When to Write Out Contrapositives Forum

[AntipodeanPhil]

If this is a dummy question, my apologies.

Do you guys write out the contrapositives during setup for ALL games with conditionals? I'm starting to think it's a waste of time for pure linear games, and for combination games where ordering is clearly the more important element (I just did preptest 30, game 2, and the contrapositives did nothing but get in my way). Any thoughts on the advantages/disadvantages?

EDIT: since opinions seem to be split, I thought I would add a poll.

[dakatz]

If this is a dummy question, my apologies.

Do you guys write out the contrapositives during setup for ALL games with conditionals? I'm starting to think it's a waste of time for pure linear games, and for combination games where ordering is clearly the more important element (I just did preptest 30, game 2, and the contrapositives did nothing but get in my way). Any thoughts on the advantages/disadvantages?

I pretty much write it out every time I can. Its just an additional rule, and while it is merely the flipside to the rule you already have, I'm a visual person so it never hurt to write it down next to the actual rule.

[AntipodeanPhil]

I've found they don't help me much for pure linear games - for conditions like "if Tom is fourth, Brad is not second." In those cases, I can easily read the rule back-to-front.

But for games where the grouping element is dominant, I need to write out the contrapositives to see the ways in which all the conditionals connect up.

Do you ever find them getting in the way during your setup, dakatz, or do I just need to organize things better?

[soj]

I write out the contrapositives if I suspect there might be conditional chains. I always diagram contrapositives on my IN/OUT column diagrams. I often write out the contrapositives to complex conditionals involving AND or OR. Other times, I don't bother.

[AntipodeanPhil]

I write out the contrapositives if I suspect there might be conditional chains. I always diagram contrapositives on my IN/OUT column diagrams. I often write out the contrapositives to complex conditionals involving AND or OR. Other times, I don't bother.

Curious. Perhaps I should be doing that. The only time when not writing contrapositives hurt me was for a game in which the central inferences involved conditional chains.

[tomwatts]

I generally write contrapositives for just about everything, except the occasional "If H is immediately before J, then Q is after both R and S" kind of thing, where it would get really messy. But for just about everything else, it takes literally seconds, so why not. Can be helpful.

[dr123]

I write out every contrapositive. You might miss a deduction if you dont write em all out

[Sloth Hero]

Coming from my limited LG experience: I've only written out the contrapositive if the variables used for the consequent/antecedent are re-used later.

Can't miss that hypothetical syllogism though. If it's there, it's probably at least key to one question. Most likely more.

[Sloth Hero]

I generally write contrapositives for just about everything, except the occasional "If H is immediately before J, then Q is after both R and S" kind of thing, where it would get really messy. But for just about everything else, it takes literally seconds, so why not. Can be helpful.

And the transposition of this would be fast.

(H,J) ⊃ ((R&S)<Q)) = If it's the case that H is immediately before J, then R and S are before Q.
~((R&S)<Q) ⊃ ~(H,J) = If it's not the case that both R and S are before Q, then its not the case that H is immediately before J.

[YaSvoboden]

For in/out games I would say definitely do them all. For a conditional in a linear game I like to just do a setup where it is true and one where it isn't true. This isn't always the best solution, like when you have multiple conditional statements in a linear game, but I find it works pretty well and makes it very easy to look at. Definitely the right choice if the conditional is connected with other rules in some way.

[AntipodeanPhil]

Coming from my limited LG experience: I've only written out the contrapositive if the variables used for the consequent/antecedent are re-used later.

Can't miss that hypothetical syllogism though. If it's there, it's probably at least key to one question. Most likely more.

So you and soj agree - only write out contrapositives for games involving chains / hypothetical syllogisms - but dr123 and tomwatts write out all contrapositives. Hmmm.

I certainly agree that the LSAT makers seem to love testing chain spotting - especially if they have hidden half the chain in a contrapositive.

[AntipodeanPhil]

For a conditional in a linear game I like to just do a setup where it is true and one where it isn't true. This isn't always the best solution, like when you have multiple conditional statements in a linear game, but I find it works pretty well and makes it very easy to look at.

Curious. I only do that if I think the conditional will be the deal deal / cental rule / whatever one calls it.

[Sloth Hero]

For in/out games I would say definitely do them all. For a conditional in a linear game I like to just do a setup where it is true and one where it isn't true. This isn't always the best solution, like when you have multiple conditional statements in a linear game, but I find it works pretty well and makes it very easy to look at. Definitely the right choice if the conditional is connected with other rules in some way.

