What you wrote sounded sensible, relevant and philosophical to me.

It is truly a moving poem. Perhaps in another thread, one day we could discuss the last verse, which apparently has troubled quite a few otherwise ardent fans over the years (myself included). But not here, 'cos it's off topic.

We sang a choral setting of the poem in a choir last year. It was really special.

Haven't worked out what I think about the issue of the OP yet, but I really enjoyed the homage in the last line to the most famous poem ever by a Canadian.

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?

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?

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.

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.

Who cares what he wrote? I dare say his mum does. I expect that, like most mums, she is proud of what her son has achieved. Getting on telly and having a book published without having to pay somebody to do it for you is something of an achievement, be the content what it may.

"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.

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'?

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.

About 20 some private initiatives to create nuclear fusion, LENR, and fission projects. Bill Gates is betting on fusion. — Posty McPostface

Fusion is a fiendishly difficult technical problem. When I attended a science summer school at Sydney Uni in 1978, everybody was talking about tokamaks and nuclear fusion as the holy grail of energy, and it seemed just around the corner.

Forty years later we are not significantly closer. It's still research labs playing around with tokamaks and hoping to one day generate enough power to replace the power needed to run the thing.

One day we'll crack the problem of scaled up fusion reactors and that'll be fantastic, but it won't be for a very long time. If fusion is the only hope against global warming then it'll be too late and we're all doomed.

Most of the effects are not chaotic. Some are. The creation of an individual hurricane is a chaotic effect but the increase in the expected number of hurricanes per year given one degree of warming is not.
Just internalising the non-chaotic effects should be enough to create a financial incentive towards renewables that is strong enough to ensure things don't get too bad. But I fear it may have been left too late.

My point is that the market is responding effectively — Posty

I don't think it's doing that unbidden. It's doing that because governments in Europe have made laws that try to internalise the externalities of fossil fuel power generation. It is that government action that has lead new coal-fired plants anywhere except in developing countries to be unfundable, because of the investment uncertainty that brings.

If it were not for government action in Europe, and the prospect that other developed countries like Canada, US and Australia may some day come to their senses and also internalise the externalities, new coal-fired plants would still be being built, and it would still be seen as the 'cheapest' solution (since we don't price the externalities).

I don't share your optimism by the way, but it is conceivable that you will be right, and I earnestly hope you are.

Be careful with saying you're not worried about climate change though. If things unfold as you suggest, affluent people in developed countries will generally be fine. But even with the warming currently regarded as inevitable - about 2 degrees C - people in Bangladesh and Pacific islands will still lose their homes to rising sea levels, enormous numbers of people in Africa will still die of drought-induced famine, and many will die from the advance of tropical diseases into sub-tropical areas. So we rich whiteys will be fine, even though we caused the problem, but poor people in developed countries will still pay the price for our greed.

I'm interested in what people think of the static problem on p21-22, of a beam supported at each end with a load in the middle. Norton says the limit case of a perfectly stiff beam is not consistent with the limit as stiffness approaches infinity of the cases with elastic beams. For finite stiffness the equation for the horizontal forces of the beam ends has a unique solution but for the infinitely stiff case it does not.

Maybe I'm misunderstanding, but I am not persuaded by this. The limit of the horizontal forces as the beam stiffness approaches infinity is zero and, that is the value that a first principles analysis of the infinitely stiff case gives us too. The load pushes downwards with force W on the beam and the ends of the beam push down on the supports with weight W/2 at each end. There is nothing in the system supplying any horizontal forces, so the horizontal forces are zero, which is equal to the limit of the finitely stiff cases.

What the lack of a unique solution to the equations for the infinitely stiff case tells us is that, in addition to providing vertical support, the supports could also push inwards against the beam or pull outwards on it, with any force at all, and the system would still remain static. That is not surprising, given the beam is infinitely stiff and hence infinitely resistant to both tension and compression. But in the absence of the system containing any elements that supply such lateral forces, the lateral force must be zero.

So I don't think this does supply the example Norton wants of a system where the behaviour in the limit is not equal to the limit of the behaviours close to the limit - which is what happens with the dome.

Not relevant to the problem, but I would have thought that, if we allow the application of lateral forces by the side supports different to the resistance to the natural lateral pull from the weight of the beam, then even in the finite elasticity cases those lateral forces can range over an interval. The more strongly they pull (push) the beam ends outwards (inwards), the less (more) the beam will sag. SO I'm not sure I can see any qualitative difference or discontinuity between the infinite and finite stiffness cases.

If that's right, then the only concrete example used to argue against the solution that suggests we should rule out the dome as an inadmissable idealisation because of the infinite curvature at the top, has failed. All that is left to argue against that solution is the second last paragraph on p21 that begins with 'It does not.' But I found that para rather a vague word salad and didn't feel that it contained any strong points. Indeed I'm not sure I understood what point he was trying to make in it. Perhaps somebody could help me with that.

I'm interested in the thoughts of others, whether they agree with Norton's or my analysis of the beam example, and whether the argument against ruling out inadmissible idealisations can stand without it.

One of the most thought-provoking posts I've read on here for quite a while! :up:

I think the confusion arises from the fact that most propositions implicitly implicit contain the words 'at <insert time proposition is stated>.' So the statement 'Bill is a bachelor', made in 2017 is actually 'Bill is a bachelor in 2017' whereas, when stated in 2020 it is 'Bill is a bachelor in 2020'.

The implicit time signature is not there in statements that explicitly quantify the time variable, such as 'Neville Chamberlain visited Munich in 1939' or 'Beethoven never married'.

If we apply the same discipline to uses of the word 'grue', of insisting on an explicit time signature as part of the proposition, wherever that makes sense, I think the anomalies that 'grue' is supposed to throw up disappear.

I agree, and so I would say that the bachelor statement is analytic (ie I would not use the 'negation is self-contradictory' definition of analytic).
But by the same reasoning the statement 7+5=12 is analytic, and Kant denied that it was.

Perhaps it's you and me against Kant. (Only on that issue. I think Kant's fabulous on many other issues)

I have nothing more to say other than language has defeated me once again. — Purple Pond

Say not 'the language has defeated me' but rather 'the language and I failed to reach an agreement'. Personally, I blame the language. :wink:

Saying the bachelor is married contradicts the definition. — Marchesk

A contradiction can be deduced from the statement together with additional axioms. But a contradiction cannot be deduced from the statement on its own, so it is not self-contradictory.

Take the definition of bachelor to be:

B is a bachelor at time t iff B has never married at any time <= t and B is adult at time t and B is human at time t and B is male at time t and B is alive at time t

We can deduce 'B is not married' from 'B has never married', but only by using an axiom that says that 'X has never been the case' entails 'X is not now the case'. Or in mathematical terms, that (x=y -> x<=y). That axiom is part of the Peano system of axioms for arithmetic, and is needed to complete the contradiction on the bachelor statement. So the statement is not self-contradictory because it requires additional axioms to reach a contradiction.

The trouble with that Britannica version is that 'self-contradictory' is not a defined term. It is not at all clear what it means. I think we can agree that A & ~A is self-contradictory. It is not so immediately clear that A & (B v ~A) & (~B v ~A) is self-contradictory, yet the proposition A & ~A can be deduced from it in a few steps.

We might say that a proposition is self-contradictory if a contradiction (statement of the form P & ~P) can be deduced from it without using any other non-logical axioms. But with that definition, very few statements would be self contradictory and, in particular, the statement 'This bachelor is married' would not be self-contradictory, even though the statement 'No bachelor is married' is used as a canonical example of an analytic truth.

The trouble is that the whole Analytic/Synthetic distinction is a hot mess of poorly defined terms, and attempts to tighten up the definitions just end up dissolving the whole problem.

thanks for that.

Given the clarification, it seems to me that if we assume that statement S: "There are no a priori synthetic truths" is true and known, then either it is

- analytic and known a priori; or
- analytic and known a posteriori; or
- synthetic and known a posteriori.

which seems to line up with your 1, 2, 3 (perhaps in a different order).

Like you, I think only the first one is feasible. To say one knows S to be true by mode 1, one would have to have a proof of it. Such a proof would be just a matter of selecting suitable premises and proceeding from there. I see no obstacle in principle to doing that. Kantians may object to some of the premises, but it wouldn't be philosophy if there wasn't an argument over premises.

The key point of interest is your suggestion that if S is true by virtue of 1 then the negation of S must be self-contradictory. Can you explain why you think that? Bear in mind that 'analytic' (in so far as it is defined at all, which is only very loosely and vaguely) is only a property of truths, not of propositions generally, so it doesn't mean anything to say that a proposition is 'analytically false'..

It sounds like you have proved that, if we assume there are no a priori synthetic truths then it follows, by proof by contradiction, that there are no a priori synthetic truths.

