Understanding Deductive Validity and Argument Patterns: Beyond Reasonable Doubt, Summaries of English Literature

Deductive validity and various patterns of argument, using examples to illustrate the concepts of chained conditional sentences, affirming the consequent, and denying the antecedent. The text also explores the idea of proof beyond a reasonable doubt and its significance in legal contexts.

Typology: Summaries

2018/2019

Uploaded on 05/29/2022

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I will talk about Deductive validity and patterns of argument, proved beyond
reasonable doubt, Shown to be more likely than not on the balance of evidence
and lastly summarizing the presentation in a few sentences.
Firstly, I will talk about some patterns or structures of argument that will be deductively
valid whatever its subject matter.
There are three cases in particular.
Case I
If A then B and if B then C and if C then D, so if A then D
If the consumption of petrol by cars across the world is not significantly reduced soon,
exhaust emissions will continue to damage the ozone layer. If this happens the
incidence of skin cancer will increase considerably and if this happens deaths from skin
cancer will increase, so if worldwide petrol consumption is not reduced skin cancer
deaths will increase.
This type of structure forms a chain of conditional sentences. It’s a series of connected
premises. where the First thing is connected to a second, and the second to a third, so
the first is ultimately also connected to the third.
This was the example from our book. Now I am gonna give you my personal example.
But no matter what, I again eat chatpate and the cycle repeats.
Case II
Now the second case is
Basically, the argument states that, given a first thing, a second thing is true. It then
AFFIRMS that the first thing is true. So, the second thing must also be true. If A then B
and A is true, so B must be true,
Eg - “If you have a driver’s license, then you must have taken the driver’s test.
You do have a driver’s license. So, you must have taken the driver’s test.
Let’s take example of Shiraf’s dog Nemo again,
If Nemo wags his tails, then he is happy.
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I will talk about Deductive validity and patterns of argument, proved beyond reasonable doubt, Shown to be more likely than not on the balance of evidence and lastly summarizing the presentation in a few sentences. Firstly, I will talk about some patterns or structures of argument that will be deductively valid whatever its subject matter. There are three cases in particular. Case I If A then B and if B then C and if C then D, so if A then D If the consumption of petrol by cars across the world is not significantly reduced soon, exhaust emissions will continue to damage the ozone layer. If this happens the incidence of skin cancer will increase considerably and if this happens deaths from skin cancer will increase, so if worldwide petrol consumption is not reduced skin cancer deaths will increase. This type of structure forms a chain of conditional sentences. It’s a series of connected premises. where the First thing is connected to a second, and the second to a third, so the first is ultimately also connected to the third. This was the example from our book. Now I am gonna give you my personal example. But no matter what, I again eat chatpate and the cycle repeats. Case II Now the second case is Basically, the argument states that, given a first thing, a second thing is true. It then AFFIRMS that the first thing is true. So, the second thing must also be true. If A then B and A is true, so B must be true, Eg - “If you have a driver’s license, then you must have taken the driver’s test. You do have a driver’s license. So, you must have taken the driver’s test. Let’s take example of Shiraf’s dog Nemo again, If Nemo wags his tails, then he is happy.

Now Nemo is wagging his tail then we can say that he is happy. Case III If A then B but B is false, so A must be false too. Basically, the argument states that, given a first thing, a second thing is true. It then DENIES that the second thing is true. So, the first thing must also not be true. Eg - If there is smoke, there is fire. There is no fire, so there is no smoke. Another example can be If I take a bath, I will wear clean clothes. If I haven’t worn clean clothes, I haven’t taken a bath. Proved beyond reasonable doubt So let us look now at arguments which prove their conclusion beyond a reasonable doubt. Ram is your greediest friend. And he was left alone in your room. Now your earphone is missing. On top of that he was seen with the same earphone the other day. Chances are that Ram is the one who stole the earphone. We cannot prove that by giving a deductive argument. In court of law too, we cannot only expect deductive arguments. It would be much too demanding and we would almost never be able to put criminals in jail. Instead, cases have to be established beyond reasonable doubt, so that we are very confident in our conclusions, even though we are aware that we might be wrong. Let’s look at this famous real life example of a murder case. The bodies of Nicole Brown Simpson and Ronald L. Goldman were found outside the house of Nicole. Simpson was accused of the brutal murder of his ex-wife, Nichole Brown Simpson, and her friend Ronald Goldman. According to the lead prosecutor, when he called O.J. to inform him that his ex-wife was dead. O.J.'s first response? Quote, who killed her, end quote. O.J. was charged with two counts of murder, Evidence found at the crime scene included a blood-stained glove left by the suspected killer, a knitted hat, and a bloody footprint.

I know you’re an army doctor and you’ve been invalided home from Afghanistan.I know you’ve got a brother with a bit of money who’s worried about you, but you won’t go to him for help because you don’t approve of him - possibly because he’s an alcoholic, more likely because he recently walked out on his wife. And I know that your therapist thinks your limp is psychosomatic - quite correctly, I’m afraid. That’s enough to be going on with, don’t you think? Tanned face, haircut, your conversation as you entered the room Bit different from my day, his phone Notice that there is nothing conclusive about Holmes’s reasoning, however impressive it may be. His reasoning is certainly not deductively valid. Holmes is arguing from past experience to present judgements, or arguing on the basis of ‘the balance of probabilities’. There is sufficient proof of all these conclusions according to Sherlock Holmes but not complete proof. Mathematically proof on a balance of probabilities is 50.1% likelihood of something having occurred. You see the scales of justice. They are evenly balanced. Both sides are the same height. But if one side has the weight of a feather added to it, causing it to go down and the other side to go up. Now that side with the weight of a feather has won. Proof greater than that is not required. Conclusion So, how do we make sure that we’re ruled by good, sound, not-flawed reasons? By perfecting the art of the argument. Probably the most familiar, and the easiest argument to carry out, is the deductive argument. The main rule of deductive arguments is: if your premises are true, then your conclusion must be true. And knowing that something is actually true is very rare, and awesome. The reason that deduction is prized by philosophers -- and lots of other important kinds of thinkers-- is that it’s the only kind of argument that can give you a real certainty. What’s great about deductive arguments is that the truth of the premises must lead to the truth of the conclusion. Thus, the standard for judging whether an inference is deductively valid is: Can you think of any way the reason(s) could be true and the conclusion false (however unlikely)? The standard for deciding whether an inference is ‘proved beyond a reasonable doubt’ is: If the reasons are true (or otherwise acceptable), is there a reasonable doubt about whether the conclusion is true?