Reconstructing Arguments
Here is the step-by-step procedure we are going to use to take an argument from prose form and put it into our reconstructed form:
A. Find the conclusion.
B. Find the explicit premises.
C. Add implicit premises or conclusions to make it strictly valid or cogent, consistent with the authors' intentions.
D. Make charitable revisions in language to make the argument valid or cogent if possible, and as strong as possible.
E. Make the language between premises and the conclusion match. If the argument has this form, for instance, "1. If P then Q. 2. P. 3. Therefore, Q" then make P in 1. and 2. match exactly.
F. Put argument into standard form. Number each premise, separate the premises from the conclusion with a line.
G. Add justifications after every line: [EP] explicit premise, [IP] implicit premise, [1,2] follows from 1 and 2.
When we encounter arguments, they are rarely presented in the organized, premise/conclusion form that we’ve been using in class. More often, they are are presented in paragraph form or as part of a speech, a lecture, or a discussion.
Putting arguments into standard form as we have been doing is useful. It allows us to separate the specific claims in the premises, we can identify the conclusion more clearly, and we can see whether the logical structure is good or bad. So we need to be able to reconstruct arguments from their organic form into standard form.
During the reconstruction process, it is best to forego any critical evaluation of the argument and withhold our objections. The goal is to give the most charitable, and strongest version of the argument on the author’s behalf that we can. It’s more important to determine what is reasonable to believe and which claims are supported by the evidence than to score points by objecting prematurely to an argument that we haven’t fully understood or reflected on. Towards that end, we should strive to make the reconstructed argument either as deductively strong or as inductively strong as we can, while making the reconstruction conform to the author’s intentions as closely as possible. The critical evaluation phase will come after we have the best reconstruction we can devise of the argument.
The best place to begin this process is to figure out what conclusion the author is intending to argue for. Once we have the conclusion, we can work backwards and figure out what premises are being given in its support, and what logical structure might be employed to prove it. Usually the conclusion is explicit, or stated. But sometimes the author will omit stating the conclusion, but it is clearly implied by the presentation and it is indicated by the logic of the premises offered. This would be an implicit conclusion. Premises can be implicit or explicit too.
What is the conclusion in this argument?
Kara's car is illegal to drive at night. All cars must have fully functioning headlights in order to be legal to drive.
It is "Kara's car is not legal to drive at night." How do we know? It should be intuitive that the ultimate goal of the reasoning and direction of what has been said it to get the audience to conclude that Kara's car is illegal to drive at night. The only other sentence is the "All cars" sentence, and the author is not offering any evidence for that, there are no reasons to support it. But if we construe the "All cars" sentence as a premise, then with the addition of an implicit premise, "Kara's car is not legal to drive at night" follows logically.
What is the implied premise? Consider the argument partially reconstructed:
All cars must have fully functioning headlights in order to be legal to drive.
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Therefore, Kara's car is not legal to drive.
We can now see that the implied premise, the reason that the author clearly depends upon and assumes in the argument but does not state explicitly is:
"Kara's car does not have fully functioning headlights." If we add that premise, the whole argument makes sense and begins to fit into a valid pattern we've seen before:
All cars must have fully functioning headlights in order to be legal to drive.
Kara's car does not have fully functioning headlights.
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Therefore, Kara's car is not legal to drive.
Notice here that we have followed the first three steps for reconstructing arguments. The next step is "Make charitable revisions in language to make the argument valid or cogent, consistent with the authors' intentions." We might have provided the implicit premise, "Kara's car has a broken headlight," thinking that would be sufficient. But "Kara's car has a broken headlight." and "Kara's car does not have fully functioning headlights" are not the same. In ordinary conversation, we would let this imprecision pass, but here we need to state that exactly the legal requirement in the first premise has not been met. Consider that the the glass cover or the trim on a headlight could be broken, but the headlight is still fully functioning. In order to make the argument strictly valid, we need to add "Kara's car does not have fully functioning headlights." Details matter in validity.
We have now addressed the concerns in D., E., and F. for this argument. What about G? What's a justification? The justification gives a pedigree or source for the line that we are attributing in our reconstruction. It makes the reason we are adding that line clear for analysis. We are going to use IP for "Implicit Premise" and EP for "Explicit Premise" and when a line follows from a logical inference like Modus Tollens or Modus Ponens from some previous lines, we will list those lines: 1,2. Now we can complete the reconstruction:
All cars must have fully functioning headlights in order to be legal to drive. (EP)
Kara's car does not have fully functioning headlights. (IP)
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Therefore, Kara's car is not legal to drive. (1,2)
See the next module on Finding the Conclusion for more details.
