Deductive arguments force us to choose betweeen the truth of their conclusions and the falsity of (one or more) of their premises. Inductive arguments do not. This, in and of itself, does not show that anything is true or false. But if an argument is deductively valid, then we simply cannot, without contradicting ourselves, deny its conclusion unless we also deny (one or more of) its premises. In this way, deductive arguments enable us to exercise critical control over our scientific debates. [105]
Tag: logic
The death of induction
It is only after a long course of uniform experiments in any kind, and we attain a firm reliance and security with regard to a particular event. Now where is that process of reasoning which, from one instance, draws a conclusion so different from that which it infers from a hundred instances that are nowise different from that single one? This question I propose as much for the sake of information, as with an intention of raising difficulties. I cannot find, I cannot imagine any such reasoning. But I keep my mind still open to instruction, if any one will vouchsafe to bestow it on me.
… It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future, since all these arguments are founded on the supposition of that resemblance. [21-2]
The asymmetry between verifiability and falsifiability
Again, the attempt might be made to turn against me my own criticism of the inductivist criterion of demarcation; for it might seem that objections can be raised against falsifiability as a criterion of demarcation similar to those which I myself raised against verifiability.
This attack would not disturb me. My proposal is based upon an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements. Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to univeral statements. [19]
Different ways of knowing
In diesem Zusammenhang wird oft ein fundamentaler Unterschied zwischen Glauben und Wissen behauptet, von dem her solche methodischen Unterschiede legitimiert werden können. Im Bereich des Wissens, vor allem in dem der Wissenschaft, scheint die Vernunft, das rationale Denken, eine ganz andere Funktion zu haben als im Bereich des sogenannten Glaubens. Während im ersten Bereich eine kritische Vernunft am Platze ist, neigt man im zweiten eher dazu, sich für eine deutende, verstehende, hermeneutische Vernunft auszusprechen oder gar die hier adäquate Verfahrensweise von der der Vernunft überhaupt abzusetzen. Man entwickelt eine Zwei-Sphären-Theorie, die gewisse tradierte Anschauungen gegen bestimmte Arten der Kritik abschirmen und einen inselhaften Bereich unantastbarer Wahrheiten schaffen soll. In diesem Bereich ist man unter Umständen sogar bereit, die Logik außer Gefecht zu setzen, damit echte Widersprüche akzeptabel werden, allerdings meist ohne die Tragweite eines solchen Unternehmens und seine Absurdität voll zu erkennen. Man ist zwar im sicheren Besitz der Wahrheit, hat aber dennoch eine gewisse Angst vor kritischer Prüfung und opfert daher oft lieber die elementare Moral des Denkens als diesen angeblich sicheren Besitz. Auf diese Weise kann man dogmatischen Verfahrensweisen mitunter eine gewisse Anerkennung verschaffen, nicht ohne daß die Isolierung verschiedener Bereiche des Denkens und Handelns voneinander jene milde intellektuelle Schizophrenie fördert, die es gestattet, die konsequente Anwendung kritischer Verfahrenweisen als Naivität zu belächeln.
On the use of authority in critical thinking
But shouldn’t an expert’s authority count for something? And isn’t there some appropriate use of authority in critical thinking?