I don't understand what you mean by "one where it is true and one where it isn't true"

The only way a conditional isn't true is if you reason from true antecedent to a false consequent.

F ⊃ T = T
T ⊃ T = T
F ⊃ F = T
T ⊃ F = F

And i dont see the point of creating a setup where T ⊃ F

but i probably misinterpreted your post

[AntipodeanPhil]

I don't understand what you mean by "one where it is true and one where it isn't true"

The only way a conditional isn't true is if you reason from true antecedent to a false consequent.

F ⊃ T = T
T ⊃ T = T
F ⊃ F = T
T ⊃ F = F

And i dont see the point of creating a setup where T ⊃ F

but i probably misinterpreted your post

I'm sure your logic professor would be pleased to see this .

YaSvoboden means "one where the antecedent is the case and one where the antecedent is not the case." Of course, it would be crazy to question the conditional.

[YaSvoboden]

For in/out games I would say definitely do them all. For a conditional in a linear game I like to just do a setup where it is true and one where it isn't true. This isn't always the best solution, like when you have multiple conditional statements in a linear game, but I find it works pretty well and makes it very easy to look at. Definitely the right choice if the conditional is connected with other rules in some way.

I don't understand what you mean by "one where it is true and one where it isn't true"

The only way a conditional isn't true is if you reason from true antecedent to a false consequent.

F ⊃ T = T
T ⊃ T = T
F ⊃ F = T
T ⊃ F = F

And i dont see the point of creating a setup where T ⊃ F

but i probably misinterpreted your post

Basically if it says if m is 3rd then n is 6th set up a diagram where the conditions are met and another where m cannot be third. If setting up a second diagram will take more than a few extra seconds then make sure there are questions that involve it, but odds are there will be at least one, in which case you will probably need to think through the consequences of the condition being met anyway and it really doesn't take more time.

This isn't exactly writing out the contrapositive, but it can make answers very obvious when you are going through the questions.

Edit: Phil got what I was saying.

[Sloth Hero]

I get it now, was confused

But this would only be practical for a rule set with 1 conditional/syllogism, correct?

[AntipodeanPhil]

I get it now, was confused

But this would only be practical for a rule set with 1 conditional/syllogism, correct?

YaSvoboden states that this might not be a good idea where there is more than one conditional. My view is that it depends on the nature of the conditional.

Suppose you were diagramming a game with 7 variables, 4 of which must be "in" and 3 "out." If you came across a conditional like:

A v B --> C + D

And also some less significant conditionals (e.g., ~E --> F), I would produce two templates for the first conditional (one for ~(A v B), one for A/B), because I would guess that it would be central to understanding game.

[flexityflex86]

If this is a dummy question, my apologies.

Do you guys write out the contrapositives during setup for ALL games with conditionals? I'm starting to think it's a waste of time for pure linear games, and for combination games where ordering is clearly the more important element (I just did preptest 30, game 2, and the contrapositives did nothing but get in my way). Any thoughts on the advantages/disadvantages?

personally, i can normally see the contrapositive in my head when i write the logic statement. i only write the contrapositive when there are two necessary conditions like if A then B and C or when a negative leads to a positive like if I see if not A then B, I'll write, "always a/b or both."

i believe when you're ready to take the LSAT, contrapositives will be such a part of your subconscious you should never really need to write them - you should just immediately read a statement as both. that said, i use formal logic throughout LR too because it takes all the bullshit confusing language they throw in, and simplifies it all into two word statements.

[AverageTutoring]

Always, always, always write them out. If for no other reason then because doing so increases your familiarity with the rules which decreases the time it takes to make deductions when going through questions. In particular, IN/OUT games mandate you jot down the contraposative.

[SanDiegoJake]

Always, always, always write them out. If for no other reason then because doing so increases your familiarity with the rules which decreases the time it takes to make deductions when going through questions. In particular, IN/OUT games mandate you jot down the contraposative.

I agree wholeheartedly. Always. Always. Always.

[Jeffort]

Always, always, always write them out. If for no other reason then because doing so increases your familiarity with the rules which decreases the time it takes to make deductions when going through questions. In particular, IN/OUT games mandate you jot down the contraposative.

I agree wholeheartedly. Always. Always. Always.

^ This

By keeping yourself in the habit of always writing out the contrapositive of each given conditional you force yourself to think about it, which decreases the possibility that you will overlook considering whether it is applicable to a given question/circumstance.

It doesn't take much time (1 second) to do, nor does it take up much space if you keep things organized.

I always write it out below the diagram of the rule and slightly indented so it's apparent that it is the contrapositive rather than a different rule:
A ---> B
~B ---> ~A