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The problem with logic

Last updated on 20 Jan 2014

This is Spock, not me…

When teaching students critical reasoning it is an article of faith that we should teach them logic. Of course, we ameliorate any benefit this might have by teaching it incomprehensibly and in artificial cases. But still, we believe logic is what is most important in philosophy and in culture generally.

Ah, culture… in which someone who wishes to assert that a position is wrong says it is “illogical”, when of course they mean “unsound” or “badly founded”. Where logic is held to be, in shows ranging from Star Trek to Fringe, the antithesis of logic, despite Hume’s dictum: “Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them.” (Treatise p415).

So, what is logic good for? Does it prohibit certain conclusions as “irrational” or “illogical” in themselves? The answer is, of course, subtle and complex, but there is a simple enough answer: logic is for transferring the truth of your premises to the conclusion, and nothing is, in itself, irrational or illogical. So I put up a conundrum, a seeming paradox. Is logic truth achieving or not? Are views ever irrational? Let’s see…

In logic, a premise is an assumed starting point. It is a sentence that asserts or denies some state of affairs. Swearing, for example, when you hit your thumb with a hammer, can never be a premise. But the sentence, “I hit my thumb with the hammer” is a sentence that asserts some claim or state of affairs (I’ll get to that locution in a bit), and so it can be a premise. For example:

P1 – I hit my thumb with a hammer

P2 – If I hit my thumb with a hammer, I will swear

C – I swore.

From the truth of the first premise P1, and the truth of the conditional, or hypothetical, or counterfactual, sentence of P2, what I will do if P1 is true, I can conclude (or predict) that the conclusion C is true. Seems simple enough, right? Well in simple inferences (arguments, as they are called. In logic, an argument does not involve the passions!), it is. But get into a real world argument and things get a lot more troublesome.

The point of logic is that if you have true premises and your argument is logically correct, then the conclusion must be true, and you are irrational if you admit both that the premises are true and the argument is correct, but the conclusion is false. This is obvious on reflection. A rational person accepts these “sound” arguments as giving the truth. What Spock ought to have been saying all those episodes is that the reasoning he was objecting to was “irrational”.

Arguments, though, in themselves, are never true or false. They are at best valid (meaning, the logic is correct). And as the truth of the premises depends upon the agreement of the persons arguing (we sometimes call these agreed premises), it may be that a valid argument does not give you a true conclusion, because in fact the premises are not themselves true – they might be falsely thought to be true by both sides, or they may be vague, or they may be open to several interpretations. And here is a problem that I have encountered in philosophy.

Consider one of the most influential books on politics ever written: Robert Nozick’s Anarchy, State and Utopia (1974). Nozich begins with a main premise:

Individuals have rights and there are things no person or group may do to them (without violating their rights). [p ix]

and from this concludes

Taxation of earnings from labor is on a par with forced labor. Seizing the results of someone’s labor is equivalent to seizing hours from him and directing him to carry on various activities. [p169]

In effect, he argues, taxation is a form of slavery.

Now Nozick’s arguments are valid enough. He interprets each of his steps in a way that the conclusion is forced. But is it irrational of me to think that taxation is not slavery? I think it is not. I dispute several of Nozick’s interpretations. For a start, I do not think rights are natural or immutable. Moreover, I think that governments should be involved in setting up infrastructure, and paying for it from taxation. It all depends upon how you interprets “rights” and “government”. I mention this particular example because Nozick’s arguments developed into a foundation for what is now called “neo-liberalism” or “neo-conservatism”, and which has driven far too many governments to lessen taxes for the public good infrastructure in favour of a choice-driven “user-pays” model over the past 35 years. It supports, for example, the “austerity” model of economics.

Why has a good philosopher and logical reasoner comes to such a strange conclusion? In part it is because he uses logic as a tool for finding the truth without at any point stepping back to consider the real world implications. The arguments are valid, but the premises are not true, or are at best interpretable in various ways, only some of which lead to the conclusion (as a side note, Nozick relies on the “social contract” theory of the state, which is in my opinion, and it is a grounded but not obvious one, false: no society has ever been founded upon the tacit or explicit agreement of its members).

Consider the ways in which the religious are sometimes demonised (yes, that is an intended irony) as illogical or irrational:

Take for example, someone who was not born in an atheist home, or a religious home, free from even hearing about religion and coincidentally he made up none of his own. Then when this man hit 21 years of age he was exposed to our world of countless religions. This man has no connection to any religion in particular and he is asked to pick one or none of them. He would notice that they are all mutually exclusive, that is no two religions can be right. He would also not be able to determine which had any validity. All he could do was read the old religious scriptures, which unfortunately almost every religion has. You could say that he could judge validity based on the most popular religion, however would you base it on people alive or people dead? Really the most popular religion of all time would not necessarily be around today, though the consensus today would be that it was ridiculous and unbelievable. This being the case, it is illogical to be religious. If someone who has never been exposed to religion comes in when he is 21 (so his brain has developed enough to make a conscious decision) and cannot make a rational decision which religion is right, that means there is not enough logic behind religion to make it a rational decision. [From here]

The view that because there are no reasons (of a certain kind) to choose a particular religion, therefore religious belief is illogical, is a total non sequitur: it does not follow. For a start, one might challenge the view that those are the only reasons for choosing a religion (they are basically empiricist assumptions that only through observation and testing are beliefs rational or logical), which Hume’s dictum denies. Secondly, it requires a notion of “rational” that no real human ever can satisfy – everyone begins their reasonings with some values or sets of beliefs that they did not acquire through reasoning. And so on. [Note: I am not arguing that religion is the best conclusion here, as I clearly do not think it is. I am talking about reasoning, not religion.]

One way to guard against conclusions that are not themselves warranted just by reasoning is to do “reality checks” along the way. The more outlandish the conclusion, the more you must examine each and every premise, and all the alternatives to it, and here is where “being logical” and “being rational” are at their most vulnerable. For some premises, any conclusion can be shown to follow validly, and where premises are not themselves supposed to be founded upon empirical (that is, publicly verifiable) data, it can easily be logical to be a libertarian or a believer in fundamentalist religion or even a belieber.

Reasoning works best when both sides test their assumptions and defend them, and the logical aspect of the arguments become just the background methodology of the argument. It is, I consider, most rational to argue opposing views to the point where all the premises are well examined and interpreted, even if logic alone will not get a resolution. In the end, the only beliefs that are “logical” are those that rest upon logical validity, and that can be manufactured upon demand. And the only beliefs that are rational are those where the argument is valid and the premises are at least plausible to the arguers. If, as often happens, an impasse is reached, then as Wittgenstein wrote:

Where two principles really do meet which cannot be reconciled with one another, then each man declares the other a fool and an heretic. [On Certainty 611]


  1. To extend on Wittgenstein’s thought- after declaring each other fools they realize that war must be declared so that one principle is proven, all the while only proving both are fools. In practice this is how religious differences get settled.

  2. Robin Ford Robin Ford

    “Reasoning works best when both sides test their assumptions and defend them, and the logical aspect of the arguments become just the background methodology of the argument etc”
    This is essentially how our legal system operates but with the addition of a jury, judge or magistrate as a finder of “fact” (incontrovertible plausibility). Unfortunately the law is framed on precept not logical validity and sophistry often wins the day. This may also be the case in philosophy and science.

  3. In a normal argument, there are four positions, not two: what I think, what you think, what I think you think, and what you think I think. In my experience, simple disagreement, i.e. you say P and I say not P, is quite rare because we never find each other in the space of possible claims. Maybe that’s why violence sometimes follows arguments. I don’t know what you’re talking about and that can be irritating, but I can locate your chin. (and vice versa, of course)

    • After reading that I think you think there are only four positions. But after reading this perhaps if you think me confident of my persuasion then maybe you think I think you think that there may be more. But if I think you stubborn then I may actually still think you think the limit is four.

  4. Is logic really about thought, or is it rules for polite discussion?

  5. Perhaps we should use one of “illogical | irrational” to mean “anti-logical | un-logical” and the other as “non-logical”.

  6. Maybe income tax is tantamount to seizing hours of paid labour, but that itself is not tantamount to slavery. It just sounds close.

    In your example with the hammer & thumb you load the argument with reasonable premises, which is really unfair to logic per se. A valid argument goes: [1] If elephants rule Mars, only then does an ape write this blog. [2] An ape writes this blog. / [C] Elephants rule Mars.

  7. Nozick’s arguments … has driven far too many governments to lessen taxes for the public good infrastructure in favour of a choice-driven “user-pays” model over the past 35 years.

    A form of modus tollens.

    • Jonathan Jonathan

      I don’t think that these governments are applying modus tollens. I don’t know what premises Nozick formulates exactly, but it seems like slavery is part of the conclusion; it follows from the premises that taxation is slavery.

      This means that reducing taxes does not logically reduce slavery, because that would be fallacious, just as one cannot say that Wilkins is going to swear less if he never touches a hammer. It would be denying the antecedent. Wilkins might have other reasons to swear. If he never swears, however, you can be sure that he did not hit his thumb with a hammer.

      So modus tollens would be more like: “I see no slavery in this country, so there are no taxes here.” That is, assuming the conditional premises are true.

      • I mean Dr Wilkins is applying modus tollens.

  8. Jonathan Jonathan

    I’ve never agreed with the notion that religion is inherently irrational, although I do believe that most people mean something different when they talk about ‘rationality’ as opposed to ‘logic’. Rationality is often used for that which is reasonable in a broad sense; it is not reasonable to really believe in the flying spaghetti monster, but it could be reasonable to believe in God, or not, regardless of philosophical concerns. A way of saying: “You should grant me this belief even if you do not share it.”

    But what makes religions rational in a more formal sense, is their tendency to treat dogmas as logical premises and proceed from that accordingly. For example, I think the problems concerning the debate around the nature of the holy trinity a debate in which logic played an important part, perhaps even an example for later scholarship and science.

  9. The arguments are sound, but the premises are not true

    I assume you mean “valid”, not “sound”?

  10. Was the author of this going for a record in baseless assertions of simply the worst argument presenter ever? Nearly every reason given for disagreeing with logic and reason (oh the irony) was an assertion with no backing.

    Sorry buddy, you disagree with logic because you obviously don’t understand it.

    Here, learn a bit about logic before even attempting your next argument:

    • Jonathan Jonathan

      Where does the author disagree with logic?

      • Some people cannot read for sense past their own expectations.

    • Harry Harry


      Nearly every reason given for disagreeing with logic and reason (oh the irony) was an assertion with no backing.

      Firstly, he doesn’t disagree with logic. He is talking about the difference between the truth/falsity of premises, and the structural validity of arguments. Secondly, your statement is an assertion without backing. You’ve asserted some conclusion without pointing out exactly where he has gone wrong. The irony indeed.

      Also, this is where I get fucking snarky: your website is fucking shit. Please spam it elsewhere. Take as an example your “why logic is vital piece,” which is flat out fucking wrong, and fails to make the distinction between formal logic, and other types, especially inductive logic. There is research in philosophy of science that shows scientific reasoning is based on a formal fallacy (affirming the consequent, google it). So by your own ontological outlook, science is one giant fallacy. Now actual philosophers that aren’t sperglords typically don’t think this is much of a problem, as scientific reasoning is still useful just unlike formal logic (hence classifying it as inductive, abductive, and various other kinds).

      Also, goddamn I can’t stand humanist atheists who make inroads into areas typically under the domain of philosophy. Your site is like that, as is other various informal fallacies on the net e.g. that “your logical fallacy is” website, which is also fucking shit. Go read a book on informal logic, subscribe to actual informal logic journals, and stop being a fucking jackass who thinks that because he has read a bunch of informal fallacies on wikipedia, that makes him a scholar on logic. Notice how you jackasses always focus on the easy stuff. No where is there talk of nonclassical logics, modal logics, proof theory, model theory, probabilistic logic, or various other logics that demand a higher state of learning or rigor. There are no fucking formal proofs on your site, no semantic tableaux, no axiomatic proofs, no natural deduction, no sequent calculi. You and your ilk use natural language as your meta-language, and pretty much butcher it up anyway. It is disgraceful, and I wish you fucking idiots would shut the fuck up.

      • Ordinarily I would caution against intemperate language, but in this case I won’t…

  11. I cannot speak to the technical distinction between “illogical” and “irrational” as seen by professional philosophers, but in common language I think we think of logical vs illogical as referring to validity of argument and rational vs irrational as having a broader interpretation – so that it may in some contexts be considered rational to be illogical (in the sense of believing something whose negation is a logically valid consequence of other things we also believe – perhaps because none of those “beliefs” are absolutely certain and because the common idea of “logical” includes a Spockian level of certainty that meaningful propositions must be either true or false)

  12. John the Plumber John the Plumber

    You say John:

    “Logic is for transferring the truth of your premises to the conclusions.”

