Rhetoric. Aristotle. Translated by W. Rhys Roberts. This web edition published by [email protected] Last updated Wednesday, July 15, at To the. about language and its uses in the West—Aristotle's Rhetoric. rhetoric of Aristotle's argument as well as by his analyses of specific categories. Aristotle, Rhetoric and Probability Katarzyna Budzynska1, Magdalena Kacprzak2 1 Institute of Philosophy, Cardinal Stefan Wyszynski University in Warsaw.
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Rhetoric is the counterpart of Dialectic. Both alike are con- cerned with such things as come, more or less, within the general ken of all men and belong to no . Theodectes)—decay of rhetoric—Demetrius of Phalerum treatment of rhetoric in. Plato's. Gorgias and Phaedrus— other rhetorical works by Aristotle—date of the. Leo Strauss, Seminar on Political Philosophy: Aristotle's Rhetoric Aristotle's Rhetoric clearly has its place in the context of Strauss's study of classical political.
Probability in rhetoric In this section we present two fields of rhetoric where the notion of probability may be applied to describe some phenomena characteristic for rhetorical actions see also Budzynska Sowing to seed as X to sun rays, while the action of the sun in scattering his rays is nameless; still this process bears to the sun the same relation as sowing to the seed. Semantics of L1 is defined in a type 1 probability structure D, , , where D is a domain, assigns to the predicate and function symbols in predicates and functions of the right arity over D, is a discrete probability function on D, i. For Aristotle, an enthymeme is what has the function of a proof or demonstration in the domain of public speech, since a demonstration is a kind of sullogismos and the enthymeme is said to be a sullogismos too. Aristotle deduces these three factors for several emotions in the chapters II. Therefore we focus on very subjective attitudes and beliefs which sometimes are contrary to reality.
While the deliberative and judicial species have their context in a controversial situation in which the listener has to decide in favor of one of two opposing parties, the third species does not aim at such a decision: The first book of the Rhetoric treats the three species in succession.
These chapters are understood as contributing to the argumentative mode of persuasion or—more precisely—to that part of argumentative persuasion that is specific to the respective species of persuasion.
The second part of the argumentative persuasion that is common to all three species of rhetorical speech is treated in the chapters II. The second means of persuasion, which works by evoking the emotions of the audience, is described in the chapters II. Though the following chapters II. The underlying theory of this means of persuasion is elaborated in a few lines of chapter II. The aforementioned chapters II. Why the chapters on the argumentative means of persuasion are separated by the treatment of emotions and character in II.
Rhetoric III. Aristotle stresses that rhetoric is closely related to dialectic. He offers several formulas to describe this affinity between the two disciplines: In saying that rhetoric is a counterpart to dialectic, Aristotle obviously alludes to Plato's Gorgias bff. This analogy between rhetoric and dialectic can be substantiated by several common features of both disciplines:. The analogy to dialectic has important implications for the status of rhetoric.
However, though dialectic has no definite subject, it is easy to see that it nevertheless rests on a method, because dialectic has to grasp the reason why some arguments are valid and others are not. Now, if rhetoric is nothing but the counterpart to dialectic in the domain of public speech, it must be grounded in an investigation of what is persuasive and what is not, and this, in turn, qualifies rhetoric as an art.
Further, it is central to both disciplines that they deal with arguments from accepted premises. Hence the rhetorician who wants to persuade by arguments or rhetorical proofs can adapt most of the dialectical equipment. Nevertheless, persuasion that takes place before a public audience is not only a matter of arguments and proofs, but also of credibility and emotional attitudes.
This is why there are also remarkable differences between the two disciplines:. Aristotle defines the rhetorician as someone who is always able to see what is persuasive Topics VI. Correspondingly, rhetoric is defined as the ability to see what is possibly persuasive in every given case Rhet. This is not to say that the rhetorician will be able to convince under all circumstances. Rather he is in a situation similar to that of the physician: Similarly, the rhetorician has a complete grasp of his method, if he discovers the available means of persuasion, though he is not able to convince everybody.
Aristotelian rhetoric as such is a neutral tool that can be used by persons of virtuous or depraved character. This capacity can be used for good or bad purposes; it can cause great benefits as well as great harms. There is no doubt that Aristotle himself regards his system of rhetoric as something useful, but the good purposes for which rhetoric is useful do not define the rhetorical capacity as such.
