Logical Approach to Scientific Theories/Laws

The manner in which scientific hypotheses are arrived at is illogical. Wrote this a few weeks ago on facebook, not sure how well written it is, and I'm going to refuse to read back through it. Its all pretty basic stuff. ~Hume's Riddle of Induction

Let H represent the hypothesis, and let I represent the test implications. The testing of an hypothesis looks something like this:
H->I (If "H" were true and the situation was like this, then "I" would be true)
I or ~I ("I" either happens or it doesn't, not "I")

In the case that "I" is false, and what you thought would be the result didn't happen, then the conclusion that deductively follows is ~H (not "H" or your hypothesis was wrong). This structure of argument is valid and also called Modus Tollens argument form.

In the case that "I" is true, the commonly arrived at conclusion is that H is true (or that your hypothesis is correct). Unfortunately that leaves us with the deductive fallacy of affirming the consequent, and an invalid argument.

Though in reality it isn't necessarily that simple, "H" is accompanied with numerous other auxiliary hypotheses which you also assume (we'll represent them as "A1&A2&...&An"). Also, the "I" is really representing another conditional "if my circumstances hold, then this event will occur" (we'll represent this as "C->E").

The new arguments structure looks something like this:

(H & (A1 & A2 & ... & An)) -> (C -> E) for simplistic sake i'll simplify this now...

(H & ((A1 & A2 & ... & An) & C)) -> E
E or ~E

In the case of not E, then any one more more of the hypothesis, the auxiliary, and the circumstances (H, An, C) were not the case. And in the case of E, commonly you would accept your hypothesis, affirming the consequent once again.

To explain why affirming the consequent is bad logic: If it rains, i'll get wet. I got wet. It rained. (well it rained, or you just took a shower, etc.)

Back to the subject, why in the case of science is this also bad logic? If you attempt to understand the positive results inductively, affirming that the positive conclusion follows, you have to assume the PUN (Principle of Uniformity in Nature, that is that "the future will be like the past"). The problem with the PUN is that the logic be it, cannot be understood deductively nor even inductively. It follows:

"In my experience, past instances of the future have turned out to be like the past instances of their pasts"
assume the PUN "the future will be like the past"
conclude the PUN "..."

This is completely ridiculous and makes the entire claim ridiculous because its just begging the question also called circular reasoning. So, the logic for justifying an already skeptical inductive maneuver is circular reasoning. The PUN is the logical equivalent of a PNN (Principle of Non-uniformity in Nature). The only difference is, people who believe in the PNN are termed crazy (saying the world will end tomorrow, etc.), but really they have as much logical basis for that statement as anyone else saying something like "all copper conducts electricity, gravity, the sun will rise, even that the next step I take an abyss won't open up under me that i'll fall in, etc."

What?

As much as I'm aware of, H -> I simply means H -> I; it has nothing to do with either ~H -> ~I or I -> H.

The assumption is a far cry.

The law of detachment is the first form of deductive reasoning. A single conditional statement is made, and then a hypothesis (P) is stated. The conclusion (Q) is deduced from the hypothesis and the statement.

However, if the conclusion (Q) is given instead of the hypothesis (P) then there is no valid conclusion.

Validity requirement for deductive reasoning compels Q -> P to be necessarily true (not "commonly arrived"), which is nowhere implied in P -> Q.
And why are we bringing "commonly arrived" into a "scientific" approach to hypotheses?

What exactly are you trying to convey? It seems to me you're saying that it's ridiculous to arrive at the above two conclusions given P -> Q (which, by the way, is a big DUH) and somehow brand that mode of thinking the "scientific" name.

Modus tollens works because of the validity of P -> Q, Q has to happen if P is true, thus if Q is false, either P -> Q is false (invalidity, but we already compels the validity, therefore excluding this case) or P is false (unsoundness).

I misinterpreted your initial statement. If I have grasped the intent of the OP correctly, then you are arguing that achieving results stated in a hypothesis do not necessarily lead to the hypothesis being true. Conditions in the hypothesis could be fulfilled by another mechanism or means of action that utilize the same reactants and conditions provided in the experimental setup. Take the following example:

It is crucial to consider the surrounding environment when choosing an appropriate buffer for a given solution. Strong monoprotic molecules such as hydrogen chloride and potassium hydroxide are not able to function as buffers in moderate pH solutions such as water. A weak acid such as potassium biphthalate is a more ideal buffer as its pH range is more acclimated for equilibrium with respect to the aforementioned aqueous environment. Due to its nature to maintain equilibrium in moderate solutions, the buffering region of potassium biphthalate should be a pH that is close to 7 as it is gradually titrated with .5M KOH, a strong monoprotic base in increments of .5 mL.

Potassium biphthalate functions as a buffering reagent in a number of biological solutions as it is able to both accept and release hydrogen protons with relative ease. When it functions under its ideal conditions, it prevents major fluctuations in pH as it serves as an intermediate process that slows down the reduction and aggregation of hydrogen ions and hydroxyl ions respectively as monoprotic base is added to the solution. Obtaining data that indicates a buffering pH of 6.9 may or may not necessarily prove the hypothesis to be true, despite satisfying the proposed requirements. It is possible that the use of distilled water could have led to the water itself being of lower pH due to the incorporation of carbon dioxide in the liquid to form carbonic acid, therefore leading to the base being neutralized by the presence of acid. A number of other conditions such as temperature and molecular solvents could also play some role in affecting a given titration on a biological solution. These caveats are taken into consideration as scientists themselves remain at odds with the potential gap between hypothesis and results. Scientists are keen to distinguish between in vivo and in vitro testing conditions and often emphasize that the discrepancy between the two is incomprehensible when it comes to the publication of their studies. Many models remain rudimentary when it comes to exploring new areas. However most models that are depended on today are not based on singular hypothesis, but rather an aggregate of hypotheses which are termed theories. In addition to consider the significance of human coincidence, experimental procedure is outlined thoroughly and practiced by peers to confirm the causality between the two factors. Science is a field that is constantly revised and modified. Even though an incorrect explanation may be initially accepted on the causality between x and y, additional experiments and discussion should gradually mete out inconsistencies and reveal the truth. After all, the structure of the atom went through numerous revisions from plum pudding to Niehls Bohr in which the study literally progressed from from structure to mechanics.

I think you're misrepresenting how the hypothesis and implications are related.

The hypothesis is not part of the logical statement - it is the logical statement itself.
Hypothesis: (P -> Q)
This hypothesis (P -> Q) is either true or false. You test it experimentally by producing P and seeing if Q occurs. The hypothesis is correct if for all states of P (true/false), the results Q fit.

If it turns out P & ~Q can be achieved, this hypothesis is wrong. If only P & Q, or ~P & ~Q, or ~P & Q, are possible, then the hypothesis is correct.

You "prove" the hypothesis by demonstrating that (P -> Q) is always true. Someone disproves it by demonstrating a case where P->Q is false.

By the way, this is known as Hume's Riddle of Induction, I'll edit the original to include this citation.

What?

As much as I'm aware of, H -> I simply means H -> I; it has nothing to do with either ~H -> ~I or I -> H.

The assumption is a far cry.


Validity requirement for deductive reasoning compels Q -> P to be necessarily true (not "commonly arrived"), which is nowhere implied in P -> Q.
And why are we bringing "commonly arrived" into a "scientific" approach to hypotheses?

What exactly are you trying to convey? It seems to me you're saying that it's ridiculous to arrive at the above two conclusions given P -> Q (which, by the way, is a big DUH) and somehow brand that mode of thinking the "scientific" name.

Modus tollens works because of the validity of P -> Q, Q has to happen if P is true, thus if Q is false, either P -> Q is false (invalidity, but we already compels the validity, therefore excluding this case) or P is false (unsoundness).

I'll suppose you understood the beginning part, since it takes little knowledge of formal logic to see. In the case that the expected event "e" occurs, it doesn't affirm that the hypothesis is correct, unless through induction which i explained later on. If "~E" that doesn't necessarily lead one to believe the hypothesis is false, but it could be one of the auxiliary hypotheses leading to the falsity or the circumstances.

