I've been reading and researching about formal and symbolic logic for some time now, mainly out of interest in rationality. But I've come to a point where the various logical systems seem more like irrelevant calculus than serious attempts to improve the art of reasoning. I think this is because of the haphazard way that I've approached the subject, and now I wonder if I should dive into informal logic to fill in the gaps.

I've avoided informal logic in the past because I thought that it isn't as rigorous as formal logic, that it strives to justify sloppy reasoning, that it caters to people who are afraid of symbolism, or who lack the discipline of what I might call "mechanical thought" (for instance, to substitute a formula for a variable in another formula requires an acquired discipline that only comes through practice). But my problem with formal logic is that when I engage in reasoning, I don't really think in symbols, and given the plurality of logical systems out there, it isn't obvious even which formal system should be used, nor the form of the argument. For instance, given the paradoxes of material implication, it isn't easy to know if the logic requires material or strict implication, or if it is one of those cases where either seems paradoxical.

Another issue I have is that most of the deductive systems I've read about are designed to be as analytic as possible. For instance, classical logic is usually designed to have a single inference rule of modus ponens, along with a series of axioms. But in natural reasoning, you would want many inference rules that correspond to the rules that are most common patterns of reasoning determined by some empirical method. Natural deduction is easiest when you already know the logical formula. But natural deduction isn't as helpful when you aren't sure if the quantifier "some" means "at least one" or "at least one but not all". Modal logic is also unnatural. For instance, I've found that usually when we talk about possibility, we mean that it is possibly true and possibly false. I'd be okay with a simple terminology conflict, but even if I really meant contingency, this is usually defined as being unnecessary which is still logically consistent with being impossible!

So...is informal logic what I'm looking for? Is it compatible with using formal methods?

  • I think your question is quite vague in a key respect, viz., what you hope to do with logic yourself. Informal logic is valuable but it is in many respects harder to use. Commit a formal fallacy and your argument goes up in flames; commit an informal fallacy or something near to one, and the argument might still work and just be compounded by the question of whether what happened was the fallacy.
    – virmaior
    Aug 11, 2014 at 0:34
  • You're right that it is vague in just that respect, maybe because I'm not too clear myself. I want to say that I want to do better in argument, and employ formal methods for more sophisticated arguments. For instance, if you say that atheists don't have beliefs because there is no doctrine as part of the definition of atheism, this is a formal fallacy, but difficult to nail if you aren't familiar with intensional logic. But it is difficult to identify if your symbolic logic is removed the practice of logic. Aug 11, 2014 at 2:14
  • By what you've suggested, what you're trying to do, I think, is use formal techniques in the analysis of convincing reasons - more of a psychological project than a mathematical project. Do you think that's a fair assessment?
    – Paul Ross
    Aug 11, 2014 at 15:22
  • I care more about logic than rhetoric, if that's what you mean. I care about if my own arguments are valid, more than I care about convincing other people that they are valid. Aug 11, 2014 at 15:34
  • That's not quite what I'm getting at. Where does the normativity of "validity" come from in your project? Is it because there is a structure to the world that good reasoning ought to follow, or is it because there is a specifically effective process of reasoning that our models ought to be constructed from? My thought is that it seems like you're looking for theories of effective reasoning processes rather than foundational principles of how the world must be.
    – Paul Ross
    Aug 11, 2014 at 16:34

2 Answers 2


First, to dispel false conceptions:

Informal logic is not the contrary of formal logic, at least for some established meanings of 'informal logic'.

'Formal logic' is usually reserved for the formal study of truth-preserving inference, like deduction. But there's nothing preventing a formal study of not necessarily truth-preserving inference, so-called ampliative reasoning. Most argumentative patterns found in everyday reasoning are ampliative, in particular defeasible reasoning.

(Please note: Just because they are not deductive, it does not mean that they are never valid. Informal logic has had a particular interest for informal fallacies in the past (see below), which might have given the impression that the standpoint of informal logic is that every non-truth-preserving argument is a fallacy. This is certainly not the case. Informal logic is interested in what makes ampliative inferences context-dependently valid.)

Indeed, informal logic as a field has many contributions obtained using formal methods (see as a random example this application of Bayesian methods to everyday arguments). Also - I have never seen an explicit mention of this - the whole (highly formal) discussion in philosophy of science about the viability of inference to the best explanation is essentially a discussion pertaining to informal logic.

1. The practice of reasoning in theory

Informal logic is not a discipline, but draws from many disciplines to carry out and study very different tasks and topics, such as:

  • competing definitions of “argument”
  • argument identification
  • burden of proof
  • the empirical study of argument
  • diagramming
  • cognitive bias
  • the history of argument analysis
  • methods of argumentative investigation
  • the role of emotion in argument
  • argumentative exchange in different social contexts

(See SEP Entry on Informal Logic)

This seems a garden variety of questions and indeed most question might be legitimate topics in vastly different disciplines: cognitive bias -> psychology; argumentative exchange in different social contexts -> sociolinguistics; etc.