Thus, Aristotle does not hesitate to concede on the one hand that his art of rhetoric can be misused. But on the other hand he tones down the risk of misuse by stressing several factors: Generally, it is true of all goods, except virtue, that they can be misused.
Secondly, using rhetoric of the Aristotelian style, it is easier to convince of the just and good than of their opposites. Finally, the risk of misuse is compensated by the benefits that can be accomplished by rhetoric of the Aristotelian style. It could still be objected that rhetoric is only useful for those who want to outwit their audience and conceal their real aims, since someone who just wants to communicate the truth could be straightforward and would not need rhetorical tools.
This, however, is not Aristotle's point of view: Even those who just try to establish what is just and true need the help of rhetoric when they are faced with a public audience. Aristotle tells us that it is impossible to teach such an audience, even if the speaker had the most exact knowledge of the subject.
Obviously he thinks that the audience of a public speech consists of ordinary people who are not able to follow an exact proof based on the principles of a science.
Further, such an audience can easily be distracted by factors that do not pertain to the subject at all; sometimes they are receptive to flattery or just try to increase their own advantage. And this situation becomes even worse if the constitution, the laws, and the rhetorical habits in a city are bad.
Finally, most of the topics that are usually discussed in public speeches do not allow of exact knowledge, but leave room for doubt; especially in such cases it is important that the speaker seems to be a credible person and that the audience is in a sympathetic mood. For all those reasons, affecting the decisions of juries and assemblies is a matter of persuasiveness, not of knowledge.
It is true that some people manage to be persuasive either at random or by habit, but it is rhetoric that gives us a method to discover all means of persuasion on any topic whatsoever. Aristotle joins Plato in criticizing contemporary manuals of rhetoric. But how does he manage to distinguish his own project from the criticized manuals? The general idea seems to be this: Previous theorists of rhetoric gave most of their attention to methods outside the subject; they taught how to slander, how to arouse emotions in the audience, or how to distract the attention of the hearers from the subject.
This style of rhetoric promotes a situation in which juries and assemblies no longer form rational judgments about the given issues, but surrender to the litigants.
Aristotelian rhetoric is different in this respect: Since people are most strongly convinced when they suppose that something has been proven Rhet. In Aristotle's view an orator will be even more successful when he just picks up the convincing aspects of a given issue, thereby using commonly-held opinions as premises. Since people have a natural disposition for the true Rhet.
Of course, Aristotle's rhetoric covers non-argumentative tools of persuasion as well. It is understandable that several interpreters found an insoluble tension between the argumentative means of pertinent rhetoric and non-argumentative tools that aim at what is outside the subject.
It does not seem, however, that Aristotle himself saw a major conflict between these diverse tools of persuasion—presumably for the following reasons: Thus, it is not surprising that there are even passages that regard the non-argumentative tools as a sort of accidental contribution to the process of persuasion, which essentially proceeds in the manner of dialectic cp. His point seems to be that the argumentative method becomes less effective, the worse the condition of the audience is.
This again is to say that it is due to the badness of the audience when his rhetoric includes aspects that are not in line with the idea of argumentative and pertinent rhetoric. The prologue of a speech, for example, was traditionally used for appeals to the listener, but it can also be used to set out the issue of the speech, thus contributing to its clearness.
Similarly, the epilogue has traditionally been used to arouse emotions like pity or anger; but as soon as the epilogue recalls the conclusions reached, it will make the speech more understandable. The systematical core of Aristotle's Rhetoric is the doctrine that there are three technical means of persuasion.
Further, methodical persuasion must rest on a complete analysis of what it means to be persuasive. A speech consists of three things: It seems that this is why only three technical means of persuasion are possible: Technical means of persuasion are either a in the character of the speaker, or b in the emotional state of the hearer, or c in the argument logos itself.
If the speaker appears to be credible, the audience will form the second-order judgment that propositions put forward by the credible speaker are true or acceptable.
This is especially important in cases where there is no exact knowledge but room for doubt. But how does the speaker manage to appear a credible person? Again, if he displayed i without ii and iii , the audience could doubt whether the aims of the speaker are good.
