Henry Prakken & Giovanni Sartor July 16, 2012 Law Logic Summerschool 2012 Session 1.1.2: Argumentation and Defeasibility Henry Prakken & Giovanni Sartor July 16, 2012

What is argumentation? Giving reasons to support or criticise claims that are open to doubt logic + dialectic Often to persuade someone else rhetoric Proponent: Regarding downloading Mp3s as copying for private use is wrong Respondent: Why? Proponent: Because it makes normal commercial exploitation of music impossible Proponent: Because it’s so easy to copy, upload and download MP3s

What is argumentation? Giving reasons to support or criticise claims that are open to doubt logic + dialectic Often to persuade someone else rhetoric Proponent: Regarding downloading Mp3s as copying for private use is wrong Respondent: Why? Proponent: Because it makes normal commercial exploitation of music impossible Proponent: Because it’s so easy to copy, upload and download MP3s Respondent: But there are quite profitable ways to sell Mp3s online Proponent: Really? Respondent: Look at iTunes Logic = compelling reasoning forms (but compelling is not always conclusive!) Dialectics: rules of debate (so not Hegelian dialectic!!!). I will only discuss the *product *of dialectic: argument and counterargument. Rhetoric: taking the audience into account (e.g. statistical arguments are not persuasive in court).

The structure of arguments

The structure of arguments: basic elements (Basic) arguments have: Premises (grounds) A conclusion A reasoning step from the premises to the conclusion Ideally the “therefore” is justified by a theory on the ‘validity’ of arguments (= logic) but it will turn out that all arguments can trivially be made valid by adding a hidden premise. Therefore, it is more interesting to focus on structural aspects of argumentation. (And modern logic tells us that the validity of arguments can be presumptive.) Conclusion therefore Premise 1 ….. Premise n

Three types of support P E is expert on P E says that P Cumulative (all premises needed for conclusion) The offer was written The offer was made in a letter in an email Alternative (one premise suffices for conclusion) S was at crime scene Aggregate (the more support the better) S’s DNA matches DNA found at crime scene Witness W saw S at crime scene

Alternative support is in fact alternative arguments The offer was written The offer was written The offer was made in a letter The offer was made in an email

If the offer was made in a letter or email then it was written Implicit premises The offer was written The offer was made in a letter If the offer was made in a letter or email then it was written

If the offer was made in a letter or email then it was written Implicit premises The offer was written The offer was made in an email If the offer was made in a letter or email then it was written

Manslaughter Intent Killed Recklessness Collision Victim died Caused by collision Drove 180 where max 80 Police radar Witness: “collision” Police report: “collision” Report coroner Report coroner Computer log file

Manslaughter Intent Art. 287 CC Killed Recklessness Collision Victim died Caused by collision Drove 180 where max 80 Police radar Witness: “collision” Police report: “collision” Report coroner Report coroner Computer log file

Causing a collision in consequence of which someone dies is killing Manslaughter Intent Art. 287 CC Killed Causing a collision in consequence of which someone dies is killing Recklessness Collision Victim died Caused by collision Drove 180 where max 80 Police radar Witness: “collision” Police report: “collision” Report coroner Report coroner Computer log file

Manslaughter Intent Art. 287 CC Killed Recklessness Collision Driving 180 where maximum speed is 80 is consciously taking the risk of a collision, which is Recklessness Intent Art. 287 CC Killed Recklessness Collision Victim died Caused by collision Drove 180 where max 80 Police radar Witness: “collision” Police report: “collision” Report coroner Report coroner Computer log file

Police radars are a reliable source of information on speed Manslaughter Intent Art. 287 CC Killed Recklessness Police radars are a reliable source of information on speed Collision Victim died Caused by collision Drove 180 where max 80 Police radar Witness: “collision” Police report: “collision” Report coroner Report coroner Computer log file

Manslaughter Intent Art. 287 CC Killed Recklessness Collision Victim died Caused by collision Drove 180 where max 80 This type of computer log file is a reliable indicator of what the radar has measured Police radar Witness: “collision” Police report: “collision” Report coroner Report coroner Computer log file

Two important features of arguments Arguments can be constructed step by step These steps often leave rules or generalisations implicit When testing arguments, they must be made explicit to reveal sources of doubt They can be unfounded They can have exceptions

Arguments and counterarguments

Three types of counterarguments (Basic) arguments have: Premises (grounds) A conclusion A reasoning step from the premises to the conclusion So arguments can be attacked on: Their premises Their conclusion The reasoning step from premises to conclusion Except if deductive

Deductive vs defeasible arguments Documents that look like avidavits usually are avidavits This document looks like an avidavit Therefore this is an avidavit All men are mortal Socrates is a man Therfore, Socrates is mortal

Deductive vs defeasible arguments Documents that look like avidavits usually are avidavits This document looks like an avidavit Therefore (presumably) this is an avidavit All men are mortal Socrates is a man Therefore, Socrates is mortal

