Logical Reasoning Foundations: Argument Mapping with Boxes and Arrows

What an Argument Map Shows

An argument map is a visual diagram of how support flows from reasons to a conclusion. Each claim is placed in a separate box, and arrows show which claims are offered in support of which other claims.

A typical map distinguishes three roles:

• Premises: starting support claims (reasons).
• Intermediate conclusions (sub-conclusions): claims that are supported by earlier premises and then used to support something further.
• Main conclusion: the final claim the text is trying to get you to accept.

Mapping forces you to answer two concrete questions for every sentence you include: (1) What is the claim? and (2) What does it support (if anything)?

Boxes and arrows: a simple notation

You can map on paper or digitally. Use this minimal notation:

• Put each claim in a numbered box: [1], [2], [3]…
• Draw an arrow from supporter to supported claim: [1] → [3].
• If two premises must work together, bracket them as co-premises: [1]+[2] → [3].
• Label assumptions explicitly as (A1), (A2) and draw them like any other premise.

Three Common Support Structures

1) Linked premises (co-premises): they need each other

Linked premises are jointly necessary to provide the intended support. If you remove one, the remaining premise(s) no longer support the conclusion in the way the author intends.

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Test: Ask, “Would this premise still give meaningful support on its own?” If not, it’s likely linked.

[1]+[2] → [3]

Example (policy claim):

[1] The city’s water pipes are over 70 years old.  +  [2] Pipes over 70 years old have a high failure rate.  →  [3] The city should replace the water pipes now.

Here, [1] alone is just a fact about age; [2] alone is a generalization about old pipes. Together they create the intended bridge to [3].

2) Convergent premises: independent lines of support

Convergent premises each support the conclusion on their own. Removing one weakens the case but does not destroy the other line(s) of support.

Test: Ask, “If I delete this premise, do the remaining premises still support the conclusion independently?” If yes, it’s convergent.

[1] → [3]  and  [2] → [3]

Example (consumer choice):

[1] This laptop has the longest battery life in its price range. → [3] You should buy this laptop. [2] It also has the best warranty in its class. → [3] You should buy this laptop.

Either battery life or warranty could be offered as a standalone reason to buy.

3) Serial chains: premise → sub-conclusion → conclusion

Serial structure happens when a premise supports an intermediate conclusion, which then supports the main conclusion. This is common in editorials where the writer builds a stepping-stone argument.

[1] → [2] → [3]

Example (workplace):

[1] Our team misses deadlines because requirements change mid-sprint. → [2] We need a stricter change-control process. → [3] We should adopt a formal ticket approval step before work begins.

Notice how [2] is both a conclusion (supported by [1]) and a premise (supporting [3]).

A Consistent Routine for Building Argument Maps

Use the same routine every time so your maps are comparable and you don’t “freehand” structure based on gut feeling.

Step 1: Clean sentences into map-ready claims

Rewrite each relevant sentence into a short, declarative claim that can be true or false. Remove rhetorical flourishes and compress lists.

• Turn questions into assertions (if the text uses them as persuasion).
• Replace pronouns with clear nouns where needed.
• Split sentences that contain two claims.

Before: “Honestly, it’s obvious we can’t keep wasting money on this outdated system!”

After (map-ready): “The current system is outdated.” and “We are wasting money on the current system.”

Step 2: Number every claim you will map

Numbering prevents you from losing track when arrows cross or when you revise. Keep numbers stable even if you move boxes around.

[1] ... [2] ... [3] ...

Step 3: Identify the main conclusion box

Place the main conclusion at the top (or far right) consistently. Everything else should ultimately point toward it, directly or through intermediate conclusions.

Step 4: Draw support arrows (not “topic” arrows)

An arrow means: “This claim is offered as a reason to accept that claim.” Do not draw arrows for mere relevance, background, or explanation unless the text is using it as support.

Quick check: If you can naturally insert “therefore” from the first claim to the second (or “because” from the second to the first), it’s likely a support link.

Step 5: Mark co-premises explicitly

When two premises are linked, show that they function as a package. Common ways:

• Bracket them together: [1]+[2] → [3]
• Draw a joining line from [1] and [2] into a single arrow toward [3]

Do not mark premises as linked just because they appear near each other. Use the “remove-one” test: if one premise alone would not support the target claim as intended, treat them as co-premises.

Step 6: Label assumptions explicitly

If the argument requires an unstated claim to make the support work, add it as an assumption box and label it. Keep assumptions separate from what the author actually said.

• Format: (A1), (A2)
• Write them as claims, not as questions.
• Attach them where they do work: usually as a co-premise with an explicit premise.

Example of placement:

[1] This supplement is “natural.” + (A1) Natural products are safer than non-natural products. → [2] This supplement is safer.