Finally, if he displayed i and ii without iii , the audience could still doubt whether the speaker gives the best suggestion, though he knows what it is. But if he displays all of them, Aristotle concludes, it cannot rationally be doubted that his suggestions are credible. It must be stressed that the speaker must accomplish these effects by what he says; it is not necessary that he is actually virtuous: Thus, the orator has to arouse emotions exactly because emotions have the power to modify our judgments: Many interpreters writing on the rhetorical emotions were misled by the role of the emotions in Aristotle's ethics: Thesis i is false for the simple reason that the aim of rhetorical persuasion is a certain judgment krisis , not an action or practical decision prohairesis.
How is it possible for the orator to bring the audience to a certain emotion? Aristotle's technique essentially rests on the knowledge of the definition of every significant emotion. According to such a definition, someone who believes that he has suffered a slight from a person who is not entitled to do so, etc.
If we take such a definition for granted, it is possible to deduce circumstances in which a person will most probably be angry; for example, we can deduce i in what state of mind people are angry and ii against whom they are angry and iii for what sorts of reason. Aristotle deduces these three factors for several emotions in the chapters II. With this equipment, the orator will be able, for example, to highlight such characteristics of a case as are likely to provoke anger in the audience.
In comparison with the tricks of former rhetoricians, this method of arousing emotions has a striking advantage: The orator who wants to arouse emotions must not even speak outside the subject; it is sufficient to detect aspects of a given subject that are causally connected with the intended emotion. For Aristotle, there are two species of arguments: A deduction sullogismos is an argument in which, certain things having been supposed, something different from the suppositions results of necessity through them Topics I.
The inductive argument in rhetoric is the example paradeigma ; unlike other inductive arguments, it does not proceed from many particular cases to one universal case, but from one particular to a similar particular if both particulars fall under the same genus Rhet. At first glance, this seems to be inconsistent, since a non-necessary inference is no longer a deduction. If the former interpretation is true, then Aristotle concedes in the very definition of the enthymeme that some enthymemes are not deductive.
But if the latter interpretation which has a parallel in An. For Aristotle, an enthymeme is what has the function of a proof or demonstration in the domain of public speech, since a demonstration is a kind of sullogismos and the enthymeme is said to be a sullogismos too.
In general, Aristotle regards deductive arguments as a set of sentences in which some sentences are premises and one is the conclusion, and the inference from the premises to the conclusion is guaranteed by the premises alone.
Since enthymemes in the proper sense are expected to be deductive arguments, the minimal requirement for the formulation of enthymemes is that they have to display the premise-conclusion structure of deductive arguments. This is why enthymemes have to include a statement as well as a kind of reason for the given statement.
Examples of the former, conditional type are: The reason why the enthymeme, as the rhetorical kind of proof or demonstration, should be regarded as central to the rhetorical process of persuasion is that we are most easily persuaded when we think that something has been demonstrated.
Hence, the basic idea of a rhetorical demonstration seems to be this: In order to make a target group believe that q , the orator must first select a sentence p or some sentences p 1 … p n that are already accepted by the target group; secondly he has to show that q can be derived from p or p 1 … p n , using p or p 1 … p n as premises.
Given that the target persons form their beliefs in accordance with rational standards, they will accept q as soon as they understand that q can be demonstrated on the basis of their own opinions. Consequently, the construction of enthymemes is primarily a matter of deducing from accepted opinions endoxa.
Of course, it is also possible to use premises that are not commonly accepted by themselves, but can be derived from commonly accepted opinions; other premises are only accepted since the speaker is held to be credible; still other enthymemes are built from signs: That a deduction is made from accepted opinions—as opposed to deductions from first and true sentences or principles—is the defining feature of dialectical argumentation in the Aristotelian sense.
Thus, the formulation of enthymemes is a matter of dialectic, and the dialectician has the competence that is needed for the construction of enthymemes. Nevertheless, this expectation is somehow misled: However, in the rhetorical context there are two factors that the dialectician has to keep in mind if she wants to become a rhetorician too, and if the dialectical argument is to become a successful enthymeme.
First, the typical subjects of public speech do not—as the subject of dialectic and theoretical philosophy—belong to the things that are necessarily the case, but are among those things that are the goal of practical deliberation and can also be otherwise.