What about this argument? First, step is to find the conclusion:
There can’t be weapons of mass destruction in Iraq. If there were, then the military forces would have found them by now, or some radicalized group of insurgents would have used them. But the military forces haven’t found them and no insurgent groups have used any.
“There can’t be weapons of mass destruction in Iraq.” is the conclusion. The author leads with it, it's supported by the other premises, and logical direction of the reasoning points to it.
Next, we should determine which explicit premises are being offered. That is, the author will most likely have presented some explicitly stated claims in support of the conclusion. Explicit premises are the ones that have been stated outright. Implicit premises are ones that the author clearly employed and expected us to understand as part of the argument, but did not write out or state.
First, what's the conclusion in this argument?
"I think she's not home. If she's home, then her car would be in the driveway."
"She's not home" is the conclusion.
What is the explicit premise? "If she's home, then her car would be in the driveway," is an explicit premise. And "Her car is not in the driveway," is an implicit premise. When we try to reconstruct it in standard logical form, we can see why the implicit premise is assumed and needed:
If she's home, then her car would be in the driveway. (EP)
What is assumed here by the author and needed to make logical sense of this argument?
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Therefore, she's not home. (1,2)
The implied premise has to be "Her car is not in the driveway." When we add it, the argument fits into our valid Modus Tollens pattern:
If she drove home, then her car would be in the driveway. (EP)
Her car is not in the driveway. (IP)
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Therefore, she's not home. (1,2)
Now consider this argument. What is the conclusion?
Positive thinking cannot help you win the lottery. If it could, then lots of people would win."
"Positive thinking cannot help you win the lottery." is the conclusion. And "If it could, then lots of people would win." is the explicit premise. An implied premise, "Lots of people do not win." needs to be added to complete the argument. Notice that when we add it, the argument becomes valid and much clearer:
1. If positive thinking could help you win the lottery, then lots of people would win the lottery. (EP)
2. Lots of people do not win the lottery. (IP)
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3. Therefore, positive thinking cannot help you win the lottery. (1,2)
You might also think that "Lots of people try to win the lottery with positive thinking." is assumed or implied. But that claim isn't necessary to add here in order to get a valid and relatively strong interpretation of the argument:
1. Lots of people try to win the lottery with positive thinking.
2. If positive thinking could help you win the lottery, then lots of people would win the lottery.
3. Lots of people do not win the lottery.
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4. Therefore, positive thinking cannot help you win the lottery.
The logical structure of the argument is now:
1. R.
2. If P then Q
3. not Q
4. Therefore, not P.
R, while relevant, doesn't contribute to the formal validity of the argument. The only valid inference here is from 2 and 3 to the conclusion 4. So let the logical structure of the argument and the requirements of validity be your guide, in part, to figure out which implicit premises must be added.
In general, once we identify the conclusion and we have the explicit premises, we are in a better position to determine which premises, if any, are implicit. Our guide for finding these will be our sense for the author’s intentions, and the logical structure of the argument that we can see emerging from the presentation. If a premise is not stated, but the author clearly has a logical structure or style of inference in mind, and adding the missing claim would make the argument valid or cogent, then that claim is probably an implicit premise.
Once we have all of the explicit and implicit premises, it would be helpful to rearrange the claims, make minor adjustments in language, and eliminate language that isn’t precise or that doesn’t match across the argument. If there are pronouns, it would be better to replace them with their antecedents. We should eliminate everything in the sentences except the words that provide essential information for the argument. So “I believe that a person cannot support capital punishment and be opposed to abortion.” can be converted to “A person cannot support capital punishment and be opposed to abortion,” or “Supporting capital punishment and opposing abortion are inconsistent positions.” The “I believe that” isn’t important or really part of the argument. Incidentally, recognizing that language like this isn’t essential in a sentence can make us better writers in the first place. “I’ve always had the opinion that American League baseball players are better than National League players,” is more clearly written without the “I’ve always had the opinion that.” For logical purposes, we're just interested in the claims or the interpretation of the claims that bear directly on the validity or cogency of the argument, and on the truth of the conclusion.
We should add justifications after every line in the reconstructed argument. Justifications indicate where the line came from. [EP] means "explicit premise." [IP] means "implicit premise." And [1,2] means that the line was inferred, either validly or cogently, from lines 1 and 2.
Consider this example of moving from the original text to a well-reconstructed argument in standard form:
The starter must be broken. If the car won't start, then it's either the starter, the alternator, or the battery that's the problem. It won't start. And we've ruled out the alternator since we just put a new one in, and it can't be the battery because it's fully charged.
The conclusion is "The starter must be broken." One explicit premise is this conditional: "If the car won't start, then it's either the starter, the alternator, or the battery that's the problem." Another explicit premise is "The car won't start." (Notice that I've changed the language to match the previous sentence exactly.) So we can put together this reconstruction:
1. If the car won't start, then either the starter is broken, the alternator is broken, or the battery is dead. (EP) (notice the editing)
2. The car won't start. (EP)
3. The alternator is not broken. (IP) (notice the editing to match language in 1)
4. The battery is not dead. (IP) (notice the editing to match the language in 1.)
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5. Therefore, the starter is broken. (1,2,3,4)
The original text needed to be edited quite a bit to get this to fit strictly into a valid argument patterns we’ve been studying. It not sufficient to just add numbers to the original text or leave those lines as originally stated. The pattern that the argument, once heavily edited and reconstructed, follows is:
1. If P, then either Q, R, or S.
2. P.
3. Not R
4. Not S
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5. Therefore, Q
This is known as an argument by elimination.
So consider this argument:
I’m pretty sure that if you get caught base jumping in a national park, it is a misdemeanor offense. And if you get convicted of a misdemeanor offense, it's a parole violation. I heard that while he was on parole, Fernando went base jumping in Yosemite and got caught. And if Fernando violates his parole one more time, immigration services is going to deport him. So I think he is going to get deported. That's too bad. He was a great guy.
The conclusion is "Fernando got deported." The sentence: I’m pretty sure that if you get caught base jumping in a national park, it is a misdemeanor offense." gets translated to this premise. Notice that the language has been adjusted to match the other premises and words have been eliminated:
"If you get caught base jumping in a national park, then you get convicted of a misdemeanor offense."
And if you get convicted of a misdemeanor offense, it's a parole violation, becomes: "If you get convicted of a misdemeanor offense, then you get a parole violation."
And this premise is also explicit: "If Fernando gets a parole violation, then immigration services is going to deport him." It is not stated, but it is clearly implied that "Yosemite is a national park."
1. If a person gets caught base jumping in a national park, then that person is convicted of a misdemeanor offense. [EP]
2. If a person gets convicted of a misdemeanor offense, then that person gets a parole violation. [EP]
3. If Fernando gets a parole violation, then immigration services is going to deport him. [EP]
4. Yosemite is a national park. [IP]
5. Fernando got caught base jumping in Yosemite. [EP]
6. Fernando got caught base jumping in a national park. [4,5]
7. Fernando got convicted of a misdemeanor offense. [1, 6]
8. Fernando got a parole violation. [2, 7]
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9. Therefore, Fernando is going to get deported. [3,8]
Notice that the implicit premise has been brought out, and all of the intermediate inferences have been stated in order to validly get to the conclusion. Compare the full reconstruction above to this much less thorough reconstruction:
1. If a person gets caught base jumping in a national park, then that person is convicted of a misdemeanor offense. [EP]
2. If a person gets convicted of a misdemeanor offense, then that person gets a parole violation. [EP]
3. If Fernando gets a parole violation, then immigration services is going to deport him. [EP]
4. Fernando got caught base jumping. [EP]
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5. Therefore, Fernando is going to get deported. [1,2,3,4]
This version seems to capture the reasoning at first glance, but it isn't valid, and several important connections haven't been stated. The longer version is correct.
Here is one more much more complicated argument in text form.
Currently the FBI and the NTSB are considering three live hypotheses about the demise of TWA flight 800. Mechanical failure is always the first option to be raised in such cases. Most plane crashes, like the recent one in the Florida everglades, are due to something along these lines. The problem with this hypothesis is that most of the wreckage has been retrieved, except for some of the most crucial areas near the blast, and no indication of mechanical failure has become apparent. The possibility of a terrorist's bomb on board is also being considered. It has happened a number of times before, and worldwide incidence of terrorist bombings are ever increasing. But again, there is no evidence, at least that is compelling, in the wreckage that there was a bomb. No terrorist group has plausibly claimed responsibility. The other possibility that is actively being considered is that the flight was shot down by a surface to air missile, maybe from the coast, but more likely and surprising, from a nearby Navy ship (180 miles) that was testing targeting systems and launching practice shots around the time of the flight's demise. Over 40 witnesses of the mid-air explosion have suggested that there was a flare of light that travelled up from the ocean to the plane shortly before it exploded. Given the problems with the other hypotheses and the evidence that indicates it was shot down, it seems that we have to accept the third possibility as the most likely, however frightening it may be.
