@ "Except" is not always a biconditional.

Consider: No apples except red ones are edible. This expresses something like "apple & edible → red". However this does *not* mean "red → apple & edible". After all, firetrucks are also red.

Here are some academic sources that support this: http://home.uchicago.edu/~ck0/classes/nu/C72/W99/translations.html and http://legacy.earlham.edu/~peters/courses/log/transtip.htm

@

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I have noticed while going through the SA and PSA questions that the answer choice must have the conclusion in the necessary condition.

This isn't true. I semi-randomly looked at three recent SA questions -- 77.4.24, 77.4.20, and 76.2.22 -- and none of the correct answer choices even mentioned the conclusions of the arguments.

This can be a pretty thorny philosophical question, but for the purposes of LSAT RC, I think it's helpful to think about the different attitudes an author might have towards a hypothesis vs. a thesis.

Someone's hypothesis is something like a working conjecture, and not something he/she is committed to. A hypothesis has some support, but the goal is to investigate it further and possibly reject it if the collective weight of the evidence demands it.

Someone's thesis, on the other hand, *is* something he/she is committed to. The author's goal isn't to investigate a thesis, but to defend it by offering evidence and whatnot to support it.

Whether a claim is a hypothesis or a thesis will depend on context. For example, consider the claim that gun restrictions reduce gun violence. If the author talks about an experiment he/she will conduct on gun laws in a small community or his/her plan to analyze historical data on gun laws and crime statistics, then the claim is acting as the author's hypothesis. If, on the other hand, the author cites a number of studies that have found correlations between gun control and lower gun violence and explains why gun control would causally lead to lower violence, or something like that, then the claim is acting as the author's thesis.

@ logic is just a branch of mathematics

Oh man, don't tell the mathematicians this.

There's a somewhat famous story about Paul Cohen (mathematician) looking down on logicians and trivializing their work. In response, some logicians challenged him to answer one of the unsolved problems of logic at the time: is the continuum hypothesis independent of ZFC? To their dismay, Cohen took their challenge and proved that the continuum hypothesis was indeed independent of ZFC, developing a completely novel (and now widely used) technique called forcing in the process!

In any case, I think this discussion about whether logic is more math or philosophy is pretty irrelevant to the original question because LSAT logic games have little to do with the academic study of logic in the first place. Rather, the kind of precise, rigorous thinking involved in solving LGs is similar to the kind of thinking involved in studying logic/math/CS/related fields.

I think this is all too convoluted. Much simpler to just understand that, classically, "A→B" is equivalent to "~A or B".

So for "~A→B", this is equivalent to "~~A or B", which is in turn classically equivalent to "A or B". This means at least one of A and B must be in.

And for "A→~B", this is equivalent to "~A or ~B". This means at least one of A and B must be out.

This is simpler than having to remember another mnemonic and involves a deeper understanding of how the LSAT treats conditionals.

You need to use context to disambiguate the scope of the negation. For this question, the second sentence clarifies the scope by saying "Once sterilized and properly sealed, **HOWEVER**, it contains no bacteria." The "however" links together the first and second sentences, and because we see that "sterilized and properly sealed" are together in the second sentence, we're able to figure out that the two are together in the first sentence as well. Thus, the negation in the first sentence takes wider scope over the conjunction, i.e. not(sterilized and sealed).

Sufficient and necessary conditions are features of conditional statements ("if P, then Q"), whereas premises and conclusions are features of arguments ("P. Therefore, Q").

In classical logics, there's something called the deduction theorem (https://en.wikipedia.org/wiki/Deduction_theorem) which intimately relates these two things, i.e. "if P, then Q" is valid iff "P. Therefore, Q" is valid.

On the LSAT, you won't really need to understand this nuance. Sufficient conditions are analogous to premises, and necessary conditions are analogous to conclusions. They're not exactly the same (conditional statements are truth-apt, arguments aren't), but conceptually, it may help to understand the analogy between the two.

I think redoing games loses its effectiveness past a certain point (for me, this is around 3 times) for exactly the reason you cite. There's really nothing that beats doing fresh games. If you're almost out, you can look for unofficial games via some LSAT prep course blogs; I know Manhattan has some self-authored games, and I suspect most of the big prep companies do as well.

