Induction and Science

It is true that you can make any inductive argument deductive by the use of arbitrary premises. This ultimately boils down to something stupid like:Premise 1: All known swans are white
Premise 2: Inductive logic leads to true conclusions.
Conclusion: All swans are whiteBut this doesn't undermine the argument that inductive logic is used in science. It just reasserts that deductive logic doesn't lead to conclusions that aren't contained in the premises that were chosen by the logician in question.Furthermore - if we agree that 'all inductive reasoning is deduction with unstated premises' then that still doesn't undermine the claim 'science uses inductive reasoning'. It means that it is equivalent to say that 'science uses deductive reasoning with unstated premises', not that the claim 'science does not use inductive reasoning' is true.

Might I suggest that your argument is therefore off topic? If something is falsifiable it means an example could arise that contradicts the conclusion. In a valid deductive argument this means we'd have to show a premise to be false:Premise 1: All swans are white.
Premise 2: X is a swan
Conclusion: X is whiteIf Premise 1 is falsifiable, it means that it is a statement that was made with incomplete information (basically by definition: it means some information could come to light that contradicts the premise). Premise 2 is a definition, so is not falsifiable. If Premise 1 is classed as a definition then by definition a black swan is not a swan and the argument is unfalsifiable.So there needs to be 'room' for wrongness, which implies a general statement was made from incomplete information that turns out to be false when further information is acquired. A1 isn't an axiom, it's a premise (assuming you are labeling A as an axiom) Your axioms here would be part of your definition of deductive reasoning, inescapable truths if you want to be saying anything at all using deduction, which you rightly don't state because it's a pain in the arse to state them all the time.Anyway, your Premise A1 would be something derived inductively by human beings observing yellow things and seeing that they are all square and deciding this was a general principle. It would be falsified by a single example of something yellow that is not a square.

But the axioms of deductive logic state that if the premises are true, the conclusion is necessarily true, as long as the deductive rules of inference are followed.The point was simply to point out that induction exists in the midst of your deductive arguments in the guise of premises if you have falsifiable deductive arguments. So even if you describe science in deductive mode - you still have induction as well. If you remove all induction completely, then you are not saying anything about the world whatsoever, and since science is about the world - you've ceased doing science and you are just doing logic. The premise needs to be falsified since the conclusion is necessarily true if the premise is (if it is valid deduction). In scientific deduction, the premises are inferred by inductive inference. Yes, this is logic, but it isn't science. Unless you have based your premise that the sun is pink empirically (which may well be true ). If you have done then the inducted form isP1: The Sun was yellow the last 10,000 times I looked at it
P2: The Sun has never been NOTyellow
C1: The Sun is always coloured yellow.Which forms the premise, P1AP1A: The sun is yellow
C1A: The sun is not greenThis then tells us something real about the actual world - which may be false. Right now it is night time, maybe by the time the sun rises next here it will have turned green. Maybe it is green right now. That makes it falsifiable and that's because of the induction behind the premise P1A. Then it wasn't anything to do with science. And the topic here is induction in science. If you've found resistance to your notions, you might well find it is because people think you are on topic when you aren't. But we're not making up rules of logic here, we're not creating a formal system. We're talking about an already existing one with already existing axioms. If you want to talk about your own logical system in which 'square things are yellow' is a necessary fundamental truth, you should start a thread on that.In your system of logic, the sun is square - since it is axiomatic that yellow things are 'square'. It doesn't mean anything because we have defined what 'yellow' or 'square' is other than if a thing has property 'yellow' it has property 'is square'. You made an error of logic I'm afraid. I said that one can create premises to make an inductive form argument a deductive one. I also pointed out that even if we accept your argument as true, it doesn't remove induction from science it just gives us another way of saying 'induction'. That doesn't mean that an inductive argument is a deduction with 'missing' premises.An inductive argument is one in which the conclusion does not necessarily follow from the premises. Sure - you can create premises out of thin air that necessarily lead to the conclusion (indeed - in some systems this is an axiom) in a deductive fashion - but then you've changed the argument.That's like saying all red cars are blue cars which I haven't sprayed blue. Sure, I can make any red car blue with enough blue paint, but it's kind of a stupid thing to go around saying, right? Of course we can change an argument, of course we can change the colour of cars, of course we can turn a poem into prose or prose into poetry. We could even make the argument that all invalid deductive arguments are valid deductive arguments with unstated premises that render them valid.So yes all X is Y after we change the things about X which differentiate it from Y.Since we're talking science - and not pure logic - we have to engage in induction at some point. You cannot deduce anything general about the empirical realm without some inductive logic, since we unavoidably can only work from specific experiences in empiricismEdited by Modulous, : No reason given.

For example? No, I would have said that if that is what I meant. I said your axiom was not an axiom used in scientific reasoning. No. I was pointing out that I was not saying what you thought I was saying. We haven't a choice, it seems. Yes, but then that would be inductive since the premises only support the conclusion with a certain degree of confidence (ie., there is some uncertainty). A deductive conclusion cannot begin 'if'. The correct argument isP1: Three Crowes wear black shoes
P2: All Crowes wear the same colour shoes
C: All Crowes wear black shoes.The reason we don't do this in science is because there is no evidence to support the empirical claim of P2. And if there were, unless it was complete evidence an inductive leap would need to be made. If Complete evidence were available no logic needed, the conclusion is observed to be true. We've gone from inductive reasoning to deductive reasoning. The reasoning has changed. I'm afraid we're stuck with invalid, silly, voodoo logic. As Hume said

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The bread, which I formerly eat, nourished me; that is, a body of such sensible qualities was, at that time, endued with such secret powers: but does it follow, that other bread must also nourish me at another time, and that like sensible qualities must always be attended with like secret powers? The consequence seems nowise necessary. At least, it must be acknowledged that there is here a consequence drawn by the mind; that there is a certain step taken; a process of thought, and an inference, which wants to be explained. These two propositions are far from being the same, I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects. I shall allow, if you please, that the one proposition may justly be inferred from the other: I know, in fact, that it always is inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connexion between these propositions is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.

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Stop deducing anything general about the empirical realm making use of inductive reasoning? Then we wouldn't be doing science, we'd be just be measuring things.Edited by Modulous, : clairified closing sentences.

OK - and what are you going to do with that premise that can say much about the world? It's the invalid silly voodoo logic. Philosophers have wrestled with it, decided it is 'technically' invalid logic, but that it's here to stay. Exactly. The premises must support the conclusion 100% in deduction. Since the conclusion is not supported 100% it is not a deductive argument. Conclusions are conditional on the the premises, not conditional statements themselves. A conditional statement 'if x then y' is itself a deductive argument or part of one, not a deductively derived conclusion. If Premise 1 is true and If Premise 2 is true then conclusion is true. That's deductive logic. If your conclusion has some conditional in it, this means a premise has been merged into the conclusion - which is misleading. Inductive logic can be perfectly honest. The conclusion is preceded with{Premises}
Therefore, with degree of support {p}
{Conclusion} What you said is fine, but it doesn't mean what I said was blatantly false. But your conclusion isn't a conclusion it is an argument. There is no change in the strength of the conclusion, they are exactly equivalent and the conclusion in each case necessarily follows from the premises - even if you choose to name your conclusions and premises 'apples' and 'bananas'.{AbE -
By adding conditionals explicitly in your wording - you aren't adding uncertainty, just redundancy. We can in fact appeal to a real axiom for this:

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Axiom of necessity
In a valid deductive argument, If the premises are true, the conclusion is necessarily true

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Conditionals are already built into the evaluation of a deductive argument, so writing them out is redundant and doesn't make the conclusion less certain than it already was.
} By inserting premises in - we've changed it from inductive reasoning to deductive reasoning. By definition, this is a change in reasoning. Yep. Unless you would assert that the statement, "Bread nourishes humans", is an unscientific conclusion - you must also accept that it is fine for science too. Whether we 'should' or not is hardly the point. We do. And what's more if you don't do it, you aren't doing science - you're just doing logic. No, it is whether it is intrinsically part of science. Which it is. Let me know when you can say something about the world 'now' with just 'observations' from then and deductions. If science is just re-ordering observations then, as I said, it is just about measuring things. This does not counter my assertion that it would just be measuring things. For all your championing deductive reasoning, and despite Hume's challenge, you've failed to provide the deductive reasoning that could lead to any scientific claim about the real world.Unless you move on and say 'these observations lead us tentatively to the conclusion that in general...with degree of support p' you aren't doing anything resembling science.Edited by Modulous, : No reason given.

If you'd rather not go down the rabbit hole of the previous post allow me to issue a challenge:Take any number observations you like as your premises.
Use only those axioms used regularly in the scientific method.
Make a scientific prediction using deduction.
You cannot make stuff up - all premises must be empirically true or tautologous.So, if your premise isAll humans are mortalYou would be asserting that you have observed the mortality of all humans.

Actually no - that's just empirical book keeping. For every action there is an equal and opposite reaction is not something that Newton observed. No - but it exists within science. Then you are now saying this is not an uncertain deduction? Then we agree. You had previously been talking about something else:

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degree of error/uncertainty in our conclusion that is related to the probability of our premises to support it

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Probability of premises to support the conclusion is not 100%, it is not deduction. It is precisely inductive logic in which the premises support, rather than necessitate 100%, the conclusion, with a potentially calculable degree of certainty. Deductive arguments say

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If...THEREFORE
or
if...THEN

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Inductive arguments say

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if...Therefore, with degree of support {p}
or
if, then with a certain level of confidence,

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If your Crowe argument is the latter - it is inductive not deductive. Where's the induction?

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all Crowes wear the same color shoes

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All Crowes? If this is possibly false then it must be inductively derived. The correct deduction should be:

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P1: Three Crowes wear black shoes.
P2: Some Crowes wear the same color shoes
c: P1 is an example of P2

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Takes the teeth out of it right? As I said - you can call premises 'bananas' and conclusions 'oranges' and wear a tutu if you like. It can be deceptive to confuse your current argument's premises and conclusions - leading to inadvertent logical fallacies. I was just pointing it out, not saying it altered the deduction. No, it is not. That was just a comment on form, to avoid potential confusion.The strength of the conclusion is part of the definition of a deductive argument: The necessity of the conclusion from the premises. As I said, adding 'if' is just redundant and does not 'weaken' the argument or its conclusion and does not add 'uncertainty' where there was once 'certainty'. I have no idea what Science is. I'm talking about the thing that scientists do, that makes them scientists...the science part. And that uses induction. I have supported it. It's fairly straight forward. Without induction all you have are a bunch of observations which you can play about with. You can saying nothing new about the world above and beyond those observations. You are just performing deductive logical exercises on a data set.Science takes data and infers knowledge from it using induction. Science doesn't stop at "Gravity has attracted masses that we've observed according to this relationship..." Sure. You have a bunch of observations recorded down. Now deduce something scientific. There's lots of science in the real world. Pick something you like, Show me the money. Not disputing that scientists rearrange their measures. But doing just that would not cover the pursuit of science, would it? Science makes predictions, develops general theories etc. I see no deductive reasoning, sorry. So yeah, specifics would be good.This:

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Newton observed some shit happening; saw it all happened in a certain way; assumed everything worked like the things he saw; concluded everything happened in that same certain way.

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Is induction, see: "assumed everything worked like the things he saw" - that's an induction. All conclusions are conditional on the premises that lead to them. In a deductive argument there is no uncertainty in this. The conclusion must be necessarily true because of the premises.This is different to the inductive argument where, if true, the premises only support the conclusion to a certain degree.This is essential in science because in science we have general laws and theories supported by non-general (ie., specific) observations.In science we cannot use the deduction
P1: All humans are mortal {we have not observed all humans}
P2: Mod is human
C: Mod is mortal.In science we'd be more in the position of having to say
P1: Every human that we have observed has died within 200 years
C1: This supports, tentatively the conclusion that all humans are mortal.
P2: We have observed Mod was a human
P3: We have observed that humans remain human until they die.
C2: (P3) gives support to the notion that all humans remain human until they die
C3: {C1}, {P2} and C2 support the conclusion, with a certain level of confidence that is not 100% "Mod is mortal." Yet you said:

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If only we admit to a degree of error/uncertainty in our conclusion that is related to the probability of our premises to support it

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So which is it: Do we have uncertainty or not? I argue that in the quote above, you are arguing for induction which is defined as having a certain degree of error related to the probability of our premises to support it. Only if the support is 100% (ie necessary) is it deductive.You asked why live in a world where premises do not necessitate the conclusion. In scientific deduction our premises have to be empirical claims. In order to make any general claim from specific empirical claims - induction has to come into it. There is no way to deduce from "Some pendulums act with the rule 'an action has an equal and opposite reaction'" to "Every action has an equal and opposite reaction" without making up stupid 'patch' premises that are not supported by evidence.You either be upfront about your voodoo induction, or you add voodoo premises. Either way, we're doing voodoo.Edited by Modulous, : No reason given.

It is not an axiom, it is a premise. It is a proposition you are using to support a conclusion, it is a premise. It is not being assumed true to see where it leads, it is not self-evident and it is not a universally accepted rule. Your argument certainly seems to be. But you seem to think you can say something about the world using deductive logic and observations. Here is what you came up with

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If Mod is human and if all humans are mortal

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I have to stop you right here. You have not observed that all humans are mortal. You can only use premises (and it is a premise even if you call it a banana (or a conclusion)) that you have observed or deduced from the given axioms.So, here is what we actually have so farP1: Mod is human
P2: Some humans are mortal
C: Mod might be mortal.We've hardly made a scientific prediction here have we? We predict that Mod might die? Great. Way to be unfalsifiable. If we play your game and say that your conclusion is

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If all humans are mortal, Mod is mortal.

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Then the only prediction we can make with this is again Mod might die.Try again, if you please.I will use inductive reasoning to make something closer to a scientific looking conclusion to show you how its done.P1: Every human that we have observed has died within 200 years of living
C1: This supports, tentatively the conclusion that all humans are mortal.
P2: We have observed Mod was a human
P3: We have observed that humans remain human until they die.
C2: (P3) gives support to the notion that all humans remain human until they die
C3: {C1}, {P2} and C2 support the conclusion, with a certain level of confidence that is not 100% "Mod is mortal."Prediction: Mod will die within 200 years.
Falsification: Mod survives to 201 years old.Edited by Modulous, : No reason given.

Hi Jon.
Let's simplify.In science we require evidence to support our conclusions. Our conclusions are general, our evidence specific. A general conclusion that is only supported to some degree by the premises (in science this is our observed evidence, we don't get to make shit up like 'all humans are mortal').Your 'conditional conclusions' are just ways of sneaking in the inductions. If there is no sneaky inductions, then your conditional conclusions are just set theory mathematics, not science which is about the real world not a hypothetical world were we have complete knowledge.In a deductive argument if the premises are true, the conclusion is necessarily true.This does not happen in science. We can never say a general conclusion is necessarily true unless we're just talking about maths or logic. There is always tentativity, there is always the possibility of an observation overturning our general laws.We're talking about real science, that makes real general laws, theories and conclusions about the real world based on a subset of evidential support. This is inductive. You might say that this is logically invalid - and we would all agree. But, as you say, it works and science is nothing if not pragmatic.You have failed to use deductions and observations to generate predictions, create general laws etc. Rather than argue incessantly over your unusual logical terminology - I take this failure as tentative support for my thesis that induction exists within science. For instance: Your conclusion could be worded as "If an inductive logic leads to a true condition here then it is necessarily also true that the sun will rise tomorrow". You've worded the argument so that this conclusion is necessarily true - but you've simply snuck the induction in under the table. You can try adding the word 'if' and bunging the proposition into the conclusion - but it still doesnt stop it being a premise to the deductive conclusion 'the sun will rise tomorrow'.I should also point out that the correct form isP1: The Sun rose today
P2: the Sun behaves the same on every day
P3: Tomorrow is a day
C: the Sun will rise tomorrowYou don't need lots of repetitions P1...Pn as you did unless you are trying to 'lend support' to P2, which would be induction. If this was a science paper - we'd have to say that P2 might be false, but it is supported by some evidence which gives us a certain confidence of its truth. This is science in the real world, Jon, not Platonic ideal empirical deductive rationalism or something. As nwr said:

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It is how philosophers claim that science works. But most philosophers do not actually do science,

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I'm talking about the actual doing of actual science - not the hypothetical ideal method of extracting absolute knowledge from an ideal data set.In real science as done by scientists not philosophers - our general conclusions can in principle be false even if all of our observations (premises) are true.You seem to think that science shouldn't make general statements from specifics and that doing this is 'sloppy'. This is nonsense. Your computer, your car, the Apollo rocket, the agriculture that provided your bread, all rely on this sloppy science. Indeed there is nothing that doesn't. You are stuck with it. Get used to it. Learn why it isn't as big a problem as you think it is. Read this - it is far from 'sloppy', even if it isn't logically valid. Ultimately, it does the job even if it cannot be proved that it should be able to the job.We're talking about the challenge of observations and saying anything about the world other than 'we made an observation'. You might observe some parent blackbirds feeding their child blackbirds. This is just an observation, it is not science. Nor is it science to rearrange this and say that some blackbird chicks are fed by some blackbird adults.It would be a scientific to say 'With some degree of support that is less than 100% - Blackbird parents care for their young"So - moving ourselves away from Platonic science and to actual science, Induction not only exists, but must be done if we're going to call it science rather than 'looking at something'. My argument trivial to prove false. Just show a single example of a predictive deductive argument that doesn't involve making stuff up. You have failed to do this. Everyone, in the history of the world since Hume first made the challenge has failed.Induction is with us as long as we don't make shit up to suit our purposes.Edited by Modulous, : No reason given.Edited by Modulous, : No reason given.

So you agree it was inductive, not deductive? That assumption is the assumption that induction works. That is: he assumed, based on a small set of 'some' would apply to 'all'. It says if the premises are true, the conclusion is. The only way to make an inductive argument deductive in science, is to insert 'induction works' as a premise, as you have time and again demonstrated. It just masks the induction. Indeed. But if we are arguing that the second premise is supported to some degree by a set of other premises (and not deductively necessitated by them), then you are still talking about an inductive leap. Sure you can make an inductive leap, and then construct a deductive argument but we're still taking the inductive leap part of science, not the deductive arguments you can make after the leap. You can't avoid the inductive leap. D-Newton either made up the claim that "that all stuff behaved the same" or he inductively concluded it. It's either not scientific, or it is induction in science. A scientific inductive argument spells out why the evidence supports the induction, mathematically calculates the degree of support the evidence gives and proposes further tests to increase the degree of support that exists for the claim. And that happens, which is why we're able to falsify inductions in science. Indeed - science is so anal about doing this that it says that if you can't do it - it isn't science. So if you explicitly agree that science uses induction and I will agree that you can insert inductively based premises to create a deductive argument and I think we're done.

Then get on topic. If you want to discuss science and induction then read my previous posts and let me know what you think within the context of the topic. I don't see any merit continuing to discuss how science uses induction with somebody, have them disagree with me, and then when their disagreements are addressed, have them turn round and tell me they weren't discussing induction within science. My counter claim is that in science, that induction will still be used, even if it is enclosed as a premise in a deductive argument. You've continuously demonstrated this with your examples - most notably was your D-Newton who explicitly used induction. The challenge for a falsifying counter-example remains open.I have never disagreed that you could turn an inductive argument into a deductive one by adding premises that meant the conclusion was necessary. I have continuously agreed with this. But in science, when we're talking about general laws and the like, the premises that you are going to be adding have that inductive quality to them, each time.Edited by Modulous, : No reason given.

This is a getting be a really boring rhetorical ploy. It could as easily be said that you deny the evidence of induction. ID proponents also make lots of denials about the evidence for evolution.What would be evidence of induction in science? If generating a general law, and supporting it with particular evidence is not sufficient - what would this evidence look like so that we might try and meet your challenge.Without knowing what you are looking for - this thread is doomed to repeat itself over and over again. If we can criticise what you are looking for - or give it to you, maybe that would give us a fresh angle before a moderator decides 600 posts is more than enough to put our best positions forward.

'Clearly refutes' is an unusual term - there are certainly papers in the scientific literature that disagree with Popper such as International Journal of Epidemiology 1998:27:543-548
Induction versus Popper: substance versus semantics, Sander Greenland, but clearly refuting something like Popper's opinions? Surely that would come down to a matter of opinion in its own right? The cited paper gives some perceived problems and areas of agreement with Popper, and that's all you are likely to get from an honest writer.But your former challenge is empty of content. I asked you, in a number of ways

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What would induction in science look like

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And your response is to take part of my formulation of my challenge 'What would be evidence of induction in science?' and try to answer that literally.But my overall question, the point of the words I wrote was to try to get you to tell me what would a clear use of induction look like? I have pointed at examples in peer reviewed work and you deny it is induction. So what would it look like so that I might try and find it in the literature.

But is it not a particular theorem that was derived from more general principles of geometry?

And if it is derived from the general principles of geometry then it does not serve as a falsifying example of the idea that deduction is deriving particulars from generals. I know, I've been arguing this for some time now, I'm glad to see you agree with this. That's why I think induction is central to science. What has this to do with the derivation of Pythagoras' Theorem?