Isn’t Logic Great?
Who doesn’t like logic? We idolize Sherlock Holmes’ ability to solve mysteries by “eliminating the impossible.” In arguments with friends, we try to prove we’re right using logic, rather than intuition or emotions. And we especially enjoy pointing out others’ logical fallacies–preferably using latin terms.
Don’t pat yourself on the back just yet. Finding logical fallacies is actually much less impressive than you might think. That’s because in the real world, all arguments violate the principles of formal logic.
Yes, perhaps every logical argument you have ever encountered was flawed.
What Is Logic?
What is logic anyways? Logic, or specifically Deductive Reasoning, is the process of using several true statements (premises) to demonstrate that another statement (the conclusion) is true. In theory, logic can help you reach profound conclusions, by compounding an unlimited number of premises. That’s why it appeals to so many rational thinkers. However, logic only works for theoretical or philosophical matters. Real life is filled with uncertainty, and that uncertainty prevents logic from working.
Don’t believe us? Here’s a simple challenge. Try to craft a useful logical argument–i.e. one in which all the premises and assumptions are true, and they combine through the rules of logic to form a useful conclusion. It’s much harder than you’d think, as the following example will illustrate.
Certainty in an Uncertain World
Let’s see how Wikipedia struggles with this challenge. Here is their attempt at a textbook example of logic:
- If it is raining, then there are clouds in the sky.
- There are no clouds in the sky.
- Thus, it is not raining.
This is a very simple logical argument, which seems practical enough. But there’s a catch. In the real world no premise is 100% true. In this example, they tried to provide premises that are certain, but still managed to fail: Rain without clouds is rare, but it can happen.
Since this premise does not apply 100% of the time, the argument is not sound. This fallacy of claiming a certain conclusion from uncertain premises is called “Appeal to Probability,” and can be found in virtually any non-hypothetical logical argument.
At this point you’re probably thinking that it’s no big deal. The premises are near certain, so the conclusion is near certain, and that’s more than enough for practical purposes. However, although this may work for simplified examples like the one above, that is rarely the case with real-world issues. We don’t need advanced reasoning to predict rain from clouds; we need it to solve tough, complex problems. Now imagine what happens when you try to build a practical logical argument in a discussion on public health, international conflicts, or immigration.
The Health Care Debate
Let’s illustrate this by picking a recent opinion piece from The New York Times, which tries to build an argument against the Affordable Care Act.
The basic points were:
- If government increases free-market competition among insurers, insurance prices will be lower.
- When prices are lower, more Americans buy their own insurance.
- If more Americans buy insurance, more will be covered.
- It is good to have more Americans covered by health insurance.
- Therefore, we should abolish the ACA.
While the conclusion may be correct, it is not due to the deduction above. Let’s examine the first two premises, which are both incredibly complex and uncertain.
- Is it true that increasing free-market competition always results in lower prices?
- Does healthcare really behave like a commodity?
- Why do countries with no free-market competition have lower health costs than the US? Are health services in those countries better or worse than in the US?
- If prices were to go down, would the coverage be equivalent?
- What about unintended consequences? For example, if doctors focus on quantity over quality then small problems might turn into large problems, which would ultimately raise the cost of care.
- Would more Americans really buy their own insurance if prices were lower? People often don’t make rational economic decisions.
- Would having non-mandatory (but cheaper) insurance result in more coverage than under a mandatory system?
Compounding Uncertainty
There are many more such questions, and each can be further broken down into smaller questions. On issues more complex than cloud-rain relationship, there may be hundreds of premises and hidden assumptions, and each comes with some uncertainty. As that uncertainty accumulates, the deduction process becomes increasingly less reliable.
Consider a case with 50 premises, that are each 95% reliable. Can you still rely on the argument? Not a good idea: all the premises will be true simultaneously less than 8% of the time! (0.95 to the 50th power). So, is our confidence that the conclusion is true only 8%? Unfortunately, we can’t even say that. It could be much more or much less. To determine that we need to evaluate many factors and use tools stronger than Logic…
If Not Logic, Then What??
If deductive arguments are useless in the real world, then how do we manage to make successful choices? What do we actually do when we think we’re using “logical arguments”? And is there a better method for drawing conclusions in an uncertain world? Those topics will be covered in part 2 of this post. In the meantime, visit Rootclaim to see analyses that avoid the pitfalls of human reasoning.
October 12, 2017 at 1:30 am
This essay is wildly wrong. When premises are untrue, the argument is unsound, not invalid. Validity refers to the formal relationship between terms, and is always defined hypothetically, “…if the premises are true…” Unsound arguments can be formally valid, but have untrue or questionable premises. For example, “Spot is a dog. All dogs have fleas. Spot has fleas” is formally valid, but likely unsound, because the premise “All dogs have fleas” is probably false.
February 11, 2022 at 11:19 am
Thanks for commenting, Jon.
As you can tell, we don’t care much for logical reasoning, so we don’t really bother with the formal terms. Please interpret words using their normal spoken meaning.
February 11, 2022 at 9:08 am
The article seems to propose that if a statement is based in some way on inductive reasoning then the argument is wrong. Ironically, the article uses inductive reasoning to make this claim. Deductive and inductive reasoning are both logical types of reasoning and two sides of the same coin. In fairness, I have not read part 2 of the article.
I do have similar convictions about the Sherlock Holmes/Arthur Conan Doyle quote though. I never liked that quote. It ignores inductive reasoning and is a non sequitor. Five contradicting things could still remain after eliminating the impossible.
February 11, 2022 at 11:13 am
Thanks for commenting, Tim.
The problem is deeper than that. All logical reasoning, whether deductive, inductive, or abductive, is irrelevant to real life. The whole concept of assigning true/false values to statements collapses under complex reasoning, as it causes uncertainty to accumulate.