Second, as opposed to well-trained dialecticians the audience of public speech is characterized by an intellectual insufficiency; above all, the members of a jury or assembly are not accustomed to following a longer chain of inferences.
Therefore enthymemes must not be as precise as a scientific demonstration and should be shorter than ordinary dialectical arguments. This, however, is not to say that the enthymeme is defined by incompleteness and brevity. Rather, it is a sign of a well-executed enthymeme that the content and the number of its premises are adjusted to the intellectual capacities of the public audience; but even an enthymeme that failed to incorporate these qualities would still be enthymeme.
In a well known passage Rhet. Properly understood, both passages are about the selection of appropriate premises, not about logical incompleteness. The remark that enthymemes often have few or less premises concludes the discussion of two possible mistakes the orator could make Rhet. One can draw conclusions from things that have previously been deduced or from things that have not been deduced yet. The latter method is unpersuasive, for the premises are not accepted, nor have they been introduced.
The former method is problematic, too: Arguments with several deductive steps are common in dialectical practice, but one cannot expect the audience of a public speech to follow such long arguments. This is why Aristotle says that the enthymeme is and should be from fewer premises. Just as there is a difference between real and apparent or fallacious deductions in dialectic, we have to distinguish between real and apparent or fallacious enthymemes in rhetoric.
The topoi for real enthymemes are given in chapter II. The fallacious enthymeme pretends to include a valid deduction, while it actually rests on a fallacious inference. Note that neither classification interferes with the idea that premises have to be accepted opinions: However, it is not clear whether this is meant to be an exhaustive typology.
When using a sign-argument or sign-enthymeme we do not try to explain a given fact; we just indicate that something exists or is the case: But there are several types of sign-arguments too; Aristotle offers the following examples:. Sign-arguments of type i and iii can always be refuted, even if the premises are true; that is to say that they do not include a valid deduction sullogismos ; Aristotle calls them asullogistos non-deductive.
Sign-arguments of type ii can never be refuted if the premise is true, since, for example, it is not possible that someone has fever without being ill, or that someone has milk without having given birth, etc. Now, if some sign-enthymemes are valid deductions and some are not, it is tempting to ask whether Aristotle regarded the non-necessary sign-enthymemes as apparent or fallacious arguments. However, there seems to be a more attractive reading: We accept a fallacious argument only if we are deceived about its logical form.
So it seems as if Aristotle didn't regard all non-necessary sign-arguments as fallacious or deceptive; but even if this is true, it is difficult for Aristotle to determine the sense in which non-necessary sign-enthymemes are valid arguments, since he is bound to the alternative of deduction and induction, and neither class seems appropriate for non-necessary sign-arguments.
Cicero, Brutus , 46—48 and Isocrates. Aristotle's book Topics lists some hundred topoi for the construction of dialectical arguments. These lists of topoi form the core of the method by which the dialectician should be able to formulate deductions on any problem that could be proposed.
Most of the instructions that the Rhetoric gives for the composition of enthymemes are also organized as lists of topoi ; especially the first book of the Rhetoric essentially consists of topoi concerning the subjects of the three species of public speech.
It is striking that the work that is almost exclusively dedicated to the collection of topoi , the book Topics , does not even make an attempt to define the concept of topos.
At any rate the Rhetoric gives a sort of defining characterization: According to this definition, the topos is a general argumentative form or pattern, and the concrete arguments are instantiations of the general topos. That the topos is a general instruction from which several arguments can be derived, is crucial for Aristotle's understanding of an artful method of argumentation; for a teacher of rhetoric who makes his pupils learn ready samples of arguments would not impart the art itself to them, but only the products of this art, just as if someone pretending to teach the art of shoe-making only gave samples of already made shoes to his pupils see Sophistical Refutations b36ff.
By recalling the houses along the street we can also remember the associated items. In Topics b28—32, Aristotle seems to allude to this technique: At least within the system of the book Topics , every given problem must be analyzed in terms of some formal criteria: Does the predicate of the sentence in question ascribe a genus or a definition or peculiar or accidental properties to the subject?
Does the sentence express a sort of opposition, either contradiction or contrariety, etc.? Does the sentence express that something is more or less the case?