I was also worse at grouping games than sequencing games, so I made it a point to cultivate good grouping game habits while practicing, such as paying special attention to whether the out group is full or making it a point to make big inferences upfront (e.g. If A cannot be with B and A cannot be with C, and if there's only one out slot, you automatically place B, C in and A out).

I personally think grouping games are more difficult than sequencing games because you need to rely on your working memory for the former more than the latter; a proper diagram makes most sequencing games trivial, but even with a good grouping diagram, you usually still need to remember that if A is in, B is out, and that one of C and D must be in, and so on. Unfortunately, I dunno how to train working memory, and some sources I read suggest that this is just developed in childhood, but maybe you'll have better luck researching this than I have. I think this is why it's important to do big inferences upfront, so that you have fewer pieces to juggle in your working memory.

@ That’s really interesting. Totally makes sense.

@

, you aware of any LSAT questions hinging on this distinction?

I'm sure there have been generic sentences in, say, some of the RC passages, but I've never seen a question that you would miss if you didn't know what generics were. The writers are usually pretty explicit in the LR section, and when this distinction would matter, I've only ever seen the writers use universals.

@ A year ago I would've taken on the challenge to defend my boy, Kripke. But having just spent 20,000 words arguing that A Puzzle about Belief is not really a puzzle, I'm less inclined to die on the hill of Kripke-fandom, haha.

Funnily enough, I feel the same way. As controversial as Naming and Necessity is, I think it gets a lot of things right, and I think the attack on descriptivism is brilliant. However, then I find out the same person who wrote Naming and Necessity also wrote Wittgenstein on Rules and Private Language, and I wonder how he could have gone so wrong.

@ For these reasons, I cannot infer from the generic statement "small animals move more rapidly than large animals" that

all

small animals share that ability. The quantity of small animals that move more rapidly than large animals is uncertain. Thus, I cannot equate the original generic statement to the universal statement "all small animals move more rapidly than large animals."

Right.

@ So in negating this generic, we simply negate it to "it's not the case that (gen) small animals move more rapidly than large animals," from which we can infer that an unspecified quantity of small animals must either move equally rapidly or less rapidly than large animals.

This is close, but not quite there. If the original statement were simply "small animals move more rapidly than large animals", then this would be spot on. However, the original generic was a modal statement, i.e. "small animals CAN move more rapidly than large animals". The negation of this negates the possibility, i.e. "small animals CANNOT move more rapidly than large animals" or "IT'S NOT POSSIBLE that small animals move more rapidly than large animals". From this, we are able to infer that NO small animals move more rapidly than large animals. What licenses this inference isn't the (gen) operator, but the negation of the modal operator "can".

It might help to think about a more intuitive analogue. Let's revisit "humans give live birth". This sentence is a generic because, while true, it's not saying that ALL humans give live birth. Now, let's modify this sentence with the modal operator "can", i.e. "humans CAN give live birth". Again, this is a generic because, while true, it's not saying that ALL humans can give live birth (males, children, seniors, infertile women, etc. can't give birth).

The negation of "humans CAN give live birth" is "humans CANNOT give live birth". This negation is saying that it's impossible for humans to give live birth, from which we infer that no humans give live birth. Likewise, "small animals CANNOT move faster than large animals" allows us to infer that no small animals move faster than large animals.

@

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Because the author is talking about these animals as sets - small animals and large animals - can we infer that he or she is talking about all small animals and all large animals? Can we thus read this statement as, "All small animals can move more rapidly than large animals can"?

It's not so straightforward. There's an interesting class of statements called "generics", which look like universals on the surface, but are actually quite different. For example, "humans give live birth" might look like a universal, but is in fact a generic. The sentence isn't saying ALL humans give live birth; after all, over 50% of the human population can't give birth at all! There's a lot of debate about how to properly analyze generics, which you can read about here: http://plato.stanford.edu/entries/generics/. The relevant takeaway is that your sentence is probably intended to be read as a generic.

Thus, your sentence, "small animals can move more rapidly than large animals", actually expresses the following proposition: "It's possible that (gen) small animals move more rapidly than large animals". The negation of this is: "It's not possible that (gen) small animals move more rapidly than large animals" (i.e. small animals canNOT move more rapidly than large animals). This is why the explanation tells you small animals must either move more slowly or at the same speed as large animals.