It can only work when discussing theoretical concepts (like we’re doing now) or when uncertainty is negligible (physics, computer science). In all other domains, you must explicitly quantify truthiness (probability), and use mathematical models that can handle it (probability theory).
September 11, 2024 at 8:44 pm
If you do Bayesian analysis rigorously then you’re using deductive logic. I did this in my PhD work. It’s hard, not impossible. https://arxiv.org/abs/1502.02272
You’re going to confuse people by presenting reasoning in the presence of uncertainty as incompatible with deductive logic.
Given how confident this essay is, it’d be nothing short of a miracle if this message gets through to anyone at your org. But I have to try, since your hearts are probably in the right place.
September 11, 2024 at 9:37 pm
Thank you Dustin. Can you give an example of how deductive reasoning can be used in the kind of analyses we do? I’ve looked through your paper, and while very interesting, the examples seem limited to statistical analysis of one piced of evidence. How would you approach the typical real world contentions that require weighing multiple pieces of contradictory evidence, where there are multiple arguments and counter-arguments for the strength of each evidence?
September 18, 2024 at 9:43 pm
Apologies for the delayed response; I was on a trip without internet access.
Over the last day I read some of the blog posts about RootClaim’s work on COVID origins, and a smaller amount about Ghouta. We need to talk!!!
In 2017 I abandoned my lonely, depressing, intended-life’s-work upon getting a tangentially-related paid job. If I’d known about Rootclaim, I would have joined forces with you guys instead.
Some remarks before I get to your questions:
I never systematized a method for _discovering_ strong, rigorous deductive arguments; I relied on largely the same chaotic process I used for discovering normal math proofs and acquiring new knowledge. But I badly needed such a method, and I’m very excited now about the effiency gains I could realize by utilizing Rootclaim’s strategies.
On the other hand, my work provides a standard for arguments/deliberations that I would argue has some serious advantages over Rootclaim’s arguments/deliberations. And as far as I can see now, the advantages are entirely complementary. I do, however, seriously need to write up something about how I would update my deliberation system proposal (which I called “Interpreted Formal Proof Dialogues”) to only depend on formalization gradually and in worst cases, where the flexibility of natural language argumentation is causing problems according to at least one dialogue participant. Uncoincidentally, that is exactly the role that formal logic has in mathematics!
To answer your questions directly:
On multiple pieces of contradictory evidence:
– First of all, focusing on one piece of evidence was just a consequence of time/energy constraints and wishing the arguments to be thoroughly assessed by *someone* other than the members of my thesis committee (and I’m not even confident I accomplished that much). I expect that I handle multiple pieces of evidence in essentially the same way Rootclaim does, though I didn’t have the insight of the evidence-grouping heuristic.
– In my thesis, Chapter 7 (note I just replaced the version on my personal webpage with a slightly updated version at arxiv.org/abs/1502.02272, where I added a brief note in bold to the beginning of this chapter), I briefly discussed how I would incorporate another piece of evidence in the smoking/cancer argument: the timing disparity between the sharp increases in lung cancer rates among men and women (smoking became popular among men years before it became popular among women, and the lung cancer rates reflect this).
On multiple arguments and counterarguments for the strength of each piece of evidence:
– As you know, deductive logic does not have canonical built-in notions of “strength” or “support”. **In the sphere of non-rushed, maximal-integrity, high-stakes deliberation**, I think the practice of publicly wielding multiple arguments “in support of” a position makes the human race much stupider overall. I think formal defeasible logic is generally a disgrace for that and other reasons; this makes me quite unpopular with most academics who fancy themselves experts in applied formal logic. Frankly, aside from math-logic (set/model theory, reverse mathematics, proof complexity and bounded arithmetic, etc) and automated theorem proving (SAT/SMT solvers, general first-order theorem proving, etc), most research involving formal logic is little more than the noise of a polite, sophisticated echo chamber. It is a very sad state of affairs for me. I tend to pay more attention to ML research these days, where the availability of objective evaluations enables higher standards — uncoincidentally the same reason the areas of math-logic and automated theorem proving are better than other formal logic-related areas.
– Counterarguments are highly systematized in my proposed system. They largely center around
– forcing the proponent to clarify their semantics and address broken rules in a progress-making way
– rejecting subjective axioms in precise, progress-making ways
– presenting counterexamples (sometimes expressed axiomatically) to contextually-sufficiently-precise axioms (“sufficiently-precise” has an explicit meaning).
– If you have two seemingly good and distinct arguments for why some evidence supports your preferred hypothesis, you are simply not finished unless there is no controversy. Otherwise, you need to make precise and justify why your arguments have a compounding effect. There is, however, one opportunity to do this kind of reasoning while developing an argument in private, or in public when it’s in support of uncontroversial axioms: A natural language string can be attached to each axiom, explaining why the intended audience should accept the axiom as true with respect to their understanding of the author’s intended semantics.
I could write for days to you guys, but in the interest of having it read, I’ll stop roughly here. My complaint about this post’s particular framing of Rootclaim/probabilistic inference in opposition to naive deductive inference (without calling it naive) is distantly secondary to my interest in collaborating with Rootclaim. I realize it’s ultimately a strategic decision, and I’d be interested in hearing the motivations — presumably accessibility is one of them. I wonder if it might be possible to satisfy those motivations without veering into this kind of rhetoric in official blog posts, since the optics of that seem to be especially bad for an organization whose mission is to make the human race wiser. But I could easily be wrong; I certainly don’t claim to have a good sense of what moves people.
October 2, 2024 at 3:22 am
Awesome. Please contact [email protected] to continue.