Does it maintain identity or diversity? Are the words used linguistically derived from words that are part of an accepted premise? Depending on such formal criteria of the analyzed sentence one has to refer to a fitting topos. For this reason, the succession of topoi in the book Topics is organized in accordance with their salient formal criteria; and this, again, makes a further mnemotechnique superfluous.
More or less the same is true of the Rhetoric —except that most of its topoi are structured by material and not by formal criteria, as we shall see in section 7. A typical Aristotelian topos runs as follows: Other topoi often include the discussion of iv examples; still other topoi suggest v how to apply the given schemes.
Often Aristotle is very brief and leaves it to the reader to add the missing elements. In a nutshell, the function of a topos can be explained as follows. First of all, one has to select an apt topos for a given conclusion.
The conclusion is either a thesis of our opponent that we want to refute, or our own assertion we want to establish or defend. Accordingly, there are two uses of topoi: Most topoi are selected by certain formal features of the given conclusion; if, for example, the conclusion maintains a definition, we have to select our topos from a list of topoi pertaining to definitions, etc.
Once we have selected a topos that is appropriate for a given conclusion, the topos can be used to construe a premise from which the given conclusion can be derived.
If the construed premise is accepted, either by the opponent in a dialectical debate or by the audience in public speech, we can draw the intended conclusion. It could be either, as some say, the premise of a propositional scheme such as the modus ponens, or, as others assume, as the conditional premise of a hypothetical syllogism.
Aristotle himself does not favor one of these interpretations explicitly. But even if he regarded the topoi as additional premises in a dialectical or rhetorical argument, it is beyond any doubt that he did not use them as premises that must be explicitly mentioned or even approved by the opponent or audience.
This topic was not announced until the final passage of Rhet. II, so that most scholars have come to think of this section as a more or less self-contained treatise.
The insertion of this treatise into the Rhetoric is motivated by the claim that, while Rhet. In the course of Rhet. After an initial exploration of the field of delivery and style III. The following chapters III. Chapters III. These are the topics of the rhythmical shaping of prose style and of periodic and non-periodic flow of speech. Again metaphors are shown to play a crucial role for that purpose, so that the topic of metaphor is taken up again and deepened by extended lists of examples.
Chapter III. The philosophical core of Aristotle's treatise on style in Rhet. Originally the discussion of style belongs to the art of poetry rather than to rhetoric; the poets were the first, as Aristotle observes, to give an impulse for the study of style. Nevertheless he admits that questions of style or, more precisely, of different ways to formulate the same subject, may have an impact on the degree of clarity: Clarity again matters for comprehension and comprehensibility contributes to persuasiveness.
In prose speeches, the good formulation of a state of affairs must therefore be a clear one. However, saying this is not yet enough to account for the best or excellent prose style, since clear linguistic expressions tend to be banal or flat, while good style should avoid such banality. If the language becomes too banal it will not be able to attract the attention of the audience. The orator can avoid this tendency of banality by the use of dignified or elevated expressions and in general by all formulations that deviate from common usage.
On the one hand, uncommon vocabulary has the advantage of evoking the curiosity of an audience. On the other hand the use of such elevated vocabulary bears a serious risk: Whenever the orator makes excessive use of it, the speech might become unclear, thus failing to meet the default requirement of prose speech, namely clarity.
Moreover, if the vocabulary becomes too sublime or dignified in relation to prose's subject matter Aristotle assumes it is mostly everyday affairs , the audience will notice that the orator uses his words with a certain intention and will become suspicious about the orator and his intentions. Hitting upon the right wording is therefore a matter of being clear, but not too banal; In trying not to be too banal, one must use uncommon, dignified words and phrases, but one must be careful not to use them excessively or inappropriately in relation to prose style and the typical subject matter of prose speeches.
Bringing all these considerations together Aristotle defines the good prose style, i. The good style is clear in a way that is neither too banal nor too dignified, but appropriate in proportion to the subject matter of prose speech.
In this respect the definition of stylistic virtue follows the same scheme as the definition of ethical virtues in Aristotle's ethical writings, insofar as both the stylistic virtue and the virtue of character are defined in terms of a mean that lies between two opposed excesses. If the virtue of style is defined as a mean between the banality involving form of clarity and overly dignified and hence inappropriate speech, it is with good reason that Aristotle speaks of only one virtue of prose style, and not of clarity, ornament by dignified expressions and appropriateness as three distinct virtues of style.