If what I have been saying is true, then courses in critical thinking should teach our students how to criticize authority instead of teaching them how to defer to it. But if this is true, then a statement by an ‘appropriate’ authority should be the first word in a critical inquiry instead of the last. It should be the word that we listen to in order to discover how things stand in a field, what its major problems are, and which of the solutions that have been proposed seem most promising. And it should be the word that we then examine and question and put to the test as we begin to think critically about the field ourselves. I have no doubt whatsoever that this use of authority is very often necessary, appropriate, and reasonable. But it is not an argument from authority. It does not pretend to be good evidence. And it is not presented as a justification of any claim. It would, however, be one that is fully consistent with the goals of critical thinking. [136]
Distinctly social
What Popper argued is that a problem classically treated as logical (the demarcation of science) is insoluble in that form. Yet science does seem distinctive, i.e. demarcatable. The solution to its distinctness is found in its institutionalised rules of inquiry. These rules can be circumvented without violating any rules of logic. In the choice or decision not to circumvent them we find the hallmark of science. Such choice is not individual but social: it is constitutive of and dependent upon institutions. Moreover, being institutions, the rules of science are not like rules of inference: discoveries about the properties of logical systems. Institutional rules can be assessed against given aims, such as fruitfulness, and be discussed and modified. Science and its distinctiveness are open to modification. [83]
Nasty little facts of logic
Although science is a social institution, it is not just another social institution. The social institution of science is obedient to special imperatives because it undertakes to explore and explain the world, to in some sense use the world as the ultimate test of its results. Science institutionalises what we know as empiricism, the attempt to learn from experience. The spine of learning from experience is logic: if we have two inconsistent statements, one of them must be false, its negation true. This uncomfortable logical fact, so often allowed to be disregarded or even flouted by other social institutions (e.g. in politics and religion), has to be taken seriously in science. The republic of science makes it difficult to evade or flout contradiction, hence the detection of one is an incipient crisis. [18]
The power of logic
Most people think that the purpose of an argument is to justify its conclusion — and to thereby establish its certainty — and that the problem with inductive arguments is that they fail to establish their conclusions with objective certainty since their conclusions may be false even if all of their premises are true. But this entirely confuses the issue, and it has even enabled inductivists to take the high ground in the debate, arguing that objective certainty is an impossible dream, and that inductive arguments are not, as a consequence, at fault for failing to achieve it.
But if the uncertainty of their conclusions were the problem with inductive arguments, then we would also have a similar problem with deductive arguments. For the premises of a deductive argument may be false. And the conclusion of a deductive argument may be false as well.
Contrary to what most people think, logical arguments cannot establish the truth, let alone the certainty, of their conclusions. And so contrary to what most people think, the problem with inductive arguments has nothing to do with the uncertainty of their conclusions.
The best that a logical argument can do is test the truth of a statement. But it can do this only by showing that its falsity is inconsistent with the truth of other statements that can only be tested and never proved. Our so-called ‘proof’ methods are really techniques for testing consistency. And the demonstration that a ‘conclusion’ follows from a ‘premise’ shows only that the falsity of the ‘conclusion’ is inconsistent with the truth of the ‘premise.’
That is all that is involved.
But so long as we regard contradictions as unacceptable, it is really quite a lot.
The inconsistency that marks a valid deductive argument — the inconsistency, that is, between the truth of is premises and the falsity of its conclusion — cannot force us to accept the truth of any belief. But it can force us, if we want to avoid contradicting ourselves, to reexamine our beliefs, and to choose between the truth of some beliefs and the falsity of others — because the falsity of the conclusion of a valid argument is inconsistent with the truth of its premises. …
And this is just another way of saying that what we call a proof actually presents us with the choice between accepting its conclusion and rejecting its premises. …
We construct logical arguments in order to persuade others of our beliefs. But the best we can do is to clarify a choice that they have to make. Inductive arguments, however, cannot even do this. [86-7]
Getting nearer to the truth
The myth of the framework can be stated in one sentence, as follows.
A rational and fruitful discussion is impossible unless the participants share a common framework of basic assumptions or, at least, unless they have agreed on such a framework for the purpose of the discussion.
This is the myth I am going to criticize.
As I have formulated it here, the myth sounds like a sober statement, or like a sensible warning to which we ought to pay attention in order to further rational discussion. Some people even think that what I describe as a myth is a logical principle, or based on a logical principle. I think, on the contrary, that it is not only a false statement, but also a vicious statement which, if widely believed, must undermine the unity of mankind, and so must greatly increase the likelihood of violence and of war. This is the main reason why I want to combat it and refute it.
As indicated, I mean by ‘framework’ here a set of basic assumptions, or fundamental principles – that is to say, an intellectual framework. It is important to distinguish such a framework from some attitudes which may indeed be preconditions for a discussion, such as a wish to get to, or nearer to, the truth, and a willingness to share problems or to understand the aims and the problems of somebody else. [34-5]
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