I misinterpreted your initial statement. If I have grasped the intent of the OP correctly, then you are arguing that achieving results stated in a hypothesis do not necessarily lead to the hypothesis being true. Conditions in the hypothesis could be fulfilled by another mechanism or means of action that utilize the same reactants and conditions provided in the experimental setup. Take the following example:



Potassium biphthalate functions as a buffering reagent in a number of biological solutions as it is able to both accept and release hydrogen protons with relative ease. When it functions under its ideal conditions, it prevents major fluctuations in pH as it serves as an intermediate process that slows down the reduction and aggregation of hydrogen ions and hydroxyl ions respectively as monoprotic base is added to the solution. Obtaining data that indicates a buffering pH of 6.9 may or may not necessarily prove the hypothesis to be true, despite satisfying the proposed requirements. It is possible that the use of distilled water could have led to the water itself being of lower pH due to the incorporation of carbon dioxide in the liquid to form carbonic acid, therefore leading to the base being neutralized by the presence of acid. A number of other conditions such as temperature and molecular solvents could also play some role in affecting a given titration on a biological solution. These caveats are taken into consideration as scientists themselves remain at odds with the potential gap between hypothesis and results. Scientists are keen to distinguish between in vivo and in vitro testing conditions and often emphasize that the discrepancy between the two is incomprehensible when it comes to the publication of their studies. Many models remain rudimentary when it comes to exploring new areas. However most models that are depended on today are not based on singular hypothesis, but rather an aggregate of hypotheses which are termed theories. In addition to consider the significance of human coincidence, experimental procedure is outlined thoroughly and practiced by peers to confirm the causality between the two factors. Science is a field that is constantly revised and modified. Even though an incorrect explanation may be initially accepted on the causality between x and y, additional experiments and discussion should gradually mete out inconsistencies and reveal the truth. After all, the structure of the atom went through numerous revisions from plum pudding to Niehls Bohr in which the study literally progressed from from structure to mechanics.

Yes, but they cannot hope to include and monitor all auxiliary hypotheses, I can imagine there are some things scientists do not even know that could be affecting experiments. It's naive to think there are not unknown A's which could affect scientific outcomes. Its also funny you mentioned the structure of the atom, that raises other questions such as the observable and unobservable, and how those play into the formulation of laws, and how exactly scientific laws should be interpreted.

I think you're misrepresenting how the hypothesis and implications are related.

The hypothesis is not part of the logical statement - it is the logical statement itself.
Hypothesis: (P -> Q)
This hypothesis (P -> Q) is either true or false. You test it experimentally by producing P and seeing if Q occurs. The hypothesis is correct if for all states of P (true/false), the results Q fit.

If it turns out P & ~Q can be achieved, this hypothesis is wrong. If only P & Q, or ~P & ~Q, or ~P & Q, are possible, then the hypothesis is correct.

You "prove" the hypothesis by demonstrating that (P -> Q) is always true. Someone disproves it by demonstrating a case where P->Q is false.

The hypothesis is not the test, the hypothesis for example is "all copper conducts electricity" so the first premise would be "if copper conducts electricity, then this piece of copper will conduct" (H -> I), you do the test and the implication then occurs or doesn't occur "this copper conducts electricity" (I or ~I), then a conclusion of sorts should follow (inductively or deductively depending on the result) "so, all copper conducts electricity". The hypothesis is simply a statement to be tested.

As you can see, you are testing for all the copper conducting electricity using a single piece of copper (or thousands, millions, etc.) even if you use inductive reasoning to arrive at the conclusion you are assuming that this piece of copper and all those in the past will be like the ones in the future. Thus, there is the problem of the PUN, which is problematic which I've already discussed.

In the case that the expected event "e" occurs, it doesn't affirm that the hypothesis is correct, unless through induction which i explained later on. If "~E" that doesn't necessarily lead one to believe the hypothesis is false, but it could be one of the auxiliary hypotheses leading to the falsity or the circumstances.

E, F and E -> F are entirely different things. E occurring has nothing to do with whether or not E -> F is a valid hypothesis, F occurring has no bearing on whether or not E occurs, E -> F being valid does not dictate anything about E or F without one of the two being bound down to a particular state.

What do you mean by E occurrence "affirming" the correctness of the hypothesis? Where is that even coming from?