However, from the times of Cicero and Quintilianus on, these three, along with the correctness of Greek or Latin, became the canonical four virtues of speech virtutes dicendi. Reading Aristotle through the spectacles of the Roman art of rhetoric, scholars often try to identify two, three or four virtues of style in his Rhetoric.
Finally, if the virtue of style is about finding a balance between banal clarity, which is dull, and attractive dignity, which is inappropriate in public speeches, how can the orator manage to control the different degrees of clarity and dignity? The next question is how to model the subjective beliefs.
One of the methods is to use tools of probabilistic logics. Then, degrees of uncertainty of the audience or other parties could be identified by the probability that a given sentence is true according to the audience. For describing degrees of belief we can assume semantics of possible worlds. Suppose a situation in which the judge considers 5 possible scenarios of a crime see Figure 2. Now, assume that during the trial one of the scenarios is refuted such that now in 3 of 4 possible scenarios the accused is guilty.
Thus the objective probability of this sentence is 1 or 0. There is no other option if we think about what happened in the reality. The probability of this statement can be only expressed in terms of subjective interpretation. That is, we can consider in how many visions of reality allowed by the judge the accused committed a crime. When we come to one real world such sentences cannot be treated as probable unless one want to express that the person committed a crime more e.
By applying subjective degrees of beliefs we can also describe which arguments are apt and affect the judge the most. It means that the argument was well-chosen. In this way we can analyze and compare power and results of arguments as well as the degrees of uncertainty of the audience.
The interesting question is: Observe that whenever I use the objectively probable premise in my argumentation its conclusion can be allowed only with some probability, namely, with some degree of uncertainty. Thus the probability of conclusion is to be understood in the subjective manner. Assume that the statistical probability of the relationship: Say that the prosecutor uses it to reason about John.
When the prosecutor is absolutely certain that John committed a crime using weapon i. Probability according to Aristotle In this section we demonstrate how Aristotle understands the notion of probability and what role it plays in his rhetoric. We want to show that Aristotle originally refers to the objective interpretation of probability, i. However, the subjective interpretation can also be found in his theory. Therefore, the probability plays a crucial role for persuasion as long as it influences the uncertainty of the beliefs.
Then, we describe why he considers this notion as especially important in the field of persuasion.
Aristotle originally uses the objective interpretation of the probability, i. There are at least three of them: First, Aristotle compares the notion of probability with the objective truth, not with subjective beliefs about the truth: Hence the man who makes a good guess at truth is likely to make a good guess at probabilities. Next, Aristotle refers to the probability as to a property of events. That is, he defines the probability as a thing that happens usually, not what we think believe that happens usually: Complexity means that a given phenomenon is influenced by various random factors.
In consequence, the sentences describing this type of phenomena cannot be exceptionless. This complexity reflects in uncertainty of our beliefs about the reality. However, initially the complexity is a property of the reality. What role does the probability play in rhetoric according to Aristotle? First, it is a basis for an enthymeme, i. Furthermore, the probability plays a crucial role in persuasion since the sentences that are probable can be much more often encountered than the necessary ones i.
The necessary and invariable facts rarely refer to the typical subjects of rhetorical speeches. Therefore, they seldom build the rhetorical syllogism. That is, it influences the guarantee of obtaining true conclusion: We can understand it as follows: Can the subjective interpretation be also found in his rhetoric?
There are some arguments for understanding his ideas in this manner. A persuader has a chance to be successful when he uses opinions of his audience as premises: Thus, what is important in rhetoric is the beliefs about the reality rather than the reality itself. Aristotle emphasizes it when he differentiates demonstrations from rhetorical syllogisms.
A demonstration is a deduction in which the premises are true and an enthymeme is a deduction in which the premises are accepted believed by someone. Although initially Aristotle treats the probability as some property of the reality, in rhetoric this notion becomes important only as long as it influences the character of opinions used in argumentation: That is, the probability is important since it generates uncertainty of our beliefs: Aristotle finds the close relation between objective and subjective probability since in his view people have a natural disposition to the true Rhet.