The conclusion is: "TWA 800 was shot down." The overall logical structure of the argument appears to be a disjunctive syllogism formed around the three likely hypotheses: "Currently the FBI and the NTSB are considering three live hypotheses about the demise of TWA flight 800." The implicit premise then is:
1. TWA 800 was either shot down, bombed by terrorists, or it suffered from mechanical failure.
A very simple way to see the rest of the reasoning here is to understand the rest of the discussion as making a case for denying the second and third possibilities. So the whole argument put in rudimentary form is:
1. TWA 800 was either shot down, bombed by terrorists, or it suffered from mechanical failure. [EP]
2. TWA 800 was not bombed by terrorists. [IP]
3. TWA 800 did not suffer from mechanical failure. [IP]
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4. Therefore, TWA 800 was shot down. [1,2,3]
This reconstruction has good and bad aspects. First, it is valid, it is clear, and it captures the overall structure of the reasoning. But there is a great deal of detail that is left out. We do not see any of the reasoning that led to premises 2 and 3. Here's a better version that expands some of the reasoning:
1. TWA 800 was either shot down, bombed by terrorists, or it suffered from mechanical failure. [EP]
2. If TWA 800 was bombed by terrorists, then we would find evidence of a bomb in the wreckage and there would be a plausible claim of responsibility by a terrorist group. [IP]
3. We did not find evidence of a bomb in the wreckage and there was not a plausible claim of responsibility by a terrorist group. [EP]
4. Therefore, TWA 800 was not bombed by terrorists. [2,3]
5. If most of the wreckage has been found and searched and there is no evidence of mechanical failure, then TWA 800 did not suffer from mechanical failure. [IP]
6. Most of the wreckage has been found and searched and there is no evidence of mechanical failure. [EP]
7. Therefore, TWA 800 did not suffer from mechanical failure. [5,6]
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8. Therefore, TWA 800 was shot down. [1,4,7]
This version is much better because it captures more of the original reasoning. And it is still valid. Notice that premises 2 and 3 from the short version have now become the conclusions of sub-arguments in the long version. This argument is still not perfect because there is no incorporation of the information about the Navy or the missile testing, or the eye witnesses. But it is a good, charitable reconstruction.
For the record, it was discovered when all of the wreckage was found, the real crash of TWA 800 was caused by mechanical failure.
How charitable should we be when we are reconstructing an argument? The idea behind being charitable is that we want to give the author as much of the benefit of the doubt as we can. We want to reconstruct the strongest argument we can on her behalf, where "strongest" is understood in terms of our inductively or deductively strong arguments concepts. It would be going too far, for the sake of charity, to completely reorder the reasoning, or add new information, or give what amounts to a different argument for the author's conclusion. Consider this simple case:
If UFOs were abducting human beings from the Earth and doing experiments on them, then there would be a lot of people who claim to have been abducted. And there are a lot of people who claim to have been abducted. So it looks like UFOs are abducting humans from the Earth.
Notice that as stated, this argument is invalid:
1. If UFOs were abducting human beings from the Earth, then there would be a lot of people who claim to have been abducted. [EP]
2. There are a lot of people who claim to have been abducted. [EP]
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3. Therefore, UFOs are abducting human beings from the Earth. [1,2]
The invalid inference is affirming the consequent.
1. If P then Q.
2. Q
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3. Therefore, P
If we changed the author's first premise to: "If there are a lot of people who claim to have been abducted, then UFOs are abducting humans from the Earth." we can make the argument valid. But we've altered what the author said too much. So you should reconstruct it following the author's logic as closely as possible. And then in your critical evaluation of the argument, you would point out that the argument is logically flawed. It is invalid. It's also not cogent. So it is ill-formed. Also notice that even if you had altered the premise to make it valid, the new premise would be false. A lot of people claiming to have been abducted is not sufficient grounds to conclude that UFOs are really abducting humans, particularly when there are other, more likely explanations. So your evaluation of the revised argument would show that the argument is still weak, but for a different reason.
So the whole procedure for reconstructing arguments again is:
A. Be Charitable: The point of is getting to the truth, not putting someone down or scoring rhetorical points.
B. Find the conclusion.
C. Find the explicit premises.
D. Add implicit premises or conclusions.
E. Make charitable revisions in language to make the argument valid or cogent if possible, and as strong as possible.
F. Put argument into standard form.
G. Add any intermediate inferences that play a roll in the larger argument.
H. Add justifications after every line: [EP] explicit premise, [IP] implicit premise, [1,2] follows from 1 and 2.