E, F and E -> F are entirely different things. E occurring has nothing to do with whether or not E -> F is a valid hypothesis, F occurring has no bearing on whether or not E occurs, E -> F being valid does not dictate anything about E or F without one of the two being bound down to a particular state.

What do you mean by E occurrence "affirming" the correctness of the hypothesis? Where is that even coming from?

I think we may be saying the same thing.

The simpler form proposed for scientific testing is:

H -> I (if H, then I)
I or ~I (either the implications the hypothesis stipulates occur or don't occur)
-------
In the case of ~I, it is deductively valid to say ~H is the case, but as I expressed later on in my initial post, it isn't just H, but various other auxiliary hypothesis and the circumstances
In the case of I, it is deductively invalid to affirm H, possibly inductively, which I comment about towards the end of my post.

I think we may be saying the same thing.

The simpler form proposed for scientific testing is:

H -> I (if H, then I)
I or ~I (either the implications the hypothesis stipulates occur or don't occur)
-------
In the case of ~I, it is deductively valid to say ~H is the case, but as I expressed later on in my initial post, it isn't just H, but various other auxiliary hypothesis and the circumstances
In the case of I, it is deductively invalid to affirm H, possibly inductively, which I comment about towards the end of my post.

And what is the point? That what you claimed is anything more than common sense? Perhaps something "scientific"?
A conclusion is arrived at logically through what is known. An alligator will sprout flowers if all is known about it is that it is green (and all green things sprout).
Whether or not the hypothesis is true is another problem. Our curve of hypothesis and the curve of "ultimate truth" barely touch each other as we move closer to the truth via gaining more and more knowledge/information. There is no absolute denying that we're all just dreamers and a God is laughing at our science and truth some place under a tree, but this is as far as we can get, with what we are given. I would call that pretty damned logical.

And what is the point? That what you claimed is anything more than common sense? Perhaps something "scientific"?

You haven't read the whole thing, if you had, you wouldn't be asking that question since I state it pretty explicitly. Eventually, if this discussion progresses we'll get to "which are the scientific regularities we should track and generalize on" (-Goodman)

The hypothesis is not the test, the hypothesis for example is "all copper conducts electricity" so the first premise would be "if copper conducts electricity, then this piece of copper will conduct" (H -> I), you do the test and the implication then occurs or doesn't occur "this copper conducts electricity" (I or ~I), then a conclusion of sorts should follow (inductively or deductively depending on the result) "so, all copper conducts electricity". The hypothesis is simply a statement to be tested.

As you can see, you are testing for all the copper conducting electricity using a single piece of copper (or thousands, millions, etc.) even if you use inductive reasoning to arrive at the conclusion you are assuming that this piece of copper and all those in the past will be like the ones in the future. Thus, there is the problem of the PUN, which is problematic which I've already discussed.

It's not problematic, you just state it as a requirement.
E: This is copper.
P: The universe continues to operate under the same rules as it always has.
I: This conducts electricity.

(E & P) -> I

If the universe does change in the future, then this hypothesis will still be correct, it just won't be useful anymore.


You could probably cut down P to some specifics - but it's implicit in any scientific work that it only holds true while all necessary conditions exist, including the consistency of the universal laws.

You haven't read the whole thing, if you had, you wouldn't be asking that question since I state it pretty explicitly. Eventually, if this discussion progresses we'll get to "which are the scientific regularities we should track and generalize on" (-Goodman)

Why would things changing make anything illogical? Deductions are built upon previously available information, going from what is known to what else can be known is in itself logic. That tomorrow won't be different from today is not a truth, but a condition necessary for any further reasoning to be built upon. Denying it is denying the "truth" behind the hypotheses, not necessarily their logicality. You can say all scientific hypotheses are wrong (just maybe not today) but to claim it to be illogical is beyond me.
A deductive argument can be valid without being sound.

It's not problematic, you just state it as a requirement.
E: This is copper.
P: The universe continues to operate under the same rules as it always has.
I: This conducts electricity.

(E & P) -> I

If the universe does change in the future, then this hypothesis will still be correct, it just won't be useful anymore.