Thus, there is no unbridgeable gap between the commonly held opinions and what is true. In fact, there is a close affinity between the true and the persuasive. Formalization of probability In order to formally model notions discussed in the previous sections we use first-order logics of probability by J. Halpern Halpern The syntax of the adopted languages is similar while their semantics are different.
Thereby we consider two systems: Analogous for other terms. Formally we consider two-sorted first-order language. Assume that is a collection of predicate symbols and function symbols of various arities. The first sort consists of the elements of , together with a countable family of object variables and describe those elements of the domain we want to reason about. Terms of the second sort represent real numbers, which we want to be able to add and multiply.
Object terms, field terms, and formulas are defined simultaneously by induction: Other Boolean connectives and the quantifier are defined in the standard manner. We call the resulting language L1. Semantics of L1 is defined in a type 1 probability structure D, , , where D is a domain, assigns to the predicate and function symbols in predicates and functions of the right arity over D, is a discrete probability function on D, i. Moreover we define a valuation to be a function mapping each object variable into an element of D and each field variable into an element of R the reals.
Given a type 1 probability structure M and a valuation v, we associate with every object resp. The definitions follow the lines of first-order logic. Here we give only main of them: Consider the following example to illustrate how we can apply the above formalization to express objective probability.
As we can observe the proposed language and its semantics allow to reason about facts when the probability of their occurrence is based on statistical information. However it is not well suited for modeling subjective probability, i. Notice that in the logic we can express that the probability that a randomly chosen accused is guilty equals 0.
At the same time we have no chance to express that the probability that a particular accused e. John is guilty equals 0. It follows from the fact that considering term wx Guilty x , the wx binds the free occurrences of x in Guilty x. Therefore replacing x with e. We call the resulting language L2. Semantics of L2 language is given by a type 2 probability structure which is a tuple D,S, , , where D is a domain, S is a set of states or possible worlds, is a function such that for every state s S, s assigns to the predicate and function symbols in predicates and functions of the right arity over D, is a discrete probability function on S.
The main difference between type 1 and type 2 probability structure is that in type 1 the probability is taken over the domain D, while in type 2 the probability is taken over the set of states S. Given a type 2 probability structure M, a state s, and a valuation v, we associate with every object resp. Again we give only main definitions: The value 0. It could be the case where a judge considers 5 possible courses of a crime and in 4 of them John is regarded as the guilty party.
Summarizing, on the one side this approach allows expressing subjective probability about properties of selected individuals. On the other side there is no possibility to reason about objective probability using L2. Notice that in some situations we need to join both probabilities. For example it is possible that degrees of belief are derived form the statistical information. Suppose we know that the probability that a randomly chosen accused person is guilty equals 0.
Next, if we know that John is accused, then we might conclude that the probability that John is guilty is 0. Now assume that w Guilty John means the probability that John is guilty. We can write the implication: See Bacchus for more details about the relation between statistical facts and degrees of beliefs. Conclusion The aim of this paper is to identify the places where the notion of probability may become useful for the inquires conducted within the framework of rhetoric.
We focus especially on two interpretations of probability theory which allows modeling subjective opinions of individuals and objective or statistical premises on which argumentation is built. We present the logical representation of those interpretations. In Budzynska-Kacprzak we presented the discussion about other formalizations which can be used for reasoning about beliefs of parties of persuasion. Our paper does not exhaust all applications of probability theory in rhetoric.
In future work we are going to continue the issue. Among other things we plan to study a probability understood as chances that an audience will believe a thesis after a specific argument has been given, b the probability as a ratio of individuals which are convinced of a thesis to all individuals in a group that is an audience of a given persuasion, c the probability as a degree of credibility of a proponent. References Aristotle Rhys Roberts translator , Dover Publications. Bacchus, F. Default Reasoning from Statistics.
National Conference on Artificial Intelligence, pp. Budzynska, K. Argumentation from Semantic and Pragmatic Perspective. The Logic of Social Research. Studies in Logic, Grammar and Rhetoric 7 20 , pp. Practical face of logic. Croatian Journal of Philosophy: Epistemology VI 17 , pp. Kacprzak Logical model of graded beliefs for a persuasion theory. Annals of University of Bucharest. Rembelski Modeling persuasiveness: Grimaldi, W. Enos, L. Agnew Eds.