Short Mapping Walkthroughs (Ads and Editorials)

Walkthrough 1: Ad with convergent support

Text: “Switch to BrightMobile. Our plans are cheaper than the big carriers, and our coverage is rated best in rural areas. So you should switch today.”

Step 1 (clean claims):

• Cheaper than big carriers.
• Best rural coverage.
• You should switch to BrightMobile today.

Step 2 (number):

[1] BrightMobile plans are cheaper than the big carriers. [2] BrightMobile coverage is rated best in rural areas. [3] You should switch to BrightMobile today.

Step 3–4 (arrows):

[1] → [3] [2] → [3]

Structure: convergent. Each reason independently supports the recommendation.

Walkthrough 2: Ad that relies on linked premises

Text: “This air purifier removes 99.9% of airborne particles. Airborne particles trigger allergies. Therefore, this purifier will reduce your allergy symptoms.”

Clean + number:

[1] This purifier removes 99.9% of airborne particles. [2] Airborne particles trigger allergies. [3] This purifier will reduce your allergy symptoms.

Map the intended support:

[1]+[2] → [3]

Assumption to label (often needed):

(A1) Removing airborne particles that trigger allergies reduces allergy symptoms.

Full map:

[1]+[2]+(A1) → [3]

Notice how [1] alone doesn’t mention allergies, and [2] alone doesn’t mention this purifier. The link is created by combining them (plus the bridging assumption).

Walkthrough 3: Editorial with a serial chain

Text: “Downtown traffic is getting worse each year. When traffic worsens, bus schedules become unreliable. If buses are unreliable, more people drive. So the city should create dedicated bus lanes.”

Step 1 (clean claims):

• Downtown traffic is getting worse each year.
• If traffic worsens, bus schedules become unreliable.
• If buses are unreliable, more people drive.
• The city should create dedicated bus lanes.

Step 2 (number):

[1] Downtown traffic is getting worse each year. [2] If traffic worsens, bus schedules become unreliable. [3] If buses are unreliable, more people drive. [4] The city should create dedicated bus lanes.

Step 3–4 (find intermediate conclusion): The text implies a stepping-stone: worsening traffic leads to unreliable buses, which leads to more driving, which worsens traffic further. To map cleanly, add an intermediate conclusion that the author is effectively using.

Add an explicit intermediate conclusion:

[5] More people will drive downtown (unless buses become more reliable).

Map:

[1]+[2] → [6] [6]+[3] → [5] [5] → [4]

Where:

[6] Bus schedules will become unreliable.

This is a serial chain with intermediate conclusions [6] and [5]. The final step ([5] → [4]) often needs an assumption about what dedicated bus lanes accomplish.

Label the assumption explicitly:

(A1) Dedicated bus lanes make buses more reliable.

Attach it where it works:

[5]+(A1) → [4]

Walkthrough 4: Editorial with mixed structure (linked + convergent)

Text: “The school should start later. Teenagers’ sleep cycles shift later, and early start times reduce total sleep. Also, districts that started later saw fewer car accidents involving teen drivers.”

Clean + number:

[1] Teenagers’ sleep cycles shift later. [2] Early school start times reduce teenagers’ total sleep. [3] The school should start later. [4] Districts that started later saw fewer car accidents involving teen drivers.

Decide structure:

• [1] and [2] work together to support a sub-conclusion about harm from early starts.
• [4] is a separate, independent line of support for starting later.

Add an intermediate conclusion:

[5] Early start times are harmful for teenagers.

Map:

[1]+[2] → [5] [5] → [3] [4] → [3]

Assumption you may need to label:

(A1) If a school policy is harmful for teenagers, the school should change it.

Attach:

[5]+(A1) → [3]

Common Mapping Mistakes (and Quick Fixes)

Mistake: putting multiple claims in one box

Fix: split into separate boxes so arrows can target the exact claim being supported.

Too big: “The product is cheap and reliable.”

Split: [1] The product is cheap. and [2] The product is reliable.

Mistake: drawing arrows from conclusions to premises

Fix: arrows should point from reason to claim supported. If you find yourself wanting the opposite direction, rewrite your boxes or re-check which claim is doing the supporting.

Mistake: treating background as support

Fix: only map what is offered as a reason. If a sentence merely sets the scene, leave it out or place it as a note (not connected by support arrows).

Mistake: missing a hidden intermediate conclusion

Fix: when the text “jumps,” add a sub-conclusion box that captures the implied step, then connect arrows in a chain.

Mistake: failing to mark linked premises

Fix: apply the remove-one test. If each premise alone would not support the target claim as intended, mark them as co-premises.

Template You Can Reuse

When you practice, copy this checklist and fill it in: