# data[].attributes.body
Here is a funny little link in case you feel you need to rehearse the basics to get clear on them or if you want to share why this is important with a friend or teach them at least the very basics:
http://junkee.com/five-steps-arguing-internet-according-philosophy/89645?utm_content=bufferc5fcd&utm_medium=social&utm_source=facebook.com&utm_campaign=buffer

# data[].attributes.body
I feel like I need to somewhat clarify this here since so few attended today's seminars. So, previously, I stated how having at least one row where all the premises are true is a sort of a criterion for validity because unless you have one, you are working with a contradiction which is just never a good thing.

Thing is, traditional logic considers contradictions valid (as stated in the whole 'technically still valid' part of what was taught earlier). You will probably be best off by stating that what you have is a contradiction which is vacuously valid because it has no rows where the premises are true and the conclusion false. It is not the sort of 'valid' which constitutes one of the conditions for soundness, though, since with vacuous validity, you can never have a set of true premises (the other criterion). But technically speaking, contradictions are valid for each and every conclusion.

# data[].attributes.body
Would the proposition, " ¬(P & ¬Q)" mean that it is "not the case that there is P and not Q"?

Sami's Answer:
That depends on the scope of the 'not the case that' (i.e. whether it only includes P or also not-Q). However, pragmatically speaking, it would mean the latter since the alternative (¬P & ¬Q) could just be stated as 'not-P and not-Q'. Natural language handles problems of scope like this pretty badly.

One even more explicit alternative would be 'it is not the case that both P and not-Q'. Also, the 'there is' in the original formulation is a bit problematic since P and Q are not entities/objects but rather, propositions/statements.

# data[].attributes.body
For those interested in, for example, the logical equivalence rules touched upon today but which are not a proper part of the module's curriculum, here is a table to work them out:
http://integral-table.com/downloads/logic.pdf
For notation in *this* table (not a truth table),
T = Tautology (necessary truth)
F = Contradiction (necessary falsehood)

# data[].attributes.body
Please can you explain questions A2 and A4?

Sami's Answer:
With pleasure. I think these examples are genuinely hard to understand until you wrap your head around the general logic rather than try and find simple heuristics.

The simple answer is that the use of 'only if' makes these sentences in which the part immediately after is a necessary condition for the other claim. This would be expressed by having the claim after 'only if' be the consequent.

More specifically, the order of the parts of a conditional claim in a sentence does not matter. Only these claims' relation to the 'if' clause matters, and that may be expressed in different ways (or even be left wholly implicit). Now, just looking for an 'if' does not suffice either because one must look at the meaning of the whole. There are ways to quantify over the 'if', including the use of 'only if' instead. Such quantification changes the meaning of the expression and thus, the logical relations it expresses. The use of 'only if' changes the role of what comes after compared to a simple 'if' which would normally be followed by the antecedent (regardless of where in the whole sentence this clause is located). 'Only if' will be followed by the consequent, regardless of where in the sentence this clause is located, because that is the way propositional logic expresses this type of necessary condition relation between two claims.

So, as I stated during the seminar, the same symbol is used because that symbol is able to express both sufficient and necessary conditions, depending on the direction which it is being read. The obvious way is to read it from left to right (and the arrow even goes that way) but necessarily, if that sufficiency relation holds, there will be a corresponding necessitation relation the other way around.

To take A4, the more specific answer would be:
A: Yasmin will get 100%.
B: Yasmin attempts all the questions.
A -> B

Using these values, A -> B means 'If Yasmin will get 100%, she has attempted all the questions' (tenses need to be adapted some of the time). This means that if she scores 100%, it will necessarily be the case that she has attempted all the questions because scoring 100% is sufficient evidence to prove that fact.

Consequently, only if Yasmin has attempted all the questions, can she score 100%. She does not necessarily manage that because she might have been wrong in places but attempting all is an enabling (i.e. necessary) condition. And once again, this returns to the fact that if she indeed scores 100% then she can only have managed that by attempting all the questions so it must be true that if she scored 100%, she must have attempted all the questions.

That roundabout will continue and continue because the two sides belong to the same coin. As stated above, the only way to understand why these exercises work the way they do is by reflecting on this connection between sufficiency and the necessity it entails (and the sufficiency entailed by necessity).

In other words, think about some simple examples and try to abstract the relation between the two parts of a condition. For example, a house fire is sufficient to produce smoke. If there is a house fire, there is smoke. Thus, if there is no smoke, there cannot be a house fire.

# data[].attributes.body
https://www.youtube.com/watch?v=rcyeHdx0Qv4 (3.00 venn diagram of a syllogism - just for anyone who didn't grasp *optional* venn diagrams like me today)

# data[].attributes.body
Can a conclusion be implied?

Sami's Answer:
Yes. As noted in 'Non-Declarative Premises?', sometimes key propositions - including the conclusion itself - might be expressed through indirect means. Also note the ambiguity of 'imply' since there is a sense in which conclusions are always implied. I take it the question is about the conclusion being expressed implicitly.

As a brief example, consider the following argument:
"If the vast majority of experts agree on global warming being real, it should be assumed to be happening. Were global warming to be happening, nations should take drastic preventative measures as well as precautions if they at all care about the future of people. As such, I wonder what the inaction by most governments tells about them, then."

I recommend trying to put that in standard form.

# data[].attributes.body
This came up in personal communication. People were asking whether a premise could be non-declarative in a text.

The answer is that in a text, one may convey a statement via indirect means. For example, an use of a rhetorical question might be obviously intended to hint at the assumed correct answer which might be used as a premise (or even the conclusion). An imperative sentence  might make a normative statement about what should be done, generally speaking.

However, in a standard form, one must use the declarative propositions conveyed via these indirect means. This requires paraphrasing and interpretation which means one might want to support their interpretation by explaining it with the help of textual evidence.

# data[].attributes.body
What is the main difference between the confirmation bias and the representativeness heuristic?
Both seem to be about making a split decision based on past experiences? (like an inductive argument)

Sami's Answer:
Categorically, both are cognitive bias, i.e. heuristic (= relatively reliable for some purpose but only to some flawed yet practically sufficient degree) elements in reasoning. You are right that both apply to forms of inductive reasoning but they embody a problematically unreliable form of it. Similarly, there is the 'inductive fallacy' which is making an unjustified assumption about an experienced pattern holding. The fact such assumptions are one's default attitude is a heuristic which leads to a bias. Mistaking correlation with causation is an example fallacious result, such as when one thinks their lucky trinket is the reason for their success because it was observed to be present whenever one was successful.

As for their differences, confirmation bias is the tendency to overvalue confirming evidence and undervalue instances to the opposite. Again, for a person to trust their lucky trinket, they likely think only of the cases where they succeeded and it was present rather than the ones where they failed despite it having been present. It is a contributing factor to bad reasoning and can only apply when there are both confirming and disconfirming instances to be processed.

Meanwhile, the representativeness heuristic is fairly different in the way it operates. It is the tendency to overvalue a match with one's representation (conception) of something over statistical probability. While this is a bit harder to connect to the example, one might think of a person with a rabbit's leg for their lucky trinket and then approximate that they are more likely to be a superstitious and a gambler rather than just a superstitious person because rabbit legs as lucky trinkets are specifically associated with gamblers. However, all superstitious gamblers are superstitious people but not vice versa, so them belonging to the latter group is objectively more likely regardless of any contributing factors. Note that the representation does not require there to have been any confirming instances to cause this effect, although oftentimes the strong association does stem from stereotypical thinking which is also linked to the confirmation bias that feeds it.

# data[].attributes.body
How do people work out the question: 'If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?' - on PP wk3 Fallacies.

Sami's Answer:
Remember that this is simply an illustration of how people tend to at first apply invalid reasoning strategies to abstract problems. In this case, one just needs to realize how by those parameters, each machine produces a widget in 5 minutes. Thus, the answer is 5 minutes since each machine need just produce one widget. Where people might go awry is thinking that each factor correlates with the others when they initially have identical values while in reality, only some are relevant.

# data[].attributes.body
Anyone else had a look at the assessment and think it's a huge jump from what we've been learning in lectures/seminars? I'm finding it difficult to even understand the arguments in the first section (section A).

Sami's Answer:
While this is technically not related to the type of content to be discussed, I think addressing any such worries holds value. Fact is, these are harder exercises but they utilize the same logic regardless. I take it no one would prefer to be thrown in the deep end from the beginning, and, on the other hand, we must advance the level requires of you to real life examples. The assignment integrates the level of complexity real life holds, and I take it the level within that scope has been chosen based on the amount of time available before the turn-in date.

However, I understand the worry. The best I can do to alleviate it is to advice looking at the big picture first before reverse-engineering what constitutes it. All the tools have been provided but applying them appropriately takes practice.

# data[].attributes.body
Here is the link, as promised:
https://bookofbadarguments.com/

# data[].attributes.body
Here are some principles which came up with a student in personal communication. Whenever you are putting arguments to standard form, use these criteria to evaluate whether you have succeeded.

1. Make your formulation as simple as possible: Elegance is a virtue in expressing arguments.

2. The requisite pieces of a standard form are: (i) one or more premises, (ii) a conclusion, and (iii) the appropriate, formal way to express each part and the argument as a whole.

3. Use whole, and independently complete propositions.