."
• 13
Logic requires total impartiality, are humans capable of this?
• 13
I haven't figured out how to quote yet, and there were many replies.

First, I recognize I was using the word validity wrong, my mistake. I was using validity as a reference to the truth of the basis of one's logic-- not whether the conclusion matched the stated axioms. I'm a rookie.

However, if validity does not equate to truth, what good is it to say a conclusion is logical? That may well be true, but if the conclusion (or axioms) are false then what good is the logic? As the classic example: all cows are purple, Socrates was a cow, therefore Socrates was purple is valid logic, but untrue and irrelevent to reality. This is why I had a bit of terminology mix-up.

Color was a bad example (which was why it was coupled with the firmness of the rock and not a stand alone example).

Suppose maybe we disagreed about whether a rock would break a certain window. What amount of logic will conclude this disagreement? We can discuss our logic til the cows come home--but only throwing a rock against that window will settle the debate because my experience of windows may be different than yours after only experiencing bulletproof glass or what have you while you are referencing regular glass windows.

Tim wood, I follow you right up to the invention of logic. Without your empirical observations you never had a need or how to invent it, so you haven't disconnected them.

I'm not in doubt of the quality of good logic, I'm in doubt of how a person knows they have good logic. I simply posit that it must be put to the test or it is just a theory.

Touche on logic to interpret (and project) your experience--It just seems that something's amiss when you use logic to interpret your experience when it is experience that both grants you the ability to logic and is the basis you use as proof of your logic's truth.

Surely you see the danger of both interpreting now and projecting in the future with the same tool--if not I will inform you--that your present (possibly incorrect) perception is now your basis for claims of both reality now and reality tomorrow, and your incorrect notions today will affect what patterns you both look for and perceive tomorrow, resulting in possible affirmation of fouled logic. This is why one (or all) must prove their perceptions are true to know that their logic represents truth.

While empiricism may be a method of forming logical conclusions it must be distinguished from simple logical arguments (such as the purple cow Socrates) which have no bearing on reality. Thus we have empiricism not being the same as just logic. One can make all sorts of clever arguments with logic alone, empiricism can (at least attempt to) weed out both untrue axioms and conclusions (neither cows nor Socrates are purple--though there may have been a cow named Socrates).

Validity is one thing, but philosophy is the love of wisdom, not the love of validity. Wisdom in my opinion equates to truth of claims, not validity of logic (which seems to only equate to a clever argument). Don't get me wrong, I do like a clever argument, and it does take wisdom to create one--but I prefer that the conclusions are true in regard to things I am going to form beliefs around.
• 232
The person's set of beliefs are, and beliefs are part of the mind. This would make minds the sort of objects that can have contradictory properties, no?

Not at all. Is my bedroom contradictory because it has a red pillow and a different not red pillow in it? The pillows/beliefs are distinct objects. It would be different if there were 1 belief that was both P and -P, but there is no such case.

PA
• 763
That's not comparable. Separate pillows are not the same object nor are they logical negations of each other. Beliefs of a single person at a specific point of time are part of the same set of beliefs (not the same belief, that's not what I said) and that set can contain inconsistencies.
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