You could probably cut down P to some specifics - but it's implicit in any scientific work that it only holds true while all necessary conditions exist, including the consistency of the universal laws.

First, I don't understand the structuring of your argument, I see a premise but wheres the rest. And why are you affirming that the universe will be like the past, that's circular reasoning.

Just a guess, but it seems to me your E & P is just an alteration to the hypothesis, "all copper conducts electricity," (this is copper, and under the basis that pieces of copper in the past have conducted, this one too will conduct) assuming what applies to the last piece will apply to this one, in which case you're saying the same thing as me. And it must necessarily follow that when you construct the entire experiment logically you arrive at the same structure I have already presented. Or maybe you need to elaborate a little more on your structuring.

Why would things changing make anything illogical? Deductions are built upon previously available information, going from what is known to what else can be known is in itself logic. That tomorrow won't be different from today is not a truth, but a condition necessary for any further reasoning to be built upon. Denying it is denying the "truth" behind the hypotheses, not necessarily their logicality. You can say all scientific hypotheses are wrong (just maybe not today) but to claim it to be illogical is beyond me.

Well, this isn't deduction we're talking about, it's induction (since we are affirming the consequence under your given presuppositions). I'm questioning how we can rationally accept any hypotheses as true, yes. It is illogical in the sense of deduction, it is bad logic to assume the PUN b/c it is the logical equivalent to employ the PNN.

It is illogical in the sense of deduction

If anything, it IS logical in the sense of deduction. Inductive reasoning allows room for the conclusion to be false where all premises are true whereas deduction does not.

If anything, it IS logical in the sense of deduction. Inductive reasoning allows room for the conclusion to be false where all premises are true whereas deduction does not.

In the case of ~E, in the case of E, its affirming the consequent (in the case of positive test results with your hypothesis, b/c you want to say and it is often said that your hypothesis is true if your experiment is positive). Inductively, as I've said, it isn't considered affirming the consequent and valid, but as I've said it raises a whole new set of problems dealing with the PUN justification.

Your justification for why its logical in the sense of deduction is that inductive reasoning allows... Those two statements don't coincide b/c deductive reasoning and inductive reasoning are not the same, and the same rules don't apply.

In the case of ~E, in the case of E, its affirming the consequent (in the case of positive test results with your hypothesis, b/c you want to say and it is often said that your hypothesis is true if your experiment is positive). Inductively, as I've said, it isn't considered affirming the consequent and valid, but as I've said it raises a whole new set of problems dealing with the PUN justification.

Your justification for why its logical in the sense of deduction is that inductive reasoning allows... Those two statements don't coincide b/c deductive reasoning and inductive reasoning are not the same, and the same rules don't apply.

It is not deductively logical because of whatever happening to inductive reasoning; they were in two separate sentences, conveying two different ideas. This is just as basic as language can get.
Assuming PUN is deductively logical because that is how the entirety of logic functions.
Bringing inductive reasoning into the picture only helped contrast (and thus make prominent) that idea, since inductive reasoning's tolerance towards invalidity most likely looks "illogical" (true premises -> untrue conclusions), thus helping color the logicality where validity is guaranteed.

And just because a result is true does not mean one is compelled to affirm the consequence. You're pulling it out of nowhere:

In the case that "I" is true, the commonly arrived at conclusion is that H is true (or that your hypothesis is correct).

Who even does this?

First, I don't understand the structuring of your argument, I see a premise but wheres the rest. And why are you affirming that the universe will be like the past, that's circular reasoning.

Just a guess, but it seems to me your E & P is just an alteration to the hypothesis, "all copper conducts electricity," (this is copper, and under the basis that pieces of copper in the past have conducted, this one too will conduct) assuming what applies to the last piece will apply to this one, in which case you're saying the same thing as me.

E & I are the hypothesis "all copper conducts electricity", that is E: it is copper, I: it conducts eletricity. (E implies I) is the same hypothesis, "if it is copper then it conducts electricity" is a direct equivalent to "all copper conducts electricity".

The statement could be written logically, with C "is copper", E "conducts electricity"
∀x: C(x) ⇒ E(x)
If your statement means something else, then could you state it in logical format like this.