@ I thought that the sentence that contains the condition in which the company allows Ann to leave was a bi-conditional and therefore we could get the contrapositive of the bi-conditional by negating both terms.

Yes, this correct. We do know that the company won't let her leave if it finds out about the fellowship.

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I can also spot a second sufficient assumption: If ann received the offer for fellowship, then the company will not allow her to take a leave of absence.

Yes, this is fine as a sufficient assumption. This, together with the stimulus, makes the argument valid.

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I just wanted to know if this thought process was also correct and that there are other potential sufficient assumptions for this question.

For any argument, there are always infinitely many sufficient assumptions. This is trivially true. Consider the following argument: P. Therefore Q.

What could you assume to make the argument valid? Well, assuming (P → Q) would make it valid. But so would assuming (P → (P → Q)). And so would assuming (P → (P → (P → Q))). And so would assuming (P → (P → (P → (P → Q)))). And so on.

You could also assume (~P or Q), (P ↔ (~P or Q)), (P ↔ (P ↔ (~P or Q))), and so on. You could also also assume (R or ~R) → Q, ((R or ~R) → Q) → Q, and so on. You could even assume (S & ~S), (S & ~~~S), (S & ~~~~~S), and so on.

As you can see, every argument trivially has infinitely sufficient assumptions.

Then there's no need to check every rule for each answer choice.

There are two ways to approach these questions.

The first way is to go through each answer choice and see if the answer choice conforms to every rule. Using this method, you do have to go through every rule for each answer choice until you find a rule that the answer choice violates.

The second way is to go through each rule and eliminate all answer choices that violate the rule. Using this method, you're wasting time by checking every rule for each answer choice. Once you eliminate all the answer choices that violate a rule, you should cross that rule off.

I'm not certain which method you're using based on your post, but it sounds like the first one, in which case you should check every rule for each answer choice until you find a rule that the answer choice violates.

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(~V <---> S) & (V <---> ~S)

This is redundant. The two biconditionals in your conjunct are equivalent.

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So is this a different way of showing the same relationship, if so do you prefer one method over the other?

No, your translation is not equivalent to textbook's and does not say the same thing. Presumably, the textbook is zoning in on the "might" keyword. They're interpreting the sentence to say that Dmitry doesn't have to play either; he just can't play both. Your translation, on the other hand, says the Dmitry must play one and he can't play both.

It's worth noting that their translation

@

said:

(S -> ~V) & (V -> ~S)

is also redundant. Both conditionals in the conjunct are equivalent (they're contrapositives of each other).

I think this is also a case where trying to gerrymander everything into conditionals can be confusing. We think naturally in ANDs and ORs, so converting to ANDs and ORs may be more intuitive for you.

Recall that 'P -> Q' is equivalent to '~P or Q'. So, converting their translation, we have '~S or ~V'. Converting your translation, we have '(S or V) and ~(S and V)'.

I used that watch. It worked fine, but the dial is a bit difficult to turn, so you may want to grow out your nails a bit for the test. Looking back, though, I personally think it was a waste of money, and I would have been fine using any regular analog watch.

If there were a way to figure it out, there would be no point in having an experimental section.

That said, statistically speaking, the scored sections usually add up to 101 questions. This isn't a great indicator, though, because often there are fewer, and occasionally there are more.

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So for example All J are F = (J --> F) and to negate we take the contrapositive (/F --> /J)

The negation of 'J → F' is not '/F → /J'. The contrapositive is logically equivalent to the conditional, so it can't be the conditional's negation. That is, the negation of P is true when P is false and is false when P is true. However, '/F → /J' is true when 'J → F' is true and false when 'J → F' is false.

That said, there are still lots of problems with the way LSAT courses translate quantified sentences. In no logic course would "all J are F" be translated into 'J → F', and I think it hurts students to do this. However, for the sake of this curriculum, you're probably better off just memorizing that the negation of "all" is "some not".

Something to keep in mind is that the February test is undisclosed. So if February is going to be your second take, you won't know which questions you missed and whatnot. This might matter if you end up waiting an application cycle for a third take. On the other hand, if the February test is your third take, it won't really matter that it's undisclosed.

What's at stake here isn't the difference between disproving and contradiction. Rather, what's at stake here is the difference between being contradicted by someone else and contradicting oneself. You can make a decent case that the opponent's claims contradict the proponent's conclusion. However, that doesn't make the proponent's argument SELF-contradictory.