Attack on conclusion Smoking increases the chance of cancer Smoking does not increase the chance of cancer E1 says so E1 is oncologist E2 says so E2 is oncologist

Attack on premise Smoking increases the chance of cancer E1 says so E1 is oncologist E1 only says that there is no evidence that smoking does not increase the chance of cancer Fragment 1 experts examination report

Attack on premise is often attack on intermediate conclusion Smoking increases the chance of cancer E1 says so E1 is oncologist E1 only says that there is no evidence that smoking does not increase the chance of cancer Fragment 2 experts examination report Fragment 1 experts examination report

Attack on inference step Smoking increases the chance of cancer Smoking does not increase the chance of cancer E1 says so E1 is oncologist E2 says so E2 is oncologist E2 is biased E2 is paid by Marlboro Experts are often biased towards who pays them

Attack on conclusion (Monge) If a person cannot be fired in malice and and s/he was fired fired, then firing him/her is a breach of contract If a person can be fired for any reason or no reason at all and s/he was fired, then firing him/her is not a breach of contract Firing Olga Monge was no breach of contract Firing Olga Monge was breach of contract Olga Monge can be fired for any reason or no reason at all … Olga Monge cannot be fired in malice … Olga Monge was fired Olga Monge was fired in malice If a person is employed at will then he or she can be fired for any reason or no reason at all Olga Monge was employed at will Employees cannot be fired in malice Olga Monge was employed

Attack on premise (Monge) Firing Olga Monge was no breach of contract Firing Olga Monge was breach of contract Olga Monge can be fired for any reason or no reason at all … Olga Monge cannot be fired in malice … Olga Monge was fired Olga Monge was fired in malice If a person is employed at will then he or she can be fired for any reason or no reason at all Olga Monge was employed at will Employees cannot be fired in malice Olga Monge was employed

Evaluating arguments Does each step instantiate an acceptable argument form/scheme? See next sessions Have all its counterarguments been refuted? Are its premises acceptable? If defeasible: what about attacks on inference or conclusion? (Has the search for counterarguments been thorough enough?) Can be indirect When is an argument “good”? A conventional answer is that it has to be deductively valid and have true premises. However, in a trivial sense all arguments can be deductively valid by adding “if other premises then always the conclusion” but this implicit premise is often plainly false. Often what is true instead is the weaker premise “If other premises then normally/usually/typically the conclusion”.

Justifying your argument: refute every attack for claim Proponent: Proponent of argument must strictly defeat opponents arguments, Opponent may weakly defeat proponent’s arguments Argument A weakly defeats argument B if A attacks B and is not weaker than B Argument A strictly defeats argument B if A attacks B and is stronger than B 28

Justifying your argument: refute every attack for claim Proponent: Opponent: Defeater 1 Defeater 2 29

Justifying your argument: refute every attack for claim Proponent: Opponent: Defeater 1 Defeater 2 Strict defeater 1.1 Strict defeater 2.1 Proponent: 30

Justifying your argument: refute every attack for claim Proponent: Opponent: Defeater 1 Defeater 2 Strict defeater 1.1 Strict defeater 2.1 Proponent: Opponent: Defeater 2.1.1 Defeater 2.1.2 31

Justifying your argument: refute every attack for claim Proponent: Opponent: Defeater 1 Defeater 2 Strict defeater 1.1 Strict defeater 2.1 Proponent: Opponent: Defeater 2.1.1 Defeater 2.1.2 Proponent: Strict Defeater 2.1.1.1 Strict defeater 2.1.1.2 32

Proponent: Opponent: Defeater 1 Defeater 2 Strict defeater 1.1 Strict Murder Killing Intent R1 Proponent: Opponent: Defeater 1 Defeater 2 Strict defeater 1.1 Strict defeater 2.1 Proponent: Opponent: Defeater 2.1.1 Defeater 2.1.2 Proponent: Strict Defeater 2.1.1.1 Strict defeater 2.1.1.2 33

Proponent: Opponent: Defeater 1 Strict defeater 1.1 Strict Murder Killing Intent R1 Selfdefence Threat to life R2 Killing R3 Exception to R1 Knife W1 says “knife” Proponent: Opponent: Defeater 1 Strict defeater 1.1 Strict defeater 2.1 Proponent: Opponent: Defeater 2.1.1 Defeater 2.1.2 Proponent: Strict Defeater 2.1.1.1 Strict defeater 2.1.1.2 34

Summary and outlook Arguments are constructed by combining applications of inference rules into inference trees Some inference rules are deductive Only premise attack Other inference rules are defeasible/presumptive Also inference and conclusion attack ‘Standard’ logic identifies the deductive inference rules Sound and complete wrt semantics Argumentation theory / epistemology identify defeasible inference rules What justifies them? Dialectical evaluation of arguments can be formalised Argument construction Refutation of counterarguments