I must be missing something, because that doesn't sound like progress.

Perhaps you can clarify what it is that you are saying. For a start it's not clear what statement 'the statement' refers to in 1, 2 and 3.

It depends where you look it up. For instance the Oxford dictionary definition is in line with what I wrote above. But let's not debate definitions. I described my worldview. I don't regard it as nihilist and I strongly reject nihilism, as I use and understand that term. If, based on my worldview outline above, you assess that I am a nihilist according to your use and understanding of that term, that's fine. It just means we use slightly different languages. No two people in the world use exactly the same language.

Do you happen to be a nihilisitic relativist? — khaled

I am a relativist in most things, but not a nihilist.

For me the difference is that both relativists and nihilists agree that there is no absolute standard whereby the truth or the value of something can be determined. But the nihilist adopts a worldview whereby they decide that nothing is true for them and nothing has value for them. The non-nihilistic relativist accepts things as being of true and of value for them, but do not insist that they must be true and of value for everybody else. Of course in practice we can observe that most things that are accepted as true and of value for one of us seem to be true and of value for most of us, because the similarities of humans are vastly greater than their differences. But that's just an observation, not a deduction.

A good example of non-nihilistic relativism is in Tim Minchin's song "If I didn't Have you (I'd probably have somebody else)". He loves his partner not because he thinks she's the smartest, most beautiful, sexiest, funniest, kindest woman on the planet, but in spite of the fact that she isn't. He loves her because she's his partner, and because she loves him.

Another example is a thoughtful, passionate fan of a football team. An example in Australia is a public intellectual Waleed Aly, who is a devoted fan of Richmond football team. He doesn't claim they're the best, or the bravest, or the coolest team in the world, and that's not why he barracks for them so ardently. He does it because they're his team, and he can acknowledge that it makes perfect sense for other people to be just as passionate about their teams. Just as Tim Minchin reckons it's reasonable for other people to prefer their life partners to his.

Far from being a nihilist, I am passionate about my politics, my ethics, my spirituality, my worldview and my aesthetic tastes. The fact that I can respect that other people may quite reasonably have different tastes, and that I don't think that mine are in any absolute sense the 'right ones' or the 'best', in no way detracts from the passion I have for mine.

Doesn't it extend to self contradictory conclusions? Because you'd have to accept the premise "Self contradictory conclusions are false" for you to say they are and there is no reason to do so. — khaled

'False' is a concept of semantics, not logic. We need to be clear whether we're discussing logic or semantics. Semantics is about interpretations of logic, and is not logic itself.

An analog in logic to your statement "Self contradictory conclusions are false" would be the Rule of Inference that exists in Classical Logic, either as a rule of inference (eg in Natural Deduction the rule is Proof by Contradiction) or implicit from other rules (eg in a Hilbert System).

If one doesn't want to use that rule, one needs to use another form of logic. I think that's what Intuitionist Logic is.

Alternatively, one can explore Paraconsistent Logics, as Graham Priest does.

Essentially, accepting (the logical equivalent of) your statement "Self contradictory conclusions are false" is simply a choice of type of logic.

The price paid to use those other logics is that they have much less power than Classical Logic, and cannot prove many things that people intuitively feel very strongly to be the case.

Naturally there can be no logical basis on which to make that choice, as the decision is pre-logical. We cannot use logic to decide which logic to use because we haven't yet got a logic to use.

But there is a reason we accept the statement in the sense of an explanation, rather than a logical proof. That explanation is that we cannot do otherwise. We are creatures that evolved to accept that statement and we cannot successfully go against our intrinsic nature.

The reason we accept it is that, like Martin Luther, we cannot do otherwise (Ich kann nicht anders).

This is why I said I expected people to try to refute P4 — khaled

If the conclusion is that, for any given conclusion that is not self-contradictory, we can always adopt some premises from which it can be deduced, then that's just basic logic, and not subject to controversy at all. I don't see why anybody would seek to refute that. I'm not sure it would even count as philosophy.

I didn't read all the responses closely, but I didn't get the sense that anybody was silly enough to try to refute that unremarkable observation about the nature of logical systems.

it was intended to demonstrate P6 — khaled

I don't know what P6 means.

One can know that a statement is true long before ever knowing why and/or how they've come to believe it. — creativesoul

I think so too

We need more additional premises than those two, to deduce ~(3+3=6). For a start we need 6<>9 and 7+2=9. We will also probably need some commutative and associative rules. So there'll be quite a few premises. But yes, given any false arithmetical statement that is not self-contradictory in the underlying language, one can make up a consistent little logical theory, not including all of arithmetic, of which that statement is a theorem.