This thematic pluralism (and disunity) is not just due to the many approaches used to tackle given questions, but is a product of the very aim of informal logic, namely to develop assess and analyze arguments that occur in natural language discourse. Since natural language is used in vastly different contexts and in a variety of ways for a variety of aims, the studies tend to multiply and branch off in different directions. Researching 'the role of emotion in argument' may be vastly different when analyzing legal arguments of lawyers in front of a jury than when studying Euclid's diagrammatic reasoning.

In this sense, informal logic vastly fulfills your desideratum that

in natural reasoning, you would want many inference rules that correspond to the rules that are most common patterns of reasoning determined by some empirical method.

On the other hand, this kind of context-sensitivity gets in the way of studying common patterns across different domains, i.e. an effort at theoretical generalization, which you seem to be interested in. Countering this case-study trend, some parts of informal logic aim to construct a comprehensive account of these different types of argumentation. Historically, these attempts have mostly been made in a field called argumentation theory, a field drawing from logic and linguistics, which intersects with informal logic.

2. The practice of reasoning in practice

Your second goal, namely to "improve the [your?] practice of reasoning" is addressed by another major domain of informal logic called "critical thinking", another intersection where the tools of informal logic are applied with an inclusive educational goal in mind, not just limited to academe. You might have come across discussions about e.g. atheism referring to informal fallacies. This is a good example of notions pertaining to early phase of the field of informal reasoning, where a theory of fallacy was predominant, that slowly trickled down from the ivory towers of academe into pop culture and can be found today in every other Reddit thread. (This SE gets its own share by hosting many questions about fallacies by people otherwise not interested in philosophy.)


So, to answer your question: Informal logic is definitely the keyword you're looking for. The bad news is that the field is not systematized and so there is no simple "Introduction to informal logic" covering all aspects you might be looking for. The moral of the story here: Don't give up just because you don't find something fitting on your first try.

  • The best advice I can give is to have a look at the brand new Handbook of Argumentation Theory at your library, skim through the contributions, read what grasps your attention and follow the bibliographic references (and ask about them on Philosophy.SE!).

    Classics in this field are (in chronological order):

    • Stephen Toulmin: The uses of argument (1959) (see the Toulmin model)
    • Chaim Perelman and Lucie Olbrechts-Tyteca: The New Rhetoric: A treatise on argumentation (1969)
    • Frans Van Eemeren and Rob Grootendorst: A systematic theory of argumentation. The pragma-dialectic approach (2004) (see Pragma-Dialectics)

    (IMO, the most interesting studies are not these big volumes - with the exception of Toulmin because of his clarity - but single papers produced in the field. So reading the Handbook might be a better idea than starting with these classics.)

  • In the "critical thinking" department the book Critical Thinking by Moore and Parker is a classic.

  • Historically, you might be interested in the "pragmatic logic" of the Polish School, which is customarily well known because of its key contributions to formal logic, less to informal logic. See Marcin Koszowy, "Pragmatic logic and the study of argumentation", 2010 (PDF).

  • Have a look at the SEP entry on Informal Logic

  • Personally speaking, a favorite application of informal logic of mine (in history of science) is Finocchiaro's analysis of Galileo's scientific arguments: Galileo and the Art of Reasoning: Rhetorical Foundations of Logic and Scientific Method (1980).

  • Thanks, @Kevin Holmes! I am myself very interested in this matter, I would welcome further questions
    – DBK
    Aug 13, 2014 at 20:31

There are many competing definitions for informal logic, but it's probably best to understand it as a retronym (like "analog clock"), a term made up to distinguish older approaches to logic from the newer, more mathematically rigorous approaches collectively known as formal logic. In other words, the various branches of formal logic were developed to reduce and eliminate the ambiguities of arguments in natural language, and thus provide a consistent, rule-governed approach to logical argument. However, in doing so, many subtleties were inevitably lost (just as converting an analog recording to digital inevitably loses some aspects of audio quality while enhancing others).

The modal logics with which you are wrestling are an attempt to pull a wider range of what can be considered by natural argument into the realm of surety represented by formal logic. However, it's arguable whether or not this has provided the desired utility and benefits (since it's not clear how well the various modal logics do actually capture the desired aspects of natural argument).

If you do make the move to informal logic, you'll be plunged back in the realm of subjectivity and ambiguity. That's still the realm, however, where nearly all substantive debate on real-world issues (i.e. abortion, gay marriage, gun control, climate change) takes place. From that point of view, the real utility of formal logic is that it gives you the mental tools and insight to better construct or critique informal arguments.

  • I really like the analog-digital recording analogy.
    – user132181
    Aug 11, 2014 at 16:57
  • Thanks, especially with regard to your last point. So you see informal logic as the glue between formal logic systems and natural language (or natural thought)? But if I purchase books on informal logic, is this what I'll find? It seems that at one time informal logic was seen as a competing alternative to formal logic, and this is not at all what I'm interested in. Aug 11, 2014 at 22:15
  • 2
    A minor quibble: "converting an analog recording to digital inevitably loses some aspects of audio quality while enhancing others" - fortunately, this is not the case, irrational audiophiles notwithstanding :)
    – DBK
    Aug 11, 2014 at 22:37

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