A self-contradictory argument is inconsistent on its own -- it's logically impossible for all of the propositions in the argument to be true at the same time. But this isn't the case for the proponent's argument. We can easily conceive of how all of the propositions in the argument COULD be true at the same time (regardless of whether they are actually true). Moreover, the opponent isn't showing that there's an internal inconsistency with the proponent's argument, but is rather bringing in additional facts that call into question the proponent's claims.

What these terms mean depend on the context.

In formal logic, "contradiction" has a very precise meaning to describe when both P and ~P are the case. This means that you can have inconsistent sets where none of the wffs are contradictions of each other. For example, consider the set of wffs {P, P→Q, ~Q}. This set is inconsistent -- there is no model in classical logic in which all three sentences are true. But there are no contradictions in this set because none of the sentences are direct negations of each other.

On the LSAT, these terms are used more colloquially, so there's not much of a meaningful difference between the two. Counterexamples are usually specific instances which are inconsistent with some general claim(s) -- e.g. "my cat Tom has no hair" is a counterexample to the general claim "all cats have hair". Contradictions are usually a bit broader and apply to any set of inconsistent sentences -- e.g. assuming there's at least one cat, "all cats have no hair" contradicts "all cats have hair". As far as I'm aware, you won't really need to understand the nuances and can treat the two terms synonymously for LSAT purposes.

Well, it's not an argument, so validity doesn't come into play. It's just an imperative sentence, like "open the door".

@ So I understand what you're saying, but just because the author doesn't explicitly state there is an implicit premise in C) doesn't mean there isn't! It could very well be the case that a delay in presentation isn't possible.

This is missing the point. The point is that in order for the stimulus to be valid, we need to assume an implicit premise. However, we don't need to assume anything implicitly to make (C) valid. (C) is already valid by itself. This is a major difference between the stimulus and (C), and this is why (C) is incorrect.

In other words, taking only what's explicitly stated, the argument in the stimulus is invalid. Taking only what's explicitly stated, the argument in (C) is valid. Thus, (C) cannot be parallel.

@ C) does differ from the stimulus in that its conclusion ends with a conditional statement, but I'd rather my conclusion be a summarization of the transitive nature between P1 and P2 (that you can't have optimal decision without a delay in presentation), rather than an absolute as is demonstrated in D) because C) does not provide an absolute conclusion (only that it is unlikely)

This misprioritizes the importance of strength over form. The most important thing for parallel reasoning questions is that the correct answer has the same argument form. But a conditional statement has a completely different logical form than a non-conditional statement, regardless of how strongly stated the non-conditional statement is. That is to say, the conclusion of both the stimulus and (D) can be represented by a single sentence symbol in propositional logic, i.e. '~P'. However, the conclusion of (C) cannot be represented by a single sentence symbol, but must be represented with a conditional, i.e. 'P→Q'. The conclusion of (C) is formally different from the conclusion of the stimulus, and this trumps other considerations such as how strongly stated the conclusion is.

What makes (D) better than (C) isn't the strength of the conclusion. What makes (D) better than (C) is that (C) is just not an instance of the same argument form.

The argument in the stimulus relies on modus tollens (P→Q, ~Q, therefore ~P) with one implicit premise:

P1: stabilize inflation → econ growth decrease

P2: econ growth decrease → full cooperation of world leaders

Implicit P3: ~full cooperation of world leaders

C: ~stabilize inflation

The argument in (C), however, is of the following form:

P1: optimal decision → examine all options

P2: examine all options → delay presentation

C: optimal decision → delay presentation

As you can see, there's no implicit premise in (C), and the argument doesn't rely on modus tollens at all. Rather, the argument in (C) is a hypothetical syllogism (P→Q, Q→R, therefore P→R), and this is a completely different argument form.

For completeness, here is the argument form for (D):

P1: safest vehicles possible → objective structural tests

P2: objective structural tests → huge cost overruns

Implicit P3: ~huge cost overruns

C: ~safest vehicles possible

A very quick way to see why (D) is a better answer than (C) is to note that (C) is an explicitly valid argument. However, without the implicit premise we've assumed for the stimulus and for (D), the arguments are explicitly invalid. Thus, (C) is not parallel to the stimulus.