I've lost track of what that example was intended to demonstrate though.

I don't think what an eighteen-month old knows is anything like as philosophical as that. My guess is that what they know is that you make the 'cup' noise when you want to draw attention to a thing that looks like what's over there. It's a game, a language game.

It isn't consistent because from P1 we can prove that 3+3=6, which contradicts the deduction that ~(3+3=6).

are you saying that the main reason we construct logical theories is because they are useful and relevant to our lives? — khaled

That's why I construct them, and I suspect it's the reason for most other people as well. In the end though, I can only speak for myself.

Arbitrary premise -> arbitrary logic
No it's
Arbitrary "life impact" -> arbitrary premise -> arbitrary logic

I don't know what role the word 'arbitrary' is playing here. It doesn't seem to fit. I either take premises that are observations or beliefs that are relevant to an actual situation I care about, or that are hypotheses and beliefs about a hypothetical situation I am interested in. I don't see how arbitrariness has anything to do with this, unless one were to say that what I care about, am interested in, observe or believe is arbitrary, in which case I'd say 'I don't see that as arbitrary but I don't mind if somebody else wants to say it is'.

C1: Every premise is true if the right premises are used to determine it's truth value
C2: Every conclusion is valid if the right premises are used to determine it's truth value — khaled

These are too vaguely stated to know what they mean.

I'm guessing that by C1 you mean 'For any proposition P, we can find a set of premises from which that proposition follows'. That gets us nowhere however, because P is a premise from which P follows, and so is ((1=1) -> P).

Further it is vulnerable to inconsistency unless we exclude propositions that are self-contradictory. For example, would you be happy to apply it to the proposition P:'0<>0'?

Certainly for any non-self-contradicting proposition we can construct a logical theory in which it is true. But that doesn't mean that theory is useful, or has any relevance to our lives.

The only way to disprove this argument is to do what P3 is.... — khaled

It's best to avoid saying things like this. Unless the argument is presented in formal logic, with the rule of inference used to justify each step clearly stated (eg 'Modus Tollens on lines 4 and 5'), it is easily invalidated, simply by pointing out that no formal justification has been provided for one or more of the steps. Breaking up a verbal attempt at persuasion into numbered lines does not constitute a formal proof.

Where's the self-deception though? I don't necessarily disagree with anything else you've said here. I just don't see how any of it amounts to self-deception.

Again, the motivation is not given, it is created. It need not be a long-term goal. It can be very mundane goals. — schopenhauer1

I am not disputing that. What I am questioning is what support you have for the belief that everybody is deceiving themself. I don't think the average animal-loving vet student has an opinion, or cares, whether their goal is given or created. They just want to achieve it. The same goes for short-term mundane goals like 'I want to go for a bike ride'.

I want to go ride my bike now for half an hour or so. And I will. Do you believe I am deceiving myself? How so?

The deception is believing the goals are anything but self-imposed — schopenhauer1

You can only speak for yourself here. Maybe you feel you are deceiving yourself, but you can have no idea whether others are. Neither can I or anybody else.

My opinion is that a young person who loves animals, dreams of being a vet and studies really hard to qualify to enter the vet degree at uni, then works really hard in the aim of getting into a really good vet practice, is not deceiving themself at all. They dearly want something, and they strive to achieve that something.

It's that they place value on goals in the first place — schopenhauer1

How can that be a deception? It is not a proposition, and only propositions can be deceptions. People either value things because they can't help but do so or they choose to value them. Either way, there is no proposition, so no scope for a deception.

Are you suggesting that people tell themselves they value a particular goal, when they don't really? That would be a self-deception, but how could we ever guess whether somebody was doing that?

Since meaning is subjective, how can one lie about it?

In any case, I doubt that many people do say to themselves that there is something more meaningful to their goals than the value they place upon them. I can't know what other people say in their heads, but it seems to me that would be a strange thing to say.

I cannot know what the difference is, as I have never been a bird, and have only ever been one human out of many billions. I see no reason to suppose that either birds or humans are lying to themselves about their feelings.

I don't know what you mean by a 'determined reason'. How does that differ from an ordinary reason?

I am also don't see any reason to suppose that people conjure preferences. At least in my case, a preference is something that I just become aware of, rather than setting out to manufacture one. I don't know what it is like for others.