    Have I got it right then that, as a truth can only be a ‘best guess’ based on the knowledge of the day, we have only reason with which to gauge the validity of the premises before we can call the conclusion a ‘best guess’ logical truth?

    I f this is so, then it gives logic a time dimension beyond the simple – this premise and this premise then give that conclusion. We must constantly apply reason, checking all the way back down the line of past premises and conclusions before we make any final conclusion. We must also apply reason to past truths if we gain new knowledge.

    With this in mind, I puzzle at the reasoning behind some of evolution theory’s logic conclusions. – For instance:

    P1 – God made everything as it was and evermore shall be – unchanging.
    P2 – The fossil record shows a general pattern of change from simple to complex.
    C – Evolution makes life change.

    This added up in Darwin’s Day – but try updating P1 with today’s knowledge.

    P1 – The universe of randomly acting particles is expanding and there is no single stable point of reference – all is change.
    P2 – The fossil record shows a general pattern of change from simple to complex.
    C – Evolution makes life change.

    This doesn’t add up. There is too much change involved. If all is change, then life changes because everything is changing, end of tale. The conclusion, evolution, as it is currently understood, becomes somewhat surplus to requirements.

    The Vatican issued a statement a couple of years back that it accepts that evolution is the cause of change in life. Surely it is the nature of our all-changing universe which is the cause of change in life. Then logic or reason would say that evolution has some outcome beyond that.

  13. One problem with logic is the two assumptions. How much logic is based solely on two absolutely necessary premises?

    • Do you mean how much reasoning is based on two premises? Obviously almost nothing is. But arguments can be deconstructed into simple arguments with a major and a minor premise almost all the time. Of course, most logical formulations can have any number of premises.

  14. Roger Shrubber Roger Shrubber

    I’m confused by the reality check. How is it different than a prejudice check? Flawed premises and equivocal evolutions of meaning are common. Are your comments about teaching logic or about applied logic as we commonly use (are used by) it or towards the platonic ideal of logic? Where does logic end and “rhetoric” begin?

  15. Eridanus Eridanus

    the problem with the premises is that they can be only a part of reality, not the whole. So the premise and arguments of Robert Nozick are only a part of reality about the role of taxes in a society. The main question is that the “worker” Nozick mentions “can work so hard” because there is a social “order” that is feeding on taxes.

    That it is, it exists a government structure that is feeding on taxes and guaranties that this “individual hard worker” that hate to paytaxes could do his work with some relative security.

    Then, the “hard-worker” Nozick mentions as a model… works in some “stable environment”… because some other guys are working hard toguaranty him to be hard worker doing his job in peace.

    This is not the whole story of an implicit social contract. It is only a little part of it.

    The summation of all desires of individuals do not result in a betterment of the whole society as had been proved by some little catastrophes like the Crash of Wall Street in 1929, or the present economic crisis after the construction boom. Then, some social minorities, sometimes not more than ten or twelve persons, can produce with their wishes of personal greed a petite catastrophe by stumbling a nation, or half a planet, into a most severe crisis.

    Then, it is difficult to present a complete premise out of something as complex as a human society. Then, the arguments based only a limited set of premises have a high probability of being wrong. A partial set of premises do not necessarily represent the problem in its totality. So it is nearly impossible to apply “logic arguments” on such a limitedpart, or “if they are logic” they must be an “imperfect sample” of logic.

    In this sense, as John arguments, the word logic is used in disputes on arguments constantly. For we call logic probably to something that “looks logic”, but it is just a mere appearance, and not the real stuff of logic.

  16. Madhu Madhu

    There is implicit logic in forming a premise. Before a premise can be applied to an argument, it must itself be found to be internally sound. This is easily achieved by explicating the premise; one must extrapolate the implications. When all implications are found not to invalidate the premise internally, then it may be used in an argument. Rather than what the article implies, it seems to me that it is more logic which is needed, not less. Developing the implications of a premise, to test its inherent soundness, requires deep and thorough logic.

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