And it must necessarily follow that when you construct the entire experiment logically you arrive at the same structure I have already presented. Or maybe you need to elaborate a little more on your structuring.

I don't know why you're so sure your structure is correct. I disagree with how it's set up.

When you're testing
∀x: C(x) ⇒ E(x)

You construct a table of pairs.

x	C(x)	E(x)	C(x) ⇒ E(x)
copper wire	T	T	T
rubber	F	F	T
gold	F	T	T
Item X	T	F	F

To disprove the statement, you would need to find item X.

It is not deductively logical because of whatever happening to inductive reasoning, they were in two separate sentences, conveying two different ideas. This is just as basic as language can get.
Assuming PUN is deductively logical because that is how the entirety of logic functions.
Bringing inductive reasoning into the picture only helped contrast (and thus make prominent) that idea, since inductive reasoning's tolerance towards invalidity most likely looks "illogical" (true premises -> untrue conclusions), thus helping color the logicality where validity is guaranteed.

And just because a result is true does not mean one is compelled to affirm the consequence. You're pulling it out of nowhere:

Who even does this?

The PUN is circular reasoning:

Say you have, "In my experience, past instances of the future have turned out to be like the past instances of their pasts" and you want to conclude the PUN. The missing premise to complete the syllogism has to be the PUN. So to conclude the PUN you have to use the PUN as the 2nd premise.

The induction occurs within the experiment syllogism, when the experiment turns out positive in terms of the hypothesis. The PUN does the opposite of what you're saying, it further scrutinizes what justification we have for performing the induction.

Science does this, look at the example I've used copper conducts electricity, the experiments in the past have been "positive" and as a result copper is regarded as a conductor. I'm saying, under what basis can we hold that as a theory/law, certainly the PUN coupled with inductive reasoning weakens the generalization.

E & I are the hypothesis "all copper conducts electricity", that is E: it is copper, I: it conducts eletricity. (E implies I) is the same hypothesis, "if it is copper then it conducts electricity" is a direct equivalent to "all copper conducts electricity".

The statement could be written logically, with C "is copper", E "conducts electricity"
∀x: C(x) ⇒ E(x)
If your statement means something else, then could you state it in logical format like this.



I don't know why you're so sure your structure is correct. I disagree with how it's set up.

When you're testing
∀x: C(x) ⇒ E(x)

You construct a table of pairs.

x	C(x)	E(x)	C(x) ⇒ E(x)
copper wire	T	T	T
rubber	F	F	T
gold	F	T	T
Item X	T	F	F

To disprove the statement, you would need to find item X.

Yeh, truth table, whatever you'd like to do in its application I suppose, there are also trees and other methods that do the same thing.

That isn't an argument though, that is an expression. I see where I may have caused confusion, this is using a hypothesis (your expression) with test implications "I" to yield a theory/law or not. I didn't think to carefully when I titled this, it should be something along the lines of Scientific theories/laws (maybe i'll try to change it). The intention of what was written is still the same, its funny because I titled it on facebook with theories/laws, but not on this.

Edit: changed title

I don't think it's fair to say that it's "illogical", in any case. When really the only logical leap made is a relatively minor one: assuming that induction works in general, because it's never failed.

Personally, I think the law of large numbers is the most telling argument in favour of induction:
Just because you don't know something is true or false, does not mean the two are equally likely.
If I claim that I've flipped 10 coins, and the result was 10 heads, it's quite proper for you to be more skeptical than if I claim that it was 4 tails and 6 heads. Probabilistically speaking, of all the outcomes after flipping 10 coins, it takes a greater amount of "faith" to believe in the least likely proposition.
In order for the universe to suddenly change, and make induction invalid, it would have to go against every scientific test to this date - every attempt to predict the future that progressed successfully. The odds of that happening at the exact moment of your test, give that it has never happened before should be considered miniscule, and thus not cause for great concern.

If you like, you could break down the universe into smaller and smaller components of time, see that the same laws have governed each of these forward progressions - and the closer you get, the more it defies probability that in the next tiny unit of time, it'll go against all history and do something new. When you have 10^40 observations to the affirmative, and none to the negative, it's fair to say your next observation is more